# SHAPE

## VISUAL ACUITY

### The range of vision by fovea

What is the sig­nif­i­cance of the uneven dis­tri­b­u­tion of cones on the sur­face of the reti­na described in the pre­vi­ous chap­ters, i.e., the fact that in its cen­tral part, espe­cial­ly in the mac­u­la, there is the largest num­ber of them, and on the periph­ery — not too many? To answer this ques­tion, it is nec­es­sary to remem­ber, first of all, that the fovea cov­ers only 1.25° of the field of vision angle (max­i­mum 2°), and the whole mac­u­la — no more than 5.5° (Hen­drick­son, 2009; Duchows­ki, 2007). This means that fovea cov­ers the area no more exten­sive than that of the thumb­nail at a dis­tance of the extend­ed hand, as can be seen by apply­ing one of the for­mu­las from the pre­vi­ous chap­ter (Hen­der­son and Holling­worth, 1999):

It can be pic­tured dif­fer­ent­ly, as well. Sup­pose that we are watch­ing a film on a 40″ LCD TV with a screen area of 5,814 cm2 from a dis­tance of 2 meters:

where h is the height, and w is the width of the rec­tan­gu­lar image. The image dis­played on the screen is pro­ject­ed over the whole reti­na, but only a small part of the image, equal to a cir­cle of approx­i­mate­ly 19 cm in diam­e­ter, falls on the macula:

Know­ing the diam­e­ter of a cir­cle we can eas­i­ly cal­cu­late its sur­face area:

which approx­i­mate­ly cor­re­sponds to 5%, i.e., 1/20 of the total screen sur­face area:

An even small­er part of the screen is pro­ject­ed onto the fovea, equal to a cir­cle with a diam­e­ter of approx. 4.4 cm:

which cor­re­sponds to only 0.3% of the total TV screen sur­face area:

To sum up this arith­metic, at every point of visu­al fix­a­tion on the TV screen, the brain is well informed about what is cur­rent­ly present only on a tiny part of it (Fig.  55). The remain­ing por­tion of the screen is viewed with incom­pa­ra­bly less­er clar­i­ty. It will be easy to learn about it when oth­er prop­er­ties of the reti­na are analyzed.

### Photoreceptors and ganglion cell receptive field

The Pol­ish word “siatkówka,” like its Eng­lish equiv­a­lent “reti­na,” derives from the word “net­work” (in Latin, rete means “net­work”). The reti­na is a com­plex, five-lay­er struc­ture made up of neu­rons lin­ing the bot­tom of the eye. In most areas, apart from lay­ers of cones and rods, there are four oth­er lay­ers of cells in the reti­na: hor­i­zon­tal cellsbipo­lar cells,  amacrine cells, and gan­glion cells.

Each cell lay­er has its spe­cif­ic func­tions. Some of these func­tions are well rec­og­nized and described, while oth­ers remain unknown. Gen­er­al­ly speak­ing, cones and rods react to light enter­ing the eye; bipo­lar, hor­i­zon­tal, and amacrine cells are involved in the ini­tial devel­op­ment of data on stim­u­la­tion of pho­tore­cep­tors, while gan­glion cells send the results of this devel­op­ment to the brain (Dowl­ing, 2009).

The first stage of visu­al data pro­cess­ing takes place already in the reti­na of the eye.  Even though there are approx. 100 mil­lion pho­tore­cep­tors on its sur­face, the infor­ma­tion on their activ­i­ty is trans­mit­ted to the brain by only 1 mil­lion gan­glion cells (Wró­bel, 2010).  It means that the brain, more pre­cise­ly, the cere­bral cor­tex, does not receive data on the con­di­tion of each pho­tore­cep­tor.  On the con­trary, the vast major­i­ty of pho­to­sen­si­tive cells are con­nect­ed in small­er or larg­er groups by hor­i­zon­tal, bipo­lar, and amacrine cells. The group of such joined pho­tore­cep­tors is, in turn, com­bined with the gan­glion cell, cre­at­ing the so-called recep­tive field of the gan­glion cell.

Since all pho­tore­cep­tors are more than 100 mil­lion and gan­glion cells are around 1 mil­lion, it is not dif­fi­cult to cal­cu­late that, on aver­age, one gan­glion cell is per 100 pho­tore­cep­tors. How­ev­er, the num­ber of cones and rods per square mil­lime­ter of reti­na depends on their dis­tance from the fovea. Sim­i­lar­ly, the num­ber of them varies from indi­vid­ual recep­tive fields depend­ing on whether they are clos­er to or far­ther from the fovea. This means that the fur­ther away from the cen­ter of the reti­na, the larg­er the recep­tive fields of the indi­vid­ual gan­glion cells are. Above the field of vision angle of 20o, the size of the recep­tive fields is about the same. They gen­er­al­ly cov­er a sur­face area for the reti­na con­sti­tut­ing approx. 1 mm2 and con­nect sev­er­al hun­dred pho­tore­cep­tors (Młod­kows­ki, 1998).

The small­est recep­tive areas of indi­vid­ual gan­glion cells are locat­ed in the mac­u­lar area and include the range of a few to sev­er­al cones. In the fovea itself, the recep­tive areas are only com­posed of indi­vid­ual cones. There are no hor­i­zon­tal and amacrine cells in this area, and infor­ma­tion from the pho­tore­cep­tor is trans­mit­ted direct­ly to the gan­glion cell through the bipo­lar cell. This is the place from which the infor­ma­tion about the image pro­ject­ed on the sur­face of the reti­na is trans­mit­ted to the brain with the accu­ra­cy of one cone diam­e­ter, i.e., three μm!  (= 0.003 mil­lime­tre) (Hen­drick­son, 2009).

### Visual acuity by fovea and periphery of the retina

A direct con­se­quence of the var­i­ous size of the recep­tive fields depend­ing on their loca­tion on the reti­na is a decrease in the vision accu­ra­cy in the periph­er­al part, where only large recep­tive fields dom­i­nate. Worse vision accu­ra­cy is expressed as a decrease in the sen­si­tiv­i­ty of the reti­na to the dif­fer­en­ti­a­tion for details of the image pro­ject­ed into the area built up from large recep­tive fields. A sin­gle sig­nal flows to the gan­glion cell from each recep­tive field, which aver­ages the activ­i­ty of all cones and / or rods that com­pose this field. The larg­er the reti­nal sur­face from which the sig­nal is aver­aged, the eas­i­er it is to lose detail. The process of aver­ag­ing the sig­nal can be com­pared to “bundling” of visu­al data into small­er, more syn­thet­ic forms (Troy, 2009).

It is worth men­tion­ing that large recep­tive fields are locat­ed in this reti­nal area, where the num­ber of cones is sta­bilised at a min­i­mum lev­el and the num­ber of rods is grad­u­al­ly decreas­ing. A rel­a­tive­ly small num­ber of pho­tore­cep­tors (which are con­nect­ed to each oth­er in large recep­tive fields) in the periph­er­al area (i.e. above 10o field of visions angle in good light­ing con­di­tions and above 20o – after dark) caus­es that the accu­ra­cy with which the brain is informed about the image pro­ject­ed onto it is rel­a­tive­ly low in a sig­nif­i­cant area of the reti­na (Fig. 56).

In order to under­stand the graph in Fig. 56 it is nec­es­sary to remind us a bit of the his­to­ry of research on visu­al acu­ity. The esti­ma­tion of visu­al acu­ity is based on a method devel­oped by Dan­ish oph­thal­mol­o­gist – Her­mann Snellen – in the mid-19th cen­tu­ry. He pro­posed that visu­al acu­ity should be defined as the ratio of the dis­tance, from which the exam­ined per­son looks at the so-called opto­type, to the dis­tance from which it should be cor­rect­ly recog­nised (Nizankows­ka, 2000). An opti­mo­type is, for exam­ple, a black let­ter E on a white back­ground, seen from such a dis­tance that its ele­ments are dif­fer­en­ti­at­ed at an angle of 1′ (1/60 of an angu­lar degree; Fig. 57).

The con­cept is sim­ple. The aim is to check whether the visu­al sys­tem of the exam­ined per­son is able to dif­fer­en­ti­ate two points on the opto­type (e.g. the dis­tance among the ser­ifs in let­ter E; Fig. 57). This is equiv­a­lent to stim­u­la­tion of two cones in the fovea, between which there is one unstim­u­lat­ed cone. It is known that the diam­e­ter of one cone is approx. 0.003–0.004 mm (i.e. approx. 3–4 µm). Tak­ing into account the dis­tance of the cones from the cen­tre of the opti­cal sys­tem of the eye in the lens, it is pos­si­ble to cal­cu­late the angle at which light would have to fall into the inte­ri­or of the eye­ball, in order to illu­mi­nate these two extreme cones. This angle is pre­cise­ly 1′.

In order to stan­dard­ise the exam­i­na­tion of visu­al acu­ity, Snellen devel­oped a chart, com­mon­ly known from oph­thal­mol­o­gist’s offices, con­tain­ing let­ters of var­i­ous heights, arranged in 11 rows (Fig. 58, left side). A record of two num­bers, e.g. 20/200, next to one of blocks of let­ter rows, means the ratio of two dis­tances: the dis­tance from which the mea­sure­ment of visu­al acu­ity is made (i.e., 20 feet, ca. 6 metres), to the dis­tance from which the let­ter in a giv­en row should be cor­rect­ly recog­nised with healthy eyes (i.e., 200 feet, ca. 60 metres). In oth­er words, if you have nor­mal eye­sight, you should recog­nise the let­ter E in a first row from a dis­tance of 60 metres.

The chart in Fig. 56 shows that the max­i­mum visu­al acu­ity using a ful­ly func­tion­ing eye is 1.0. Only one small reti­nal area, i.e. the fovea (marked with a ver­ti­cal dot­ted line at point 0) has such effi­cien­cy. A visu­al acu­ity of 1.0 cor­re­sponds to the abil­i­ty to recog­nise let­ters cor­rect­ly in the eighth row (high­light­ed in red) of the Snellen chart at a dis­tance of 20 feet (20/20 feet = 6/6 meters).

Let us sup­pose that the small­est let­ters that the exam­ined per­son cor­rect­ly recog­nis­es at a dis­tance of 20 feet (6 metres) are the let­ters C and J in the sec­ond row of the Snellen chart (Fig. 58). They should be cor­rect­ly recog­nised from a dis­tance of 100 feet (approx. 30 metres). This means that the lev­el of blurred vision of this per­son is 0.2 (20/100 = 0.2) and (s)he def­i­nite­ly requires glass­es to cor­rect this visu­al impair­ment. When we look at this Fig. 56 again, you will notice that a visu­al acu­ity index, equal to (or less than) 0.2, cor­re­sponds to the visu­al acu­ity of the image pro­ject­ed on the reti­na above 15o, i.e. its area lying far beyond the macula.

To real­ize how blurred this image is, it is enough to look again at Fig. 58. Two pic­tures are shown on the right side, illus­trat­ing how Snellen charts are most like­ly to be viewed by short-sight­ed peo­ple who require vision cor­rec­tion between ‑1 and ‑3 diop­tres. There is no sim­ple con­ver­sion of the Snel­len’s visu­al acu­ity index into diop­tres, but it can cer­tain­ly be said that the Snellen index equal to (or less than) 0.2 cor­re­sponds to the sharp image more or less sim­i­lar to the one seen by a short-sight­ed per­son with a refrac­tion defect of ‑3 dioptres.

In oth­er words, if we assume that the max­i­mum (or equal to 1.0) visu­al acu­ity is asso­ci­at­ed with the fovea, it con­sti­tutes only 20% above the 15o angle of view, which means that it is five times small­er and even small­er with each suc­ces­sive degree (angle).

### The world’s most famous smile

Var­ied res­o­lu­tion of image encod­ing in dif­fer­ent parts of the reti­na can sig­nif­i­cant­ly affect the sense of the image. Mar­garet Liv­ing­stone (2000), a neu­ro­sci­en­tist influ­enced by Ernst Gom­brich’s sug­ges­tion (2005), noticed that view­ing Leonar­do da Vin­ci’s Mona Lisa she had the impres­sion that Mona Lisa smiled at her dif­fer­ent­ly, depend­ing on which part of the paint­ing she focused her eyes on. The key fac­tor is the dis­tance between the viewed frag­ment and the lips of the Leonard’s mod­el. The fur­ther this frag­ment is locat­ed from her mouth (e.g. back­ground or hands), the more her smile becomes cheer­ful. Accord­ing to Liv­ing­stone, the answer lies in the dif­fer­ence between a blurred (out-of-focus) image and a sharp one. The fur­ther away our gaze is from Mona Lisa’s mouth, the smoother, fuller and more sen­su­al it becomes.

Using a com­put­er graph­ics pro­gram, Liv­ing­stone repro­duced the image of the Mona Lisa’s face, when it was clear­ly seen with cones in the fovea and when her image was pro­ject­ed onto two dif­fer­ent periph­er­al parts of the reti­na. Tech­ni­cal­ly, Liv­ing­stone first blurred the image with a Gauss­ian blur and then raised the con­trast of the processed image, thus sim­u­lat­ing the loss of res­o­lu­tion that is typ­i­cal of periph­er­al vision. I have repeat­ed this pro­ce­dure; its effects can be seen in the Fig. 59.

By jux­ta­pos­ing the effects of these treat­ments, it turned out indeed, that the less clear Mona Lisa’s face is, the more cheer­ful her smile is. In oth­er words, while the con­tent of a cen­tral­ly record­ed paint­ing is a lady with a slight­ly reflec­tive facial expres­sion, the con­tent of the same paint­ing, but record­ed periph­er­al­ly, is a girl who smiles cheer­ful­ly and more sen­su­al­ly at the per­son look­ing at her.

Liv­ing­stone (2000) sug­gest­ed that her hypoth­e­sis explain­ing the mys­te­ri­ous smile of Mona Lisa depend­ing on the dis­tance of the viewed frag­ment of the paint­ing from her mouth is at least as like­ly as a ref­er­ence to Leonar­do da Vin­ci’s tech­nique of soft­en­ing the edges of paint­ed objects and their parts (sfu­ma­to). I will return to this tech­nique lat­er in this book as it enables us to bet­ter under­stand the role, which the con­tours of the seen objects play in their interpretation.

### On central and peripheral vision in painting and photography

In ref­er­ence to the major­i­ty of paint­ings and pho­tographs, one can say that almost their whole sur­face is filled with equal­ly clear objects. Excep­tions include – and not always – e.g. dis­tant plans in the land­scape, unspec­i­fied back­ground or effects obtained by reduc­ing the depth of field. How­ev­er, there are also exam­ples of paint­ings whose com­po­si­tion is empha­sised by the sharp­ness of some frag­ments and the almost com­plete lack of sharp­ness of oth­ers. When we look at some of Rem­brandt’s self-por­traits, we will dis­cov­er that only the artist’s face has been paint­ed with great atten­tion to detail while the pres­ence of oth­er frag­ments is mere­ly sig­nalled (e.g. hands) (Fig. 60 and Fig. 61).

Sim­i­lar effects can be seen in some works by Hen­ri de Toulouse-Lautrec and August Renoir (Fig. 62 and Fig. 63), as well as many oth­er artists.

An expres­sive face, in com­par­i­son to oth­er parts of the paint­ing, is undoubt­ed­ly a fac­tor that attracts atten­tion of an observ­er, but also almost mag­net­i­cal­ly forces him/her to focus atten­tion on that detail only. These paint­ings per­fect­ly illus­trate the intu­ition of artists who use a mech­a­nism of cen­tral and periph­er­al vision. Assum­ing that these paint­ings are being observed in the muse­um from a dis­tance of about 1.5 m and that the mac­u­la cov­ers a max­i­mum of 5.5o of the field of vision angle, it turns out that the artists per­fect­ly recon­struct­ed the rela­tion between the image sur­face being cap­tured cen­tral­ly and the one being periph­er­al­ly recorded.

The effects in the pre­sent­ed paint­ings can also be achieved with the use of a pho­to­graph­ic method, through the manip­u­la­tion of the depth of field (Fig. 64).

The depth of field is the dis­tance between two view­ing planes locat­ed in front of and behind the plane of field of view D, on which the opti­cal sys­tem of the cam­era or the eye is set (Fig. 65). All images pro­ject­ed on planes lying between ‑D and +D shall be record­ed with almost the same sharp­ness as the image in plane D. The depth of field does not depend on the accom­mo­da­tion of lens, but on the size of the aper­ture or the pupil. The small­er the depth of field, the longer it is, i.e. it enables to clear­ly record more ele­ments lying on the far-reach­ing dimen­sion. This effect is much eas­i­er to achieve and use in pho­tog­ra­phy than in painting.

At the end of this chap­ter, I would like to men­tion one more exam­ple of a painter whose sur­re­al­is­tic paint­ings are filled with objects and spaces pro­gram­mat­i­cal­ly pre­sent­ed with dif­fer­ent sharp­ness (Fig. 66 A). Chris Berens – a mod­ern Dutch painter fas­ci­nat­ed by the works of: Frans Hals, Jan Ver­meer and Rem­brandt Har­men­szoon van Rijn – has devel­oped an orig­i­nal paint­ing tech­nique. Unlike his mas­ters, he paints with draw­ing ink on paper. He states that their prop­er­ties are sim­i­lar to oil paints, but simul­ta­ne­ous­ly enable to obtain com­plete­ly new visu­al effects. Indeed, look­ing at his paint­ings we can get the impres­sion that some­thing bad is hap­pen­ing to our eyes. It seems as if the opti­cal sys­tem of the cam­era had not one, but many depths of field at the same time.

Togeth­er with Aga­ta Kró­likows­ka we showed between ten and twen­ty paint­ings cre­at­ed by Chris Berens to more than fifty peo­ple exam­ined. When they were view­ing the paint­ings, we record­ed the move­ment of eye­balls of the exam­ined per­sons using the SMI iView X Hi Speed ​​1250 Hz ocu­lo­graph. The results of the study in rela­tion to the paint­ing in Fig. 66 A are shown graph­i­cal­ly in Fig. 66 B.

The paint­ing in Fig. 66 B is com­posed of 2 super­im­posed paint­ings. The first paint­ing shows only black irreg­u­lar lines. This is the result of graph­i­cal analy­sis, the pur­pose of which was to deter­mine the edges lying at the junc­tion of the most con­trast­ing points in Fig. 66 A; in oth­er words, those with the great­est sharp­ness. There are no edge marks in the paint­ing in fuzzy or blurred areas.

The sec­ond pic­ture is an atten­tion map, i.e. a graph­i­cal­ly pre­sent­ed record of the eye move­ments of the exam­ined per­sons. Col­ored spots indi­cate how often the exam­ined per­sons looked at dif­fer­ent parts of a giv­en paint­ing and how long they main­tained their gaze on them. The red col­or is an indi­ca­tor of the great­est atten­tion devot­ed to a giv­en frag­ment of the paint­ing; suc­ces­sive­ly: yel­low, green, light blue, dark blue and lilac. Places devoid of col­or are those which were prac­ti­cal­ly unno­ticed by the exam­ined per­sons. Both tech­niques of graph­ic analy­sis of paint­ings and ocu­lo­mo­tor data are pre­sent­ed in more detail in the next chapter.

In this chap­ter, it is enough to note that there is a close rela­tion­ship between the loca­tion of black edges and the visu­al atten­tion giv­en to a spec­i­fied frag­ment of a paint­ing. The clear­er the frag­ment is, the more will­ing we are to look at it. This is not always the case, but we cer­tain­ly start view­ing each visu­al scene from those places that enable us to read its mean­ing accurately.

To sum up, with ref­er­ence to all illus­tra­tions pre­sent­ed in this chap­ter, one can pose a ques­tion as to what caus­es that some of their parts we see clear­ly and oth­ers we do not. The loss of clear­ness of a giv­en frag­ment of a paint­ing or a pho­to­graph is asso­ci­at­ed pri­mar­i­ly with a decrease in the sharp­ness of the con­tours of paint­ed or pho­tographed objects and their parts.  In oth­er words, we see vague­ly because the bound­aries, lying at the point of con­tact of two planes dif­fer­ing in bright­ness, are tonal­ly inter­pen­e­trat­ed, blurred and do not enable to deter­mine where one plane ends and the oth­er begins. See­ing con­tours not only allows us to see an object, but also to dis­tin­guish it from oth­er objects present in the visu­al scene.  Dis­tin­guish­ing objects and their parts on the basis of shapes deter­mined by their con­tours is a basic func­tion of the sight (Marr, 1982; Ratliff, 1971). I will deal with this issue in the next chapter.

### CONTOURS OF THE THINGS YOU SEE

What hap­pens at the bor­ders is the only infor­ma­tion you need to know: the inte­ri­or is bor­ing (Hubel, 1988)

### Image and contour luminance

If we exam­ine a pho­to­graph through a mag­ni­fy­ing glass, in gen­er­al we would not be able to see many con­tour lines, name­ly lines which, by cir­cling the frag­ments of the visu­al scene lying next to each oth­er, mark the shapes of objects and their parts depict­ed in the scene.  In Fig.  67 there is the left eye­’s cor­ner of the clear­ly pho­tographed girl from the back­ground of the pre­vi­ous chap­ter, enlarged 32 times. It is dif­fi­cult to find the con­tour lines here, nev­er­the­less look­ing at a small pho­to on the left side in Fig. 67 there is no doubt where clear­ly out­lined edges of the eyes, lips or hair of the pho­tographed girl are locat­ed, where her face ends and the back­ground begins. This is large­ly deter­mined by the width of the tonal band which sep­a­rates dif­fer­ent­ly illu­mi­nat­ed planes of paint­ed or pho­tographed objects and their parts from each oth­er and by the size of the dif­fer­ence in bright­ness (lumi­nance) of these planes. The nar­row­er the tonal band sep­a­rat­ing two planes is and the greater the dif­fer­ence in these planes bright­ness is, the eas­i­er iden­ti­fi­ca­tion of their bor­der­lines, i.e. the con­tour would be. But how does the visu­al sys­tem set this limit?

Accord­ing to David Marr and Ellen C. Hil­dreth (1980), the cre­ators of one of the math­e­mat­i­cal algo­rithms that sim­u­late the process of edge detec­tion by the human eye, con­tours of things are a man­i­fes­ta­tion of the so-called dis­con­ti­nu­ity of lumi­nance. Con­tin­u­ous lumi­nance is typ­i­cal of planes whose light­ning changes grad­u­al­ly over rel­a­tive­ly large space. On the oth­er hand, the small­er the space in which the sur­face illu­mi­na­tion changes, the high­er pos­si­bil­i­ty of edge iden­ti­fi­ca­tion. Cur­rent­ly, major­i­ty of com­put­er soft­ware for image pro­cess­ing has built-in edge detec­tion algo­rithms. From the point of view of edge detec­tion issues in ques­tion, it is worth look­ing more close­ly at their oper­a­tion mode.

After iso­lat­ing the lumi­nance chan­nel from the col­or­ful repro­duc­tion of the paint­ing of Madame Hen­ri­ot cre­at­ed by Pierre-Auguste Renoir, we will see the image in full grayscale, from white to black (Fig. 68 A). If we analyse the paint­ing in order to iden­ti­fy the bor­der­lines between the planes with great­est dif­fer­en­ti­a­tion in terms of bright­ness, we will see the out­line of the mod­el’s face con­tours and cloth­ing, which in the orig­i­nal pic­ture are per­ceived as most clear (Fig.  68 B). In oth­er words, we have an impres­sion that some part of the paint­ing is sharp, because we see the con­tours in it.  The lips, nose, hair out­line and, espe­cial­ly, the eyes of Madame Hen­ri­ot are clear­ly high­light­ed by the con­tour lines. In turn, oth­er parts of her body and cloth­ing, which are below the face, are blurred because it is impos­si­ble to dis­tin­guish sen­si­ble shapes based on the few frag­ments of con­tour lines cre­at­ed as a result of edge analy­sis. How­ev­er, there are two excep­tions. One is approx­i­mate­ly in the mid­dle of Madame’s neck­line and, as we sus­pect, it is an out­line of jew­ellery. The sec­ond, a lit­tle to the left, is Renoir’s signature.

Accord­ing to David Marr and Ellen C. Hil­dreth (1980), the cre­ators of a math­e­mat­i­cal algo­rithm that sim­u­late the process of edge detec­tion by the human eye, con­tours of things are a man­i­fes­ta­tion of the so-called  dis­con­ti­nu­ity of lumi­nance. Con­tin­u­ous lumi­nance is typ­i­cal of planes light­ning of which changes grad­u­al­ly over rel­a­tive­ly large space. On the oth­er hand, the more pos­si­ble edge iden­ti­fi­ca­tion, the small­er the space in which the sur­face illu­mi­na­tion changes. Cur­rent­ly, major­i­ty of com­put­er soft­ware for image pro­cess­ing have built-in edge detec­tion algo­rithms. From the point of view of the edge detec­tion issues in ques­tion, it is worth look­ing more close­ly at their oper­a­tion mode.

After iso­lat­ing the lumi­nance chan­nel from the col­or­ful repro­duc­tion of the paint­ing of Madame Hen­ri­ot cre­at­ed by Pierre-Auguste Renoir, we will see the image in full grayscale, from white to black (Fig. 68 A). If we analyse the paint­ing in order to iden­ti­fy the bor­der­lines between the planes with great­est dif­fer­en­ti­a­tion in terms of bright­ness, we will see the out­line of the mod­el’s face con­tours and cloth­ing, which in the orig­i­nal pic­ture are per­ceived as most clear (Fig.  68 B). In oth­er words, we have an impres­sion that some part of the paint­ing is sharp, because we see the con­tours in it.  The lips, nose, hair out­line and, espe­cial­ly, eyes of Madame Hen­ri­ot are clear­ly high­light­ed by the con­tour lines. In turn, oth­er parts of her body and cloth­ing, which are below the face, are blurred because it is impos­si­ble to dis­tin­guish sen­si­ble shapes based on the few frag­ments of con­tour lines cre­at­ed as a result of edge analy­sis. How­ev­er, there are two excep­tions. One is approx­i­mate­ly in the mid­dle of Madame’s neck­line and, as we sus­pect, is an out­line of jew­ellery. The sec­ond, a lit­tle to the left, is Renoir’s signature.

To prove that the eyes of the observ­er are par­tic­u­lar­ly focused on search­ing for the most con­trast­ing places in the visu­al scene, as their analy­sis gives the great­est chance to recog­nise the con­tours of the objects locat­ed in it, it is worth not­ing the result of an ocu­lo­mo­tor exam­i­na­tion, which we con­duct­ed in our lab­o­ra­to­ry with Anna Szpak on a group of 38 stu­dents (19 women and 19 men aged around  22 years) The task of the exam­ined per­sons was to watch repro­duc­tion of a dozen or so paint­ings, on a 23″ Apple Cin­e­ma HD Dis­play (1920 x 1200 pix­els) mon­i­tor. There is the paint­ing cre­at­ed by Renoir among these paint­ings. The exam­ined per­sons were not lim­it­ed by time, but we record­ed their eye­balls move­ment, using SMI iView X Hi Speed 1250 Hz ocu­lo­graph all the time. The results of this study, pre­sent­ed in the form of a visu­al atten­tion map, are pre­sent­ed in Fig. 69.

Com­par­ing the records in Fig.  68 A and in Fig. 69, it is easy to see that the great­est inter­est of the exam­ined per­sons was gen­er­at­ed by the face and the above men­tioned two ele­ments dis­tin­guished by a high­er con­trast, i.e. brooch  in the neck­line of the dress and sig­na­ture of the artist.  It is worth men­tion­ing that a col­or­ful atten­tion map in Fig. 69 includes aver­aged infor­ma­tion about both the num­ber of points which tem­po­rary fix­ate the sight on a giv­en frag­ment of a paint­ing, and the time of these fix­a­tions, for all per­sons exam­ined in total.

Since the areas with increased con­trast between the planes lying next to each oth­er gen­er­at­ed much more inter­est than oth­er areas in the paint­ing, it is worth answer­ing the ques­tion which neu­ro­phys­i­o­log­i­cal mech­a­nism is respon­si­ble for this effect.

### Ernst Mach’s Bands

In 1865, the Aus­tri­an physi­cist, philoso­pher and psy­chol­o­gist – Ernst Mach – pub­lished an arti­cle in which he pro­posed a con­cept to explain the visu­al illu­sion, char­ac­terised by addi­tion­al thin (but dis­tinct) bands (lighter on the side of a lighter plane and dark­er on the side of a dark­er plane) that can be seen along the edges of planes with dif­fer­ent bright­ness, lying next to each oth­er (Fig. 70 A).

Look­ing clos­er at a uni­form­ly white sur­face of the rec­tan­gle (Fig. 70 A) for a while, we can notice a nar­row, slight­ly lighter line locat­ed just in front of the edge of the grey rec­tan­gle. It seems that this line is even whiter than white­ness of the whole rec­tan­gle. In fact, there is no lighter line there, as evi­denced by the analy­sis of the pic­ture in a dig­i­tal pho­to edit­ing pro­gram. A sim­i­lar effect can also be observed on the black side of the first rec­tan­gle on the left, although it is slight­ly more dif­fi­cult to see it. Para­dox­i­cal­ly, despite the 100% black­ness of the plane, the ver­ti­cal band seems to be even “black­er”. In order to see it, it is enough to focus your gaze longer at the place where the black plane begins to light­en and the line will be ful­ly vis­i­ble. The visu­al illu­sion in ques­tion is known as Mach bands. For com­par­i­son, when the tran­si­tion between black and white is con­stant, as shown in Fig. 70 B, then you can­not see the addi­tion­al bands sep­a­rat­ing dark frag­ments of the plane from the light ones.

One of the most emi­nent experts on the con­cept by Ernst Mach was Floyd Ratliff (1919–1999), a psy­chophys­i­ol­o­gist and bio­physi­cist, who for many years con­duct­ed stud­ies on opti­cal illu­sions, espe­cial­ly those relat­ed to the con­trast of col­or and light­ness. He was also a fan of Neo-impres­sion­ists’ works, inte­ria alia on the grounds that they were fas­ci­nat­ed by the pre­sen­ta­tion of the phe­nom­e­nal­i­ty of the world in a way as it appears in the sub­jec­tive acts of visu­al per­cep­tion (Ratliff, 1992).

Analysing the paint­ing The din­ing room, cre­at­ed by Paul Signac, Ratliff (1971), he noticed that the artist — con­scious­ly or uncon­scious­ly — paint­ed some objects tak­ing into account the illu­sion of Mach bands (Fig. 71 A).

A few shad­ows are cast on the table sur­face by a book, a sal­ad bowl, a carafe, a plate, a box and a hand (Fig. 71 B). At the edge con­tact point between a dark­er object and a slight­ly lighter shad­ow, Signac slight­ly light­ened the shad­ow to empha­sise the con­trast between it and the object that casts it. A per­son view­ing a paint­ing has no doubts what shape a giv­en object has been paint­ed, because the shad­ow is addi­tion­al­ly sep­a­rat­ed from the object with a lighter band. It is an excel­lent illus­tra­tion of Mach bands, paint­ed in the way the brain “sees” them.

The paint­ing Bathers at Asnières by Georges Seu­rat is anoth­er exam­ple of the artist’s clar­i­fi­ca­tion of the con­tact point of two planes with sim­i­lar light­ing (Fig. 72). In the places marked with arrows, the painter dark­ened (black arrows) or light­ened (white arrows) the back­ground to empha­size the sep­a­ra­tion of the fig­ure from the back­ground. What is inter­est­ing, although it con­sti­tutes a sig­nif­i­cant inter­fer­ence in the way the rel­a­tive­ly uni­form water back­ground is paint­ed, with­out pay­ing atten­tion to this detail it is almost unnoticeable.

His­to­ry of art pro­vides many exam­ples of paint­ings from dif­fer­ent cul­tures, epochs and styles in case of which the authors intu­itive­ly used Mach’s illu­sion to high­light the con­trast between objects depict­ed in the visu­al scene. Those inter­est­ed in var­i­ous exam­ples of such works can see pub­li­ca­tions of Michael F. Mar­mor and James G. Ravin (1997; 2009), Piotr Przy­bysz and Piotr Markiewicz (2010), Floyd Ratliff (1992) and Robert L. Sol­so (1996). Chi­nese painters from sev­er­al thou­sand years ago, Renais­sance mas­ters and mod­ern painters alike used this tech­nique in their works with equal success.

Are Mach bands just an inter­est­ing opti­cal illusion?

Not at all. It turns out that they are a man­i­fes­ta­tion of the activ­i­ty of one of the most impor­tant visu­al mech­a­nisms aimed at iden­ti­fi­ca­tion of the con­tours of the things viewed, by increas­ing the con­trast between adja­cent planes with dif­fer­ent bright­ness lev­els. This makes it eas­i­er to dis­tin­guish the com­po­nents in one object and sep­a­rate them from each oth­er. In par­tic­u­lar, this mech­a­nism is use­ful for those parts of the pic­ture, which are pro­ject­ed onto periph­er­al parts of the reti­na, locat­ed far from the fovea.

### Once again about the structure of the retina: ON and OFF channels

In order to under­stand how the mech­a­nism respon­si­ble for strength­en­ing the con­tours of the objects seen works, one needs to go deep into the reti­na and look clos­er at its com­plex struc­ture (Dacey, 2000). As indi­cat­ed ear­li­er, it con­sists of five lay­ers of cells: (1) pho­to­sen­si­tive rods and cones, (2) hor­i­zon­tal cells, (3) bipo­lar cells, (4) amacrine cells and (5) gan­glion cells (Fig.  73). Pho­to­sen­si­tive cells, that is pho­tore­cep­tors (lay­er 1), react to light enter­ing the eye. Hor­i­zon­tal cells (lay­er 2) and amacrine cells (lay­er 4) con­nect the pho­tore­cep­tors in the recep­tive fields and have a direct or indi­rect effect on bipo­lar cell activ­i­ty (lay­er 3). These, in turn, trans­mit sig­nals both from pho­tore­cep­tors and from recep­tive fields to gan­glion cells (lay­er 5). Final­ly, the gan­glion cells trans­mit elec­tri­cal sig­nals deep into the brain via their long axons.

As you can see, the cere­bral cor­tex is informed about the dis­tri­b­u­tion of light in the visu­al scene not only by the stim­u­la­tion of the pho­tore­cep­tors them­selves, but also by the activ­i­ty of the cells con­nect­ed to them, com­pos­ing the entire retina.

The hor­i­zon­tal cells are locat­ed just below the pho­tore­cep­tors and they are con­nect­ed to them through a net­work of pro­jec­tions, called den­drites (Fig. 74). Pho­tore­cep­tors inter­con­nect­ed by means of one hor­i­zon­tal cell cre­ate its recep­tive field. One such a cell can be inter­con­nect­ed by sev­er­al to sev­er­al dozen photoreceptors.

In turn, each pho­tore­cep­tor can con­nect not only to one, but at least to two hor­i­zon­tal cells. Such an arrange­ment of con­nec­tions between pho­to­sen­si­tive and hor­i­zon­tal cells results in the for­ma­tion of large groups of pho­tore­cep­tors in the reti­na. Each such group, in con­nec­tion with a sin­gle gan­glion cell through bipo­lar cell, cre­ates recep­tive field of this gan­glion cell.

It is worth not­ing that data on the state of stim­u­la­tion of par­tic­u­lar pho­tore­cep­tors in the reti­na of the eye — except for a small area of the fovea — are not trans­mit­ted to the cere­bral cor­tex. On the con­trary, infor­ma­tion at the exit of the reti­na is low­er by at least two orders of mag­ni­tude than infor­ma­tion enter­ing the retina.

The part of pho­tore­cep­tors locat­ed in the cen­tral part of the recep­tive field of the gan­glion cell is con­nect­ed not only to the hor­i­zon­tal cell but also direct­ly to the bipo­lar cell. This is par­tic­u­lar­ly impor­tant, as infor­ma­tion on the state of stim­u­la­tion of pho­tore­cep­tors form­ing the whole recep­tive field is trans­mit­ted to gan­glion cell only through the bipo­lar cells. This net­work of con­nec­tions is best seen on the cross-sec­tion of the gan­glion cell recep­tive field (Fig. 75). Pho­tore­cep­tors in the cen­tral area of the hor­i­zon­tal cel­l’s recep­tive field are addi­tion­al­ly con­nect­ed by den­drites of the bipo­lar cell.

To sum up, recep­tive fields of the gan­glion cell cre­at­ed by a net­work of inter­re­lat­ed hor­i­zon­tal cells can be divid­ed into two areas: cen­tral area, in which the pho­tore­cep­tors are oper­at­ed by both the hor­i­zon­tal and bipo­lar cells, and the periph­er­al area, the so called are­o­la, in which the pho­tore­cep­tors are inter­linked only by means of the hor­i­zon­tal cell. Infor­ma­tion on bright­ness of the image pro­ject­ed onto the recep­tive field depends on the num­ber of pho­tore­cep­tors stim­u­lat­ed in the cen­tral area and in the periph­er­al area, as well as on light inten­si­ty (Matthews, 2000). It also depends on cer­tain spe­cif­ic prop­er­ties of bipo­lar and gan­glion cells.

There are indeed two types of bipo­lar cells in the reti­na of the eye: ON and OFF cells. Each type of bipo­lar cell is asso­ci­at­ed with the cor­re­spond­ing gan­glion cell, also of ON and OFF types. Com­bi­na­tion: pho­tore­cep­tor (or pho­tore­cep­tors) → ON bipo­lar cell → ON gan­glion cell is called the ON chan­nel, while com­bi­na­tion: pho­tore­cep­tor (or pho­tore­cep­tors) → OFF bipo­lar cell → OFF gan­glion cell is called the OFF chan­nel (Longstaff, 2002).

If the light of a high­er inten­si­ty than aver­age illu­mi­na­tion in a giv­en area of the reti­na falls on a pho­tore­cep­tor (or pho­tore­cep­tors) con­nect­ed direct­ly to ON chan­nel, i.e. to the mid­dle of the recep­tive field, the gan­glion cell would inter­pret this sig­nal as an infor­ma­tion about the stim­u­la­tion with light of this pho­tore­cep­tor or group of pho­tore­cep­tors. The high­er num­ber of stim­u­lat­ed pho­tore­cep­tors in the mid­dle of the recep­tive field and the less num­ber locat­ed in the periph­ery of the recep­tive field — the stronger reac­tion of the gan­glion cell (Fig. 76, line (a), col­umn: ON).

The OFF-gan­glion cell will react in a very sim­i­lar way when the light of low­er inten­si­ty than the aver­age inten­si­ty of light in a giv­en reti­nal area falls on the pho­tore­cep­tors placed in the cen­tre of its recep­tive field. The gan­glion cell will then inform the brain that the image pro­ject­ed onto the reti­nal area is dark (Fig. 76, line (a), col­umn: OFF).

To sum up, the ON-chan­nel informs the brain about the posi­tion of bright spots in a paint­ing, where­as the OFF-chan­nel con­veys infor­ma­tion about the posi­tion of dark spots.

If the cen­tral part of the OFF-gan­glion cell recep­tive field is illu­mi­nat­ed and its are­o­la remains in the shade, the gan­glion cell will not react. It is sim­i­lar when the cen­tral part of the ON-gan­glion cell recep­tive field remains dark and only the are­o­la is illu­mi­nat­ed (Fig. 76, line (b), columns: ON and OFF). Although gan­glion cells will not react in both cas­es, it is also a valu­able piece of infor­ma­tion for the brain, because it says some­thing about the bright­ness of dif­fer­ent points of an image pro­ject­ed onto the reti­na. Since the num­ber of ON- and OFF-chan­nels in the reti­na is the same and they are more or less even­ly dis­trib­uted side by side, the brain is con­stant­ly informed about the stim­u­la­tion of pho­tore­cep­tors, regard­less of whether they are exposed to intense light or locat­ed in the shade (Har­ris and Humphreys, 2002).

A slight­ly less “inter­est­ing” sit­u­a­tion for the brain is when all pho­tore­cep­tors in the gan­glion cell recep­tive field record light of sim­i­lar inten­si­ty, regard­less of its bright­ness. The sig­nal strength, trans­mit­ted by both ON- and OFF-chan­nels, will be bal­anced then and the gan­glion cell will react with mod­er­ate inten­si­ty, typ­i­cal of its spon­ta­neous activ­i­ty (Fig. 76, line ©, columns: ON and OFF). From the point of “view” of the brain, infor­ma­tion about the uni­form bright­ness of a larg­er frag­ment of a paint­ing means that a giv­en frag­ment of the sur­face (not the edge) of some object or back­ground is pro­ject­ed onto a giv­en recep­tive field. Accord­ing to David Hubel (1988), the inte­ri­ors of planes with uni­form light inten­si­ty are sim­ply unin­ter­est­ing for the brain.

### Lateral inhibition as a contrast enhancement mechanism

It is time to return to the expla­na­tion of Mach illu­so­ry bands.  Accord­ing to his hypoth­e­sis, the lighter and dark­er bands vis­i­ble at the meet­ing point of sur­faces with dif­fer­ent bright­ness are asso­ci­at­ed with the lat­er­al inhi­bi­tion mech­a­nism, which con­sists in mutu­al decreas­ing of the activ­i­ty of inter­con­nect­ed cells.  Of course, Mach did not have the tech­ni­cal pos­si­bil­i­ties to ver­i­fy the hypoth­e­sis empir­i­cal­ly, yet his pre­sump­tion was accurate.

Even though the recep­tive field of the gan­glion cell clus­ters even sev­er­al hun­dred pho­tore­cep­tors, its sur­face still does not exceed 1 mm².  Just like the hor­i­zon­tal cells form con­nec­tion net­works with­in the recep­tive field of a sin­gle gan­glion cell, the recep­tive fields of var­i­ous gan­glion cells do not work sep­a­rate­ly, but are con­nect­ed with each oth­er. Amacrine cells, as well as oth­er interneu­rons, play a par­tic­u­lar­ly impor­tant role in inter­con­nect­ing the recep­tive fields of gan­glion cells (see lay­er 4 in Fig. 73). Both types of cells are con­nect­ed to bipo­lar cells at the out­put, i.e. just before they are con­nect­ed to the gan­glion cell. With such a site of con­nec­tion to a bipo­lar cell, amacrine cells have full “knowl­edge” of what sig­nal is being trans­mit­ted from a giv­en recep­tive field to the gan­glion cell. This is also the last moment to do some­thing with this sig­nal. It can be either rein­forced or inhibited.

Many amacrine cells only inhib­it the activ­i­ty of bipo­lar cells. How­ev­er, this is not quite point­less. On the con­trary – it con­sti­tutes the basis for edge detec­tion of the seen objects. To put it sim­ply, lat­er­al inhi­bi­tion mech­a­nism – the activ­i­ty of cells that inhib­it “in side­line” the lev­el of stim­u­la­tion of adja­cent bipo­lar cells – can be explained with a sim­ple draw­ing (Fig. 77).

Scheme in Fig. 77 presents hypo­thet­i­cal reac­tions of six gan­glion cells lying at the con­tact point of two areas of dif­fer­ent bright­ness.  Gan­glion cells are con­nect­ed with six recep­tive fields that are per­pen­dic­u­lar to the edges of these areas. The sur­face is illu­mi­nat­ed (white) on the left side and lies in the shade (grey) on the right side.

In order to illus­trate the lat­er­al inhi­bi­tion mech­a­nism, accord­ing to Gary G. Matthews (2000), we accept the fol­low­ing assump­tions: (1) bright­ness of the image sur­face on the right side is less than half of the image sur­face on the left side on the con­ven­tion­al bright­ness scale (2) hin­der­ing influ­ence of amacrine cells on a sig­nal trans­mit­ted by the bipo­lar cell to the gan­glion cell is 20% light inten­si­ty in a giv­en area, i.e. in the area illu­mi­nat­ed by 100 units the amacrine cell reduces the sig­nal lev­el in the bipo­lar cell by 20 units and in the area illu­mi­nat­ed by 50 units the sig­nal is decreased by 10 units and (3) each bipo­lar cell is con­nect­ed by amacrine cells to two adja­cent bipo­lar cells. The rest is sim­ple arithmetic.

The first two bipo­lar cells on the left receive a sig­nal with a bright­ness of 100 units of light stim­u­lat­ing them from the pho­tore­cep­tors. Just before con­nect­ing to the gan­glion cell, the sig­nal trans­mit­ted by the bipo­lar cell is inhib­it­ed, i.e. low­ered by two amacrine cells by 40 units (20 units each by the right and left amacrine cells). As a result, both gan­glion cells receive infor­ma­tion from bipo­lar cells that their recep­tive fields reg­is­tered light with an inten­si­ty of 60 units (100 — 20 — 20 — 20 = 60). Sim­i­lar process­es take place in two bipo­lar cells on the right side of the graph. Because they are lit by less intense light (50 units), near­by amacrine cells low­er the sig­nal trans­mit­ted by them by only 10 units each (20% of 50 units). As a result, gan­glion cells receive infor­ma­tion about the bright­ness of these areas at the lev­el of 30 units (50 — 10 — 10 — 10 = 30).

How­ev­er, the most inter­est­ing are the results of sub­tract­ing the val­ues rep­re­sent­ing the size of the sig­nal trans­mit­ted by bipo­lar cells in the vicin­i­ty of the edge between two planes of dif­fer­ent light inten­si­ty. Although a bipo­lar cell locat­ed on the bright side of the plane receives infor­ma­tion about 100 units of light from pho­tore­cep­tors, the total lev­el of its inhi­bi­tion by two amacrine cells is not 40, but 30 units. The rea­son for this is that the bipo­lar cell near­est to the shade is inhib­it­ed by a sin­gle amacrine cell at the lev­el of 10 rather than 20 units of light, because the recep­tive field to which it is con­nect­ed is stim­u­lat­ed by light of an inten­si­ty of 50 units rather than 100. In total, the gan­glion cell receives infor­ma­tion that its recep­tive field is sat­u­rat­ed with light of 70 units (100 — 20 — 10 = 70) and not 60 units, as the gan­glion cells locat­ed more to the left of it are informed. And this is the brighter Mach band on the side of the more intense­ly lit plane of the image.

It is enough to imag­ine a few dozen rows of recep­tive fields, anal­o­gous to the ones shown in Fig. 77, which are per­pen­dic­u­lar to the bor­der of light, and from one brighter point we have a whole sequence of them arranged along the bright edge of the illu­mi­nat­ed surface.

The cal­cu­la­tion is anal­o­gous to the first recep­tive field on the shad­ow side. The bipo­lar cell is also oth­er­wise inhib­it­ed by amacrine cells lying on its right and left side. As a result, the gan­glion cell receives infor­ma­tion about a band dark­er than the whole sur­face on the right side of the pic­ture (50 — 20 — 10 = 20). This is the dark­er Mach band on the shad­ed side of the image plane.

The per­cep­tion of dif­fer­ences in bright­ness near the edges of two planes of dif­fer­ent lumi­nance is also illus­trat­ed by the graph in Fig. 78. On the brighter side of the edge, the sub­jec­tive­ly per­ceived bright­ness of the image sur­face is clear­ly pro­nounced, while on the dark­er side of the edge, the bright­ness reduc­tion is equal­ly evident.

Obvi­ous­ly, it should be remem­bered that the edge detec­tion between two planes of dif­fer­ent bright­ness is pos­si­ble as a result of the appear­ance of a sim­i­lar sig­nal in gan­glion cells at the same time, com­ing from sev­er­al or more recep­tive fields lying next to each oth­er. It is worth men­tion­ing that the mech­a­nism of tem­po­ral group­ing of sim­i­lar sig­nals from the reti­na to the brain plays a very impor­tant role in detect­ing the spa­tial ori­en­ta­tion of iden­ti­fied edges. As we remem­ber, the cells form­ing columns in the pri­ma­ry visu­al cor­tex (V1) are involved in the analy­sis of this edge fea­ture for objects being viewed.

Last­ly, it is worth recall­ing three issues once again.

First­ly, Mach bands are an illu­sion, i.e. they do not actu­al­ly exist in the image pro­ject­ed onto the reti­na. If they were applied to a paint­ing (e.g. by Paul Signac, Fig. 72), it was only made to empha­sise their pres­ence in the sub­jec­tive expe­ri­ence of seeing.

Sec­ond­ly, Mach bands are a man­i­fes­ta­tion of the neu­ro­phys­i­o­log­i­cal mech­a­nism used to increase the con­trast among adja­cent sur­faces char­ac­terised by dif­fer­ent light saturation.

Third­ly, and final­ly, they coun­ter­bal­ance the blurred vision of those parts of the pic­ture that are pro­ject­ed par­tic­u­lar­ly on the periph­er­al parts of the reti­na, thus increas­ing the like­li­hood of see­ing the con­tours of the objects in those places in the visu­al scene.

### Contour — the foundation and skeleton of the image

The use of con­tour draw­ing to depict the seen objects is the most nat­ur­al and the old­est human skill. This is evi­denced by both the illus­tra­tions of ani­mals and peo­ple (dat­ed to 20 000 – 30 000 years ago), locat­ed on the walls of the caves of: Altami­ra, Las­caux or Chau­vet (Fig. 79), rock draw­ings in Gob­us­tan (Fig. 80 A), as well as chil­dren’s draw­ings (Fig. 80 B). It is inter­est­ing that, although the objects we see do not usu­al­ly have any edges, when draw­ing them we imme­di­ate­ly use lines that sig­ni­fy edges when try­ing to present their shapes in a pic­ture. The drawn con­tour line, con­trast­ed with the back­ground, unam­bigu­ous­ly sep­a­rates the planes that belong to the things seen and to the back­ground, or that mark impor­tant parts of these things. At the same time, dele­tion of the con­tour exempts the visu­al sys­tem from con­duct­ing com­plex con­trast enhance­ment oper­a­tions by the lat­er­al inhi­bi­tion mech­a­nism, because the edge is the result of this mech­a­nism pro­ject­ed on the image plane. It is an artis­tic styl­i­sa­tion of lat­er­al inhi­bi­tion effects. When draw­ing an out­line on the image plane, we show the world record­ed at the out­put of the reti­na towards the brain.

It is worth real­is­ing the impor­tance of con­tour dis­cov­ery as a pri­ma­ry imag­ing tool. Before the first draw­ings or stone carv­ings appeared, our ances­tors only carved spa­tial objects. Most often they depict­ed women or ani­mals and musi­cal instruments.

About 30,000 years before Christ, or per­haps even ear­li­er, humans dis­cov­ered that three-dimen­sion­al objects — even if they do not have con­tours — can be rep­re­sent­ed on a flat sur­face with the use of a scorched piece of wood or a fin­ger dipped in mud.   I believe that this dis­cov­ery, being the expres­sion of the inge­nious intu­ition of our fore­fa­ther, belongs to the canon of mile­stones in the his­to­ry of human civ­i­liza­tion, equal­ly as the mas­tery over fire and for­ma­tion of the ver­bal lan­guage foun­da­tions, based on the use of con­ven­tion­al signs. Indeed, it is hard to imag­ine at what stage of civ­i­liza­tion devel­op­ment we would be at present if our ances­tors did not mas­ter the abil­i­ty to present the world in a flat pic­ture. It may be that we would still be wait­ing in our caves for the bril­liant Leonard of Chauvet.

