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.More generally, different parts of the face are encodable by reusing descriptions of other parts, thus allowing for compact algorithms describing the whole: the defining features of the face have low algorithmic complexity12-14, given a description model15,16 based on simple geometric feature detectors.Hence the image may be viewed as an example of low-complexity art11.Mathematicians find beauty in a simple proof with a short description in the formal language they are using.Facial attractiveness may reflect a similar correlation between beauty and subjective simplicity.Our results indicate that neither average faces obtained by blending nor certain attractive, digital caricatures thereof7 are as attractive as a particular face whose essential features are compactly encodable using a simple but novel geometric construction method.Future analysis of attractive low-complexity face types other than the one in Figure 1 may profit from examining the significance of other, especially 3-dimensional, fractal geometric patterns.Generation of aesthetic faces by artists may also provide clues as to how human face recognition works.1.Galton, F.J.Nature 18, 97-100 (1878).2.Galton, F.J.Anthrop.Inst.Gt Br.Ir.8, 132-142 (1878).3.Jastrow, J.Science 6, 165-168 (1885).4.Stoddard, J.T.Science 8, 89-91 (1886).5.Langlois, J.H.& Roggman, L.A.Psychol.Sci.1, 115-121 (1990).6.Alley, T.R.& Cunningham, M.R.Psychol.Sci.2, 123-125 (1991).7.Perrett, D.I., May, K.A.& Yoshikawa, S.Nature 368, 239-242 (1994).8.Mandelbrot, B.The Fractal Geometry of Nature (San Francisco: Freeman, 1982).9.Cunningham, M.R.J.Pers.Soc.Psychol.Sci.50, 925-935 (1986).10.Cunningham, M.R., Barbee, A.P.& Pike, C.J.Pers.Soc.Psychol.Sci.59, 61-72 (1990).11.Schmidhuber, J.Leonardo 30, 97-103 (1997).or12.Kolmogorov, A.N.Probl.Inform.Transm.1, 1-11 (1965).13.Solomonoff, R.J.Inform.and Control 7, 1-22 (1964).14.Chaitin, G.J.J.ACM 16, 145-159 (1969).15.Wallace, C.S.& Boulton, D.M.Computer J.11, 185-194 (1968).16.Rissanen, J.Automatica 14, 465-471 (1978).17.Shannon, C.E.Bell System Technical J.27, 379-423 (1948).18.Hochreiter, S.& Schmidhuber, J.Accepted by Neural Computation (1998).19.Hochreiter, S.& Schmidhuber, J.Neural Computation 9, 1-43 (1997). Figure 1: Low-complexity female face designed according to rules illustrated in Figures 2-5 below.See text for details.Click for an enlarged version (188 K). Figure 2: Explanation of the short algorithm describing the essential features of Figure 1's low-complexity face based on 3 superimposed grids.The scheme enforces simple facial proportions based on powers of 2.The sides of the quadratic frame are partitioned into 24 equal intervals.Large squares (thick lines) are responsible for basic contours, smaller ones (by factors of 2-n n = 1,2,.) for details.Shifted copies of circles (omitted for clarity) inscribable in thick-lined squares of Figure 2, scaled by powers of 2, account for transitions between non-parallel face contours such as facial sides and chin. Figure 3: Selected feature-defining lines of the grid rotated by arcsin 2-3. Figure 4: Selected lines of the grid rotated by -arcsin 2-3. Figure 5: Selected lines of the grid rotated by 45o.Copyright © by Juergen Schmidhuber, 1998-05-29.Images above may not be used for commercial purposes of any kind (e.g., as templates for computer animation or plastic surgery) without explicit written consent by the author.Comments, criticism, suggestions welcome: juergen@idsia.ch.Do not hesitate to contact me if you are a publisher interested in publishing related work, or if you have 3D face modeling software that you'd like to share!Back to7 [ Pobierz całość w formacie PDF ]
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.More generally, different parts of the face are encodable by reusing descriptions of other parts, thus allowing for compact algorithms describing the whole: the defining features of the face have low algorithmic complexity12-14, given a description model15,16 based on simple geometric feature detectors.Hence the image may be viewed as an example of low-complexity art11.Mathematicians find beauty in a simple proof with a short description in the formal language they are using.Facial attractiveness may reflect a similar correlation between beauty and subjective simplicity.Our results indicate that neither average faces obtained by blending nor certain attractive, digital caricatures thereof7 are as attractive as a particular face whose essential features are compactly encodable using a simple but novel geometric construction method.Future analysis of attractive low-complexity face types other than the one in Figure 1 may profit from examining the significance of other, especially 3-dimensional, fractal geometric patterns.Generation of aesthetic faces by artists may also provide clues as to how human face recognition works.1.Galton, F.J.Nature 18, 97-100 (1878).2.Galton, F.J.Anthrop.Inst.Gt Br.Ir.8, 132-142 (1878).3.Jastrow, J.Science 6, 165-168 (1885).4.Stoddard, J.T.Science 8, 89-91 (1886).5.Langlois, J.H.& Roggman, L.A.Psychol.Sci.1, 115-121 (1990).6.Alley, T.R.& Cunningham, M.R.Psychol.Sci.2, 123-125 (1991).7.Perrett, D.I., May, K.A.& Yoshikawa, S.Nature 368, 239-242 (1994).8.Mandelbrot, B.The Fractal Geometry of Nature (San Francisco: Freeman, 1982).9.Cunningham, M.R.J.Pers.Soc.Psychol.Sci.50, 925-935 (1986).10.Cunningham, M.R., Barbee, A.P.& Pike, C.J.Pers.Soc.Psychol.Sci.59, 61-72 (1990).11.Schmidhuber, J.Leonardo 30, 97-103 (1997).or12.Kolmogorov, A.N.Probl.Inform.Transm.1, 1-11 (1965).13.Solomonoff, R.J.Inform.and Control 7, 1-22 (1964).14.Chaitin, G.J.J.ACM 16, 145-159 (1969).15.Wallace, C.S.& Boulton, D.M.Computer J.11, 185-194 (1968).16.Rissanen, J.Automatica 14, 465-471 (1978).17.Shannon, C.E.Bell System Technical J.27, 379-423 (1948).18.Hochreiter, S.& Schmidhuber, J.Accepted by Neural Computation (1998).19.Hochreiter, S.& Schmidhuber, J.Neural Computation 9, 1-43 (1997). Figure 1: Low-complexity female face designed according to rules illustrated in Figures 2-5 below.See text for details.Click for an enlarged version (188 K). Figure 2: Explanation of the short algorithm describing the essential features of Figure 1's low-complexity face based on 3 superimposed grids.The scheme enforces simple facial proportions based on powers of 2.The sides of the quadratic frame are partitioned into 24 equal intervals.Large squares (thick lines) are responsible for basic contours, smaller ones (by factors of 2-n n = 1,2,.) for details.Shifted copies of circles (omitted for clarity) inscribable in thick-lined squares of Figure 2, scaled by powers of 2, account for transitions between non-parallel face contours such as facial sides and chin. Figure 3: Selected feature-defining lines of the grid rotated by arcsin 2-3. Figure 4: Selected lines of the grid rotated by -arcsin 2-3. Figure 5: Selected lines of the grid rotated by 45o.Copyright © by Juergen Schmidhuber, 1998-05-29.Images above may not be used for commercial purposes of any kind (e.g., as templates for computer animation or plastic surgery) without explicit written consent by the author.Comments, criticism, suggestions welcome: juergen@idsia.ch.Do not hesitate to contact me if you are a publisher interested in publishing related work, or if you have 3D face modeling software that you'd like to share!Back to7 [ Pobierz całość w formacie PDF ]