Vol.-ICS-6 No.3 /3/8 Input.8.6 y.4 Fig....5 receptive field x 3 w x y Machband w(x =

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1 DOG(Difference of two Gaussians 8 A feedback model for the brightness illusion Shoji Nodasaka and Asaki Saito We consider mechanism of the Hermann grid. The mechanism is usually explained by effects of on-center receptive fields lateral inhibition. We suppose that optical illusion is caused by a process of edge detection in early vision, and perform numerical experiments. DOG functions are used to detect edges in eight detection. By summing up these functions, we obtain almost same figure as we recognize. The Hermann grids circle also seems to be glimming. To analysis the glimming circles, we construct a new model that adopts feedback connections between the lateral geniculate nucleus and parts of early vision, and conduct some numerical experiments.. Future University Hakodate. Ernst Mach Vol.-ICS-6 No.3 /3/8 c Information Processing Society of Japan

2 Vol.-ICS-6 No.3 /3/8 Input.8.6 y.4 Fig....5 receptive field x 3 w x y Machband w(x = πσe e x σe x a πσi e σ i (σ i =.6σ e x x s(x w(x x x z f (x z f (x = w(x xs(x dx ( x= Fig. 4 output s (x 3 y = y = DOG w(x ( 4 x c Information Processing Society of Japan

3 Vol.-ICS-6 No.3 /3/8 3. DOG ( wl(x, y = e πσ x,e x σ x,e e πσ x,i x σ x,i e πσ y y σ y ( 5 Fig. 5 Hermann grid 8 wl θ(k = wl(x cos θ y sin θ, x sin θ + y cos θ (3 θ = kπ, (k =,..., 7 ( Fig. 6 cause of Hermann grid. Ludimar Hermann?? c Information Processing Society of Japan

4 Vol.-ICS-6 No.3 /3/8 7 z Fig. 7 output z z Fig. 8 contour line of output z DOG (5 w k (x, y = x +y x +y πσe e σe a πσi e σ i (5 s (x, y (6 z (x, y = w k (x x, y y s (x, ydxdy (6 x= y= wl θ s (x, y (7 ( z θ(k(x, y = wl θ(k (x x, y y s(x, ydxdy (7 x= y= z k 9 9 Fig. 9 Hermann grid s output by proposal technique 6. Fig. z 8 ( contour line of Hermann grid s output by proposal technique S n+ (x, y = αz + βs n (x, y (8 < α <, < β < (9 (8 β S n+ αz ( = β S n αz ( β β ( = β S n αz ( β (... = β n S αz (n ( β S n+ = β n ( S S n = β n ( S αz β αz β + αz β + αz β (n (3 (n (4 4 c Information Processing Society of Japan

5 Vol.-ICS-6 No.3 /3/8 情報処理学会研究報告 図 出力の初期状態 Fig. initial state of output z の出力 図 から z7π/8 Fig. output from z to z7π/8 が得られる ここで n とすると β < より αi Sn = β となる 図 3 n = の出力の状態 Fig. 3 state at n = (5 σx,e = 8., σx,i =.6 sigmax,e, σy = 5. として計算を行った結果を示す 図 が出力の初期状態で S(, =.579 である 図 3 が n = 5 のときの状態 ( で S(, 5 =.495 である これは αi /( β = =.9.579/( (.9 =.4947 とほぼ等しい値になっている 7. 考察と結論 7. ヘルマン格子錯視の発生について ヘルマン格子錯視が発生する原因について従来は受容野のオン領域とオフ領域による刺 激の相互作用によって 白色と黒色のコントラストが強まった結果交差点の個所に灰色の円 図 4 S(, の値:横軸 x 縦軸 S(, Fig. 4 value of S(, :y-axis-x x-axis:s(, が現れるという説明がされていた それを数値計算で検証した結果 交差点の個所に円が現 れたが 我々が知覚するものと比べてサイズが小さく 周囲の白い部分とのコントラストの 差がなだらかであるため原因を十分に説明できているとはいえない 一方本研究の提案手法 5 c Information Processing Society of Japan

6 Vol.-ICS-6 No.3 /3/8 7.,,, p ,,, pp Ben S. Webb., Chris J. Tinsley, Nick E. Barraclough, Alexander Easton, Amanda Parker and Andrew M. Derrington.: Feedback from V and inhibition from beyond the classical receptive field modulates the responses of neurons in the primate lateral geniculate nucleus Visual Neuroscience, Vol.9, pp ( 4 Matteo Caradini, David J. Heeger.: Summation and division by neurons in primate visual cortex, Science, 7 May, Vol.64, pp ( Matteo Carandini.: Linearity and Normalization in Simple Cells of the Macaque Primary Visual Cortex, The Journal of Neuroscience, November, 7(, pp ( c Information Processing Society of Japan

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