### Between the Upper Palaeolithic and contemporary times

Although the his­to­ry of art pro­vides many exam­ples of the use of con­tour lines as a means of artis­tic expres­sion, in West­ern Euro­pean paint­ings they were for many cen­turies used almost exclu­sive­ly to pre­pare sketch­es, which were then care­ful­ly hid­den under a lay­er of paint.  It was not until the rev­o­lu­tion in art at the turn of the 19th and 20th cen­turies that the con­tour ceased to be mere­ly an ele­ment of aux­il­iary draw­ing but it was includ­ed in the arse­nal of mod­ern means of expres­sion. Artists such as Paul Cezanne, Hen­ri Matisse, Pablo Picas­so and Roy Licht­en­stein, as well as many oth­er con­tem­po­rary artists, not only did not hide the con­tours of the paint­ed objects and their parts but, on the con­trary, they clear­ly sep­a­rat­ed them from each oth­er with strong strokes of brush­es, achiev­ing a com­plete­ly new artis­tic qual­i­ty (Fig. 81 A, B, C and D).

In such method of paint­ing one can notice echoes of the method used for depict­ing the world thou­sands of years ago. Although there is no con­fir­ma­tion of Pablo Picas­so’s pres­ence in the guest book of the Cave of Altami­ra, it is him who is cred­it­ed with the famous sen­tence that “after Altami­ra, every­thing is decadence”.

### From a distance or at a close range: Camille Pissarro vs Pieter Bruegel the Elder

We see objects from dif­fer­ent dis­tances. We see more of their details at a close range, and none or less from a dis­tance. The loss of the clar­i­ty of details as a deriv­a­tive of the dis­tance from an object being seen is increas­ing­ly felt in rela­tion to those ele­ments of the image that are pro­ject­ed onto the periph­er­al areas of the reti­na rather than onto the fovea. This undoubt­ed weak­ness of the visu­al sys­tem, how­ev­er, is by no means a major lim­i­ta­tion for painters. On the con­trary, visu­al exper­i­ments in which artists use vari­able eye res­o­lu­tion to con­vey dif­fer­ent con­tent to their recip­i­ents are not uncom­mon. The works of many artists from var­i­ous peri­ods and paint­ing tra­di­tions are the evi­dence for that.

To start with, it is worth con­fronting two paint­ings that are sep­a­rat­ed by over 300 years of expe­ri­ence and reflec­tion on visu­al art. The first paint­ing, clos­er to our times, was cre­at­ed in Impres­sion­ist style, the sec­ond one belongs to the ear­ly Renais­sance tra­di­tion of Flem­ish painting.

Pis­sar­ro’s paint­ing (Fig. 82) is the exam­ple of Impres­sion­ist paint­ing which is char­ac­terised by a typ­i­cal lack of care for the shapes of the depict­ed objects, sharply marked flash­es of light and thick­ly laid paint.  What does this paint­ing represent?

This ques­tion can be cor­rect­ly answered only if the reti­nas of the eyes of the observ­er do not reg­is­ter it very accu­rate­ly, i.e. through the periph­er­al parts, which are char­ac­terised by low res­o­lu­tion, or as a result of increas­ing the dis­tance from which it is seen. As the dis­tance between the fovea and the object being seen increas­es, the few­er cones reg­is­ter the same pic­ture plane and thus the res­o­lu­tion of the pic­ture decreases.

An inter­est­ing visu­al phe­nom­e­non occurs with respect to Pis­sar­ro’s work. Para­dox­i­cal­ly, the more clear the details of the scene depict­ed on the paint­ing, the low­er their res­o­lu­tion (obvi­ous­ly, e.g. at 500 metres dis­tance, we would prob­a­bly hard­ly see any paint­ing on the wall). The solu­tion to this para­dox lies not in the paint­ing, but in the mind of the observer.

Let us see how the analysed paint­ing looks at close dis­tance.  The low­er left frag­ment in shown in a close-up in Fig. 83 A. When we look at this frag­ment in the con­text of the whole paint­ing (i.e. at a cer­tain dis­tance), then we have no doubt that it presents a piece of pave­ment, a crowd of passers-by, illu­mi­nat­ed shop win­dows and a tele­phone booth with a light­ed light bulb inside.

After per­form­ing a close-up and edge detec­tion based on the bright­ness of the adja­cent pic­ture planes, we can say that the shape of any object found in this frag­ment of the paint­ing does not resem­ble any human being (Fig. 83 B).  It is sim­ply impos­si­ble to see peo­ple here as well as all the oth­er objects men­tioned with­out ref­er­ence to the whole paint­ing.  We only see irreg­u­lar spots sur­round­ed by edges, which by no means can serve as a basis that enable the view­er to con­struct any sen­si­ble scene.

So how does it hap­pen that on the basis of irreg­u­lar, col­ored spots and edges which do not pro­duce sig­nif­i­cant fig­ures in a close-up we can see any­thing in Pis­sar­ro’s paint­ing? This ques­tion can­not be answered by refer­ring to sen­so­ry data only, i.e. the data being trans­ferred from recep­tors to the brain (i.e. bot­tom-up). For prop­er inter­pre­ta­tion of this paint­ing, ref­er­ences to pre­vi­ous expe­ri­ences of view­ing sim­i­lar scenes are nec­es­sary. These expe­ri­ences are record­ed in the observer’s brain and some­how applied top-down to the scene being watched. This is how the paint­ing’s con­tent is pro­duced “in the mind” of the recip­i­ent – by pro­ject­ing their own mem­o­ries on the ambigu­ous plane of col­or­ful spots and shapes. And that is how a sen­si­ble scene is created.

Although one may dis­agree with David Mar­r’s assump­tion (1982) that all items of infor­ma­tion for recog­nis­ing objects being seen are avail­able from the reti­na, many of them pro­vide use­ful hints for inter­pret­ing this scene undoubt­ed­ly. View­ing Pis­sar­ro’s paint­ing from a greater dis­tance cer­tain­ly does not improve the sharp­ness for detail view of indi­vid­ual objects. How­ev­er, the greater dis­tance enables to see gen­er­al out­lines of the order of objects depict­ed in the paint­ing. By blur­ring the details, larg­er frag­ments of the paint­ing merge with one anoth­er, which form reg­u­lar struc­tures, delin­eat­ed by the illu­so­ry lines of per­spec­tive (Fig. 84).

First of all, it turns out that the paint­ing has been paint­ed in accor­dance with the Renais­sance per­spec­tive rules, cod­i­fied by Fil­ip­po Brunelleschi (Gom­brich, 2009; Janows­ki, 2007). Per­spec­tive lines divide it into at least four clear­ly sep­a­rat­ed parts: the top part (with­out addi­tion­al lines), two side parts (with a pre­dom­i­nance of ver­ti­cal lines) and the bot­tom part (with hor­i­zon­tal and ver­ti­cal lines). Notic­ing this order is the basis not so much to see but to remem­ber the details of sim­i­lar paint­ings depict­ing a street and super­im­pose them on this scheme.

The reverse side of Pis­sar­ro’s The Boule­vard Mont­martre at Night is The Pro­ces­sion to Cal­vary by Peter Bruegel the Elder. The painter placed over 500 human fig­ures and near­ly a hun­dred dif­fer­ent ani­mals and objects on the sur­face of the paint­ing less than 1 m² (Fig. 85).

There­fore, on the basis of a gen­er­al view of the work, even the tenth part of what is its con­tent can­not be sur­mised. All one needs to do is look at a few frag­ments of the paint­ing to under­stand how many sto­ries, anec­dotes and sym­bols it con­tains.  Each of these frag­ments could con­sti­tute a sep­a­rate paint­ing. Each of them is sub­ject the same laws of per­cep­tion, which make it pos­si­ble to iden­ti­fy the con­tours of the fig­ures locat­ed in each visu­al scene (see Fig. 86). The only con­di­tion for see­ing them is mov­ing clos­er to the paint­ing.  By mov­ing one’s eyes from one place to anoth­er, Bruegel’s work is read like a book. It is not only a rep­re­sen­ta­tion of space, but also of the change in time, marked by oth­er sta­tions of the Cross placed in dif­fer­ent parts of the painting.

Com­par­ing the con­tours of the objects paint­ed by Pis­sar­ro and Bruegel (Fig. 83 B and 86 B), we imme­di­ate­ly notice the dif­fer­ence in the con­cept of rep­re­sen­ta­tion of the visu­al scene in paint­ing.   The eas­i­ly recog­nis­able shapes of hors­es, peo­ple and objects in Bruegel’s paint­ing cor­re­spond to the pro­jec­tion, almost ran­dom, Pis­sar­ro’s spots. Both painters use the eye res­o­lu­tion of the observers (who admire the artistry with which they present their own vision of the scene being watched) dif­fer­ent­ly. What con­nects them, how­ev­er, is that they leave the recip­i­ent no choice. Either their works are viewed from a cer­tain dis­tance or it is not known what is depict­ed on them.

### From Mannerism to mozaika.com

When it comes to con­sid­er­a­tion regard­ing the sharp­ness of paint­ings viewed from dif­fer­ent dis­tances, it is worth pay­ing atten­tion to sev­er­al oth­er exam­ples of visu­al art works. Unlike Pis­sar­ro’s and Bruegel’s works, they all present fun­da­men­tal­ly dif­fer­ent con­tent when viewed from a close or far dis­tance. Their parts being seen from a close dis­tance are as sen­si­ble as the fig­ures in Bruegel’s paint­ings, but they blur and trans­form into new con­tent (as in Pis­sar­ro) with the increase of the dis­tance from the paint­ing. There is a lit­tle of mag­ic and illu­sion in this, but, above all, they are a man­i­fes­ta­tion of exper­i­ment­ing with the pos­si­bil­i­ties of the human eye by “igno­rant neu­ro­sci­en­tists” (cf. Ramachan­dran and Hirstein, 1999; Zeki, 1999).

One of the pre­cur­sors of Sur­re­al­ism is the Ital­ian Man­ner­ist, Giuseppe Arcim­bol­do. His pas­sion was paint­ing in such a way that his paint­ings depict­ed still life com­posed of veg­eta­bles, fruit, leaves and flow­ers when viewed close­ly, while, when viewed from a cer­tain dis­tance, they depict­ed por­traits or genre scenes. Arcim­bol­do also paid equal atten­tion to the pos­si­ble faith­ful rep­re­sen­ta­tion of the com­po­nents of the por­trayed fig­ures, as well as to high­light­ing their spe­cif­ic facial fea­tures (Fig. 87 A and B).

Mex­i­can artist, Octavio Ocam­po, a Sur­re­al­ist and pre­cur­sor of con­tem­po­rary poly­mor­phic paint­ing, con­ducts sim­i­lar exper­i­ments on change­able res­o­lu­tion of view­ing paint­ings. Sim­i­lar­ly to Arcim­boldo’s paint­ings, Ocam­po’s paint­ings some­times also has two, even more, lay­ers of con­tent that are dis­cov­ered depend­ing on the dis­tance from which they are viewed. The almost six-metre long fres­co on the wall of the Infor­ma­tion Cen­ter of the Tech­no­log­i­cal Insti­tute of Celaya, Mex­i­co, gives a spe­cial oppor­tu­ni­ty for this (Fig. 88). Three faces of a pre­his­toric hominid, homo sapi­ens and Albert Ein­stein are viewed from a dis­tance almost imme­di­ate­ly, but only in a clos­er look they turn into a group of run­ners, sym­bol­is­ing human evolution.

When paint­ing the fres­co, Ocam­po par­tic­u­lar­ly made sure that the faces dom­i­nat­ed the atten­tion of view­ers. This is clear­ly revealed by the con­tour analy­sis con­duct­ed on the basis of the mono­chrome ver­sion of this fres­co (Fig. 89).

The out­line of the face def­i­nite­ly dom­i­nates the out­line of run­ning peo­ple and it is not until we see the face that we real­ize which ele­ments they are com­posed of.

The ocu­lo­graph­ic data col­lect­ed dur­ing the tests con­duct­ed in our lab­o­ra­to­ry that were already men­tioned in this chap­ter (see descrip­tion to Fig. 69) pro­vide one more inter­est­ing hint regard­ing the per­cep­tion of the human face, in par­tic­u­lar the eyes. We showed the repro­duc­tion of the Ocam­po’s Fres­co to our test sub­jects and while they were watch­ing it, we record­ed the move­ment of their eye­balls. It turned out that facial recog­ni­tion imme­di­ate­ly directs the atten­tion of the human test sub­jects towards the eyes which become the most impor­tant ele­ments of the paint­ing (Fig. 90; arrows point­ing to the right).

The strength of the eye detec­tion mech­a­nism in the visu­al scene is also con­firmed by two bluish spots. The first spot can be found in the upper left cor­ner of the paint­ing, where the “Divine eye” is locat­ed. The sec­ond spot is locat­ed in the mid­dle of the paint­ing (Fig. 90; arrows point­ing to the left). The inter­est of the test sub­jects in the shape locat­ed in the mid­dle of the paint­ing is espe­cial­ly inter­est­ing, because there is actu­al­ly no eye in this place, but the shape of the out­lined fig­ure present there, in com­bi­na­tion with the facial image, sug­gests such a possibility.

A sim­i­lar idea was imple­ment­ed a few years ear­li­er by Sal­vador Dalí. On the wall of his the­ater-muse­um, he paint­ed a por­trait of his naked wife – Gala, look­ing out the win­dow. This excel­lent work, in one of its sev­er­al ver­sions, com­bines both con­cepts of using dif­fer­ent ranges of vision res­o­lu­tion, depend­ing on the dis­tance from which it is viewed (Fig. 91).

With his char­ac­ter­is­tic bril­liance, Dalí offers the recip­i­ent at least two paint­ings in one, depend­ing on the dis­tance from which they are viewed. The clos­er of these dis­tances enables to see the fig­ure of a naked woman and also the cru­ci­fied Christ from sky per­spec­tive.  They were paint­ed with great care. The con­tours of these fig­ures can be iso­lat­ed eas­i­ly, although the con­nec­tions between them do not explain each oth­er with­out the ref­er­ence to facts of the artist’s life his­to­ry, and, in par­tic­u­lar, the peri­od in which the paint­ing was cre­at­ed. How­ev­er, if the paint­ing is viewed from a greater dis­tance, e.g. 20 metres, which is pos­si­ble in the place of its expo­sure, then the observer’s eyes can see the char­ac­ter­is­tic out­line of Abra­ham Lin­col­n’s bust (Fig. 92 A). Dete­ri­o­ra­tion of visu­al acu­ity (for exam­ple, achiev­able by squint­ing) enables see­ing a new order of things encod­ed in the paint­ing and apply­ing to it the char­ac­ter­is­tic facial fea­tures of one of the most famous images of the president.

For com­par­i­son, I present a pho­to­graph of the bust of the US Pres­i­dent in Fig. 92 B, which (in Fig. 92 C) has been manip­u­lat­ed in the same way as Dalí’s painting.

Anoth­er image that well illus­trates the dis­cussed phe­nom­e­non of vari­able res­o­lu­tion of vision, depend­ing on the dis­tance from which it is viewed, has been cre­at­ed auto­mat­i­cal­ly by the Mozai­ka [Mosa­ic] V3.5 pro­gramme. The idea of this pro­gram­me’s func­tion­ing con­cerns the use of the exist­ing dig­i­tal pho­to or cli­part col­lec­tion to cre­ate a new image in such a way that for each source pho­to the pro­gramme deter­mines its dom­i­nant col­or and bright­ness, and then deter­mines its place in the new mosa­ic image on that basis (Fig. 93 A and B).

In 2008, for the use of Barack Oba­ma’s first pres­i­den­tial cam­paign, Anne C. Sav­age, a pho­tog­ra­ph­er, pre­pared a poster-mosa­ic com­posed of 6.000 col­or pho­tographs of faces (Fig. 94).  In this way, she want­ed to express her impres­sions of Oba­ma’s ral­lies, in which count­less crowds of lis­ten­ers par­tic­i­pat­ed. The prin­ci­ple of devel­op­ing this poster is the same as using the Mozai­ka [Mosa­ic] pro­gramme. There­fore, if some­one wish­es, they can attempt to find their pho­to­graph among oth­ers, e.g. around the Chief’s eyes (Fig. 95).

And final­ly, a unique mosa­ic designed for the beat­i­fi­ca­tion of Pope John Paul II (Fig. 96). His beat­i­fi­ca­tion por­trait was print­ed on can­vas mea­sur­ing 55 x 26 m (1.400 m²) and hung on May 1, 2011, on the facade of the Tem­ple of Divine Prov­i­dence in War­saw’s Wilanów. What is most remark­able in this pic­ture is that it was cre­at­ed from com­po­si­tion of 105 thou­sand pho­tographs sent by the Poles for this occa­sion. On the web­site portretjp2.com.pl you can see this mosa­ic at close dis­tance and even find the place of your pho­to­graph (obvi­ous­ly, if it was donat­ed for this pur­pose and we are real­ly lucky).

### Contour of objects and chiaroscuro

After a jour­ney to the mosa­ic world of pic­tures viewed from close and far dis­tance, it is time to revis­it the issue of see­ing the con­tours of objects, in par­tic­u­lar, three-dimen­sion­al ones.  Vision is giv­en to us to pri­mar­i­ly recog­nise objects on the basis of con­tours and to behave towards them in an ade­quate man­ner.  Their con­tour, how­ev­er, is not enough, since where there is light, there is also a shad­ow which also has its own con­tour. For the visu­al sys­tem, there­fore, there aris­es the prob­lem of dif­fer­en­ti­at­ing the con­tour of objects from the con­tour of the shad­ow they cast. There­fore, the eye­sight must also deal with this com­pli­ca­tion towards recog­nis­ing the object.

Objects are seen by means of the light falling on them, which is reflect­ed by them and falls onto the eye, plac­ing their image on its back wall. The type of image that appears on the reti­na’s “screen” depends not only on the inten­si­ty of light, but also on its length and direc­tion. The light can be dif­fused or direc­tion­al, as well direct­ed to an object from dif­fer­ent sides. All these fac­tors have a direct impact on the con­trast of the visu­al scene and, con­se­quent­ly, on the clar­i­ty of the con­tours of viewed objects, as well their recognition.

These few obvi­ous sen­tences make us aware of the tasks that the eye (and then the brain) have to deal with in order to cor­rect­ly recog­nise the visu­al scene. One of the obsta­cles is the shad­ow cast by objects. The object shown in Fig. 97 A is a dam­aged axle with toy car wheels.

The object was illu­mi­nat­ed from behind with direc­tion­al light with medi­um inten­si­ty. Since the wheels are black, just like the shad­ow they cast, it is not easy to recog­nise what this object is at first glance. The out­line of con­tours, estab­lished in accor­dance with the pro­ce­dure adopt­ed in all such analy­ses in this book, con­sti­tutes a per­fect­ly illus­trat­ed basis for this dif­fi­cul­ty (Fig. 97B).  The object and its shad­ow merge into one, expres­sive, although com­plete­ly unknown, shape. Only reject­ing the hypoth­e­sis that the entire con­tour out­lines one object, directs atten­tion to oth­er ele­ments of this image (e.g. reflec­tions of light on wheels and a steel axle con­nect­ing them, which do not appear on the shad­ow). Estab­lish­ing and ver­i­fy­ing per­cep­tu­al hypothe­ses is, how­ev­er, a com­plete­ly dif­fer­ent sto­ry that is beyond our con­sid­er­a­tion and con­cerns the areas of high­er men­tal processes.

The above-men­tioned David Marr and Ellen C. Hil­dreth (1980), as well as Marr (1982), attempt­ed to han­dle the prob­lem of for­ma­tion of object rep­re­sen­ta­tion on the basis of its con­tour, which may be “dis­tort­ed” by means of e.g. chiaroscuro. Analysing the con­tours of objects and their shad­ows, they point­ed out that the con­tour of a cast shad­ow is gen­er­al­ly much less reg­u­lar and wider than the objec­t’s con­tours (Fig. 98 A and B).

This dif­fer­ence in the shape of both con­tours is sig­nif­i­cant­ly influ­enced by the tex­ture sur­face on which a shad­ow is cast. Even a much less reg­u­lar edge of an object than the edge of a porce­lain cup, in nine­ty-nine cas­es per one hun­dred, will cast a shad­ow with an even less reg­u­lar edge. It seems that the assump­tion con­cern­ing the dif­fer­ence in the con­tours of objects and their shad­ows refers to such a large num­ber of cas­es which we encounter on every­day expe­ri­ence that it can be con­sid­ered as suf­fi­cient­ly jus­ti­fied. There­fore, every­thing indi­cates that the visu­al sys­tem has a spe­cial mech­a­nism to dif­fer­en­ti­ate the qual­i­ty of the con­tour in order to sep­a­rate the edge of the object from the edge of its shad­ow, and, on this basis, to accu­rate­ly recog­nise the viewed object.

It should be men­tioned that the prob­lem of actu­al and illu­so­ry con­tours is solved almost imme­di­ate­ly if the pho­to­graph with a mug (Fig. 98) is seen not through the per­spec­tive of still pho­tog­ra­phy but through the per­spec­tive of every­day expe­ri­ence of watch­ing objects in three dimen­sions and thus being in motion. We can look at this object from dif­fer­ent per­spec­tives and we will quick­ly notice its new con­tours. The observer’s move­ment as well as the move­ment of the object play an extreme­ly impor­tant role in the accu­rate recog­ni­tion of objects. The two-dimen­sion­al pic­ture pre­vents this kind of analy­sis and that is why the use of spe­cial tricks to high­light the spa­tial­i­ty of objects is required.

The use of shad­ow is one of the most impor­tant ele­ments of the lan­guage of images. It was the insep­a­ra­ble shad­ow cast by eye­brows on Don Vito Cor­leone’s (Mar­lon Bran­do) eyes, which gave his face an expres­sion of mys­tery in the film The God­fa­ther, while in the pho­to­graph of cyclists, the shad­ow enabled the inver­sion of the nat­ur­al order of things. In this case, it is the shad­ow that casts the object (Fig. 99 A and B).

### Illusory contours

The prob­lem of sep­a­rat­ing the edge of the object from the edge of its shad­ow is at least as com­plex as the prob­lem of recog­nis­ing the object whose image has been deprived of some frag­ment of the con­tour, e.g. by exces­sive light­ning (see the right part of the cup in Fig. 98), sim­i­lar bright­ness or col­or in rela­tion to its oth­er parts or the back­ground it is on. Then, the pres­ence and loca­tion of the out­line lines can only be guessed. Despite the fact that the eye is equipped with excel­lent mech­a­nisms for extract­ing the shapes of objects seen, nev­er­the­less, with­out mech­a­nisms at lat­er stages of the visu­al path­way, it would be impos­si­ble to solve this prob­lem. Rüdi­ger von der Hey­dt, Esther Peter­hans and Gün­ter Baum­gart­ner (1984), von der Hey­dt and Peter­hans (1989) and Peter­hans and Von der Hey­dt (1989) stat­ed that the same cell groups in the V2 cor­tex of pri­mates react sim­i­lar­ly to both read­i­ly iden­ti­fi­able and illu­so­ry con­tours. The results of anal­o­gous human stud­ies have revealed that the per­cep­tion of illu­so­ry con­tours involves sig­nif­i­cant­ly more brain areas than in pri­mates (see Men­dola, Dale, Fis­chl, Liu et al., 1999).

An inter­est­ing illus­tra­tion of the illu­so­ry con­tours can be found, for instance, on posters by Hans Rudi Erdt (see Zelan­s­ki and Fish­er, 2011; Fig. 100 A and B). Many of the cloth­ing, body parts, or faces of peo­ple depict­ed on these posters are not sep­a­rat­ed from oth­er parts, nev­er­the­less, we have no doubt about their shapes. The pre­vi­ous visu­al expe­ri­ence, which tells where the out­line lines should be locat­ed, also plays a huge role.

Even more sophis­ti­cat­ed exper­i­ments on the implied con­tours in the paint­ing were con­duct­ed by the above-men­tioned Octavio Ocam­po (Fig. 101). The lack of many out­line lines is not the only char­ac­ter­is­tic of his com­po­si­tions. This sur­re­al vision of objects (flow­ers, but­ter­flies, birds and trees), almost scat­tered all over the paint­ing, does not pre­vent you from see­ing both the illu­so­ry out­lines and the sub­tle, girl­ish fea­tures of the paint­ed faces.

### Sfumato: from Leonardo da Vinci to Wojciech Fangor

Study­ing the con­tours of paint­ed objects led Leonar­do da Vin­ci to devel­op his favourite paint­ing tech­nique, called sfu­ma­to. The Ital­ian word sfu­ma­to means fog­gy, vague. This tech­nique involves blur­ring the lines between the light and dark planes of the paint­ing.  On the one hand, this caus­es the edges of objects to be blurred and some­times even impos­si­ble to iden­ti­fy. As a result, the visu­al sys­tem respon­si­ble for edge detec­tion can­not sep­a­rate sur­faces belong­ing to dif­fer­ent objects from one anoth­er. On the oth­er hand, how­ev­er, the ambigu­ous lines between the object and its back­ground, or among its parts, allow for a less lim­it­ed inter­pre­ta­tion of what it is seen.

In a sense, the lack of unam­bigu­ous con­tours enlivens the paint­ing, makes it more mys­te­ri­ous and metaphor­i­cal, and thus more inter­est­ing. Among oth­ers, Ernst Gom­brich (2005), Robert L. Sol­so (1996) and Mengfei Huang (2009) explain in this way the mys­tery of Mona Lisa’s smile (Fig. 102 A), whose lips and eyes do not have any sharp fea­tures, but only their remain­der that enables their dif­fer­ent inter­pre­ta­tions. “Some­times it seems that she mocks us, anoth­er time it seems that we see sad­ness in her smile. This all sounds quite mys­te­ri­ous and so it is; such impres­sion is often made by great works of art,” states Gom­brich about his impres­sions con­cern­ing con­tacts with Liza (2005, p. 300).

Using the con­tour analy­sis method based on the bright­ness dis­tri­b­u­tion, it is very easy to ver­i­fy the hypoth­e­sis explain­ing the ambi­gu­i­ty of Mona Lisa’s facial expres­sion (Fig. 102 B).

It tran­spires that while the out­lines of the eyes are still quite clear, the edges of the nose and mouth are much less vis­i­ble. They are just a sub­tly drawn sketch, not a fin­ished ver­sion that clear­ly defines the mod­el’s facial expres­sion.
An excel­lent exam­ple of the use of the sfu­ma­to tech­nique by Leonar­do da Vin­ci, who even bet­ter reveals the prop­er­ties of this tech­nique, is the paint­ing Saint John the Bap­tist, paint­ed between 1513 and 1516 (Fig. 103 A). Leonar­do was emo­tion­al­ly attached to this paint­ing no less than to the beloved Mona Lisa. He had nev­er sold it and want­ed to have it on his deathbed.

The result of the analy­sis of this paint­ing with the use of brightness/contrast fil­ter reveals a seri­ous prob­lem con­cern­ing deter­mi­na­tion of the out­line lines (Fig. 103 B). Most of them can­not be seen at all, because the range of tonal tran­si­tions between the light spot of the body and the dark back­ground is so wide that it is impos­si­ble to tell where the back­ground ends and the fig­ure of the prophet begins. John the Bap­tist emerges from the thick dark­ness like an appari­tion and only the inner part of the arm and hand with a raised index fin­ger as well as a small part of the fore­head are vis­i­ble more clear­ly. Even his face is high­ly ambigu­ous. It might be both male and female face, mature or youth­ful, smil­ing or seri­ous. Through the form of char­ac­ter pre­sen­ta­tion, the paint­ing encour­ages the recip­i­ent to project their own mem­o­ries, moods and needs. This is all because the visu­al sys­tem has dif­fi­cul­ty in iden­ti­fi­ca­tion of the con­tour lines.

The sfu­ma­to tech­nique was also often used by oth­er Renais­sance artists, e.g. Raphael Sanzio and Geor­gione. This tech­nique is also used nowa­days. Woj­ciech Fan­gor, the Pol­ish painter, obtained inter­est­ing opti­cal effects by means of this tech­nique. Its mul­ti-col­ored cir­cles with blurred edges pul­sate, increase and decrease; they are active, as if they were alive (Fig. 104 A). All these effects result from a main dif­fi­cul­ty in deter­min­ing the edges of the fig­ures viewed by the observer’s visu­al sys­tem (Fig. 104 B).

### How light creates the contour in Georges Seurat

Georges Seu­rat also played with the con­tour line of the objects he viewed.  He did not actu­al­ly use the con­tour of the object like the line sep­a­rat­ing the object from the back­ground or from oth­er objects in the scene. Through a sub­tle change of hue, sat­u­ra­tion or bright­ness, and dili­gent­ly jux­ta­posed thou­sands of col­ored dots, he empha­sised only the pres­ence of a new object. In this way, the light brown tree sep­a­rates from the Seine’s blue water, and white sails sep­a­rate from the sandy shore (see Fig. 105 A).

Sub­ject­ing the paint­ing to con­tour analy­sis, we obtain a com­plete­ly oppo­site effect than the one we observed after con­duct­ing an anal­o­gous analy­sis, for instance, in Saint John the Bap­tist by Leonar­do da Vin­ci. In Seu­rat, the excess of con­tour lines is over­whelm­ing (Fig. 105 B). The vis­i­ble edges of tree trunks or sails are by no means the result of a line out­lin­ing their shapes, but the result of the den­si­ty of hun­dreds of small lines sur­round­ing indi­vid­ual points of this pointil­list com­po­si­tion. Fur­ther­more, it would be in vain to look for some objects in the con­toured ver­sion, if we did not see them in the orig­i­nal, e.g. a canoe and a girl in a bright dress, with a red flower in her jet black hair, sit­ting in it.

The effect of the dis­ap­pear­ance of the canoeist in the con­tour ver­sion, although she is clear­ly vis­i­ble in the orig­i­nal ver­sion, made also this paint­ing list­ed among the best­sellers shown to thir­ty-eight peo­ple exam­ined in the ocu­lo­graph­ic exper­i­ment men­tioned in this chap­ter, which we con­duct­ed with Anna Szpak. The results of the study have revealed an inter­est­ing reg­u­lar­i­ty. It turned out that the canoeist is the most-viewed object in the paint­ing (Fig. 106). How­ev­er, this may be only the inter­est in the only human fig­ure in the scene. Nev­er­the­less, it can­not be ruled out that in addi­tion to edge detec­tion based on con­trasts of bright­ness, the visu­al sys­tem is also equipped with anoth­er cod­ing mech­a­nism for shape recog­ni­tion. It is a col­or detec­tor, which, in the case of this paint­ing, pro­vides slight­ly dif­fer­ent items of infor­ma­tion than a lumi­nance analyser.