An Attempt at Handling Beauty by Computer (計算機による美の扱いの試み)

Notes

第23回プログラミング・シンポジウム報告集 (Proceedings of the 23rd Programming Symposium), January 1982, pp. 164–173, 10 pp. plus the IPSJ rights notice. Both authors at RIKEN. The body of the paper is a handwritten Japanese manuscript (typeset only in the equations, figure captions, the picture list and Table 1); the scan is from the IPSJ Digital Library (情報学広場, WPRO1982019), which digitised the old symposium proceedings in 2020 after a rights search. The text layer is unusable OCR. This is the automatic-composition experiment Sasaki refers back to in RIKEN News (1987) and in Artistic Aspects of Computer Art (1993), both also here. Computer art, the Sasakis begin, is well known, but "pictures generated by computers" are really generated by people using the computer as a tool, since the computer has no ability whatever to judge beauty; treating beauty by computer is a fascinating problem for artificial intelligence that almost nobody has touched, and existing work only analyses pictures syntactically. They restrict themselves to composition, the property decided first and the most important for beauty, and simplify a picture to a finite number of objects with given shapes and weights; a good composition is then a beautiful arrangement of those objects, and they define a "Beauty function" of the object positions whose maximum is the most beautiful arrangement. Strategy: beautiful compositions share common features, so extract them from masterpieces and use them as necessary conditions (the musical analogy: the Fourier transform of any good melody obeys |Re g(ν)|, |Im g(ν)| ≤ g₀/|ν|, and building that in would already implant a little intelligence). Fourteen monochrome reproductions were read with a picture digitiser, normalised and contrast-thresholded, and their moments E(xⁱyʲ) computed: Botticelli's Birth of Venus, the Mona Lisa, Raphael's Madonna of the Goldfinch, Delacroix's Liberty Leading the People, Ingres's Grande Odalisque, Millet's Gleaners, Manet's Déjeuner sur l'herbe, Van Gogh's Starry Night, Seurat's Grande Jatte, Kōrin's white plum, Picasso's Three Musicians, Hokusai's Great Wave, and, for comparison, two of Mutsuko Sasaki's own, My Portrait and Nemophila. The moments barely differ from picture to picture (Table 1), which they read as the common features of good composition: E(x) ≈ 0 (left–right balance about the centre), E(y) ≈ −0.1 (the weight sits a little below centre, giving stability) and E(x²) ≈ E(y²) ≈ 0.34, almost the uniform value of 1/3 (the elements, background included, should spread over the whole canvas). Composition is then generated by modelling the distribution of each of twelve low-order moments across the masterpieces as a normal distribution and taking the Beauty function B as their product, so that maximising B means minimising a weighted sum of squares G = Σ cᵢ²(E(zᵢ) − μᵢ)², a standard minimisation; practical fixes keep elements inside the canvas (a penalty that grows outside |x|, |y| > 0.95) and place many elements five at a time in order of weight. Two experiments: with corner triangles fixed as background and the computer placing the remaining squares (Fig. 1), and with every square placed by the computer under a function tuned to pull elements in from the edges (Fig. 2); both are far better than random placement but dull, since, in Plato's terms, they have unity without variation. Turning two squares into heavier octagons fixed at golden-section points (Figs. 3–4) introduces variation and a focus, and the gain is obvious even to a layman. The discussion draws the lesson: the quality of a composition depends not only on placement but on the motif and the maker's intention, which a computer cannot decide, though once a motif such as serenity is chosen it could choose bluish colours; and the Beauty function, built by averaging moments over many pictures, erased the correlations between element positions in which variation lives, so it enforced unity alone. They were redefining it with correlations, which they expected would also open the way to colour: contrast, resonance and the expression of emotion by overall colour.