幾何視錯覺在人類的視覺系統中是客觀存在的現象，Oppel-Kundt illusion, Muller-Lyer illusion, and Horizontal-Vertical illusion是幾何視錯覺中的三大長度錯視。其中，Oppel-Kundt illusion是最古老的幾何視錯覺，其特點是其非單調性的長度變化依賴於填充符的數目。本研究主要聚焦於Oppel-Kundt illusion，旨在通過量化實驗的方式探究各種填充符變量在不同參照距離的刺激物中非單調的變化規律，進而將這種規律應用於條紋服飾的設計之中。
條紋服飾在視覺上具備調節人體身材比例的作用，但使用何種填充方式仍是一個有待解決的問題。故本研究首先使用5種特殊比例矩形定義了服裝的外觀，分別是1∶√2，1∶1.618，1∶√3，1∶2和1∶√5。然後在這5種比例的基礎上定義出5個參照距離，分別是84pixels，97pixels，104pixels，120pixels和134pixels，並通過心理物理標準變量匹配範例的方式探究各種填充符變量在5個參照距離下的錯視規律。填充符變量由標準個數1至17根填充符，厚度為1pixel、2pixel、4pixel、8pixel和明度為黑、黯淡灰、深灰、淺灰等填充符組成。之後，將實驗量化的結果用於調節三種特殊的體型，分別是下半身較短及較長、身材偏胖和身材偏瘦，並通過問卷調查的方式進行驗證。
結果顯示，實驗量化的結果有助於改善人們對三種特殊體型的感知，具體而言，下半身較短及較長的人若能選擇填充方式為1pixel,範圍10-12根黑色條紋服飾便可以修正人體的比例；身材偏胖的人若能選擇填充方式為7根8pixel黑色條紋服飾便可以在視覺上“顯瘦”；身材偏瘦的人若能選擇填充方式為8pixel,2根淺灰色的條紋服飾便可以在視覺上“顯胖”。

The geometric illusion in the human visual system is an objective phenomenon. Oppel-Kundt illusion, Muller-Lyer illusion, and Horizontal-Vertical illusion are the three main length illusions in a geometric optical illusion. Also, the Oppel-Kundt illusion is the oldest geometric optical illusion, which is characterized by a non-monotonic length variation of the filling amount. This research mainly focuses on Oppel-Kundt illusion, explores the non-monotonic change law of various filler variables in different reference distances, through quantitative experiments, and then applies this law to the design of striped clothing.
Striped clothing has the effect of adjusting the proportion of the human body visually, but which filling method to use is still a problem to be solved. Therefore, this study first used five special ratio rectangles to define the appearance of the clothing, namely 1:√2, 1:1.618, 1:√3, 1:2, and 1:√5. Then define 5 reference distances based on these 5 ratios, namely 84pixels, 97pixels, 104pixels, 120pixels, and 134pixels, and use psychophysical standard variables matching to explore the illusion rules of various at 5 reference distances. The filler variable is composed of the number of 1 to 17 fillers, the thickness is 1pixel, 2pixel, 4pixel, 8pixel, and the lightness is black, deep gray, dark gray, light gray. After that, the quantitative results of the experiment were used to adjust three special body types, which are the lower body was shorter and longer, overweight and skinny, then verified by the questionnaire survey.
The results show that the quantitative results of the experiment can help improve people’s perception of the three special body types. Specifically, people with shorter and longer lower bodies can choose a filling of 1 pixel and a range of 10-12 lines, black striped clothing can be corrected the proportion of the human body; if you are overweight, you can choose to fill in 7 lines, 8pixel black striped clothing, you can be visually "slim"; if you are skinny, you can choose to fill in 8pixel, 2 light gray stripes Clothing can be visually "fat".

Armstrong, R. A., & Cubbidge, R. P. (2014). The Eye and Vision: An Overview. In Handbook of Nutrition, Diet and the Eye , Academic Press, pp. 3-9.
Bertulis, A., Surkys, T., Bulatov, A., & Gutauskas, A. (2009). Three-part Oppel-Kundt illusory figure. Medicina, 45(11), pp.871-877.
Bondarko, V. M., Bondarko, D. V., Solnushkin, S. D., & Chikhman, V. N. (2018). Modeling of optical illusions. Journal of Optical Technology, 85(8), pp .448-454.
Bulatov, A., & Bertulis, A. (1999). Distortions of length perception. Biological cybernetics, 80(3), pp.185-193.
Binetti, N., Aiello, M., Merola, S., Bruschini, M., Lecce, F., Macci, E., & Doricchi, F. (2011). Positive correlation in the bisection of long and short horizontal Oppel–Kundt illusory gradients: Implications for the interpretation of the “cross-over” effect in spatial neglect. cortex, 47(5), pp.608-616.
Cañadas, A. M., & Vanegas, N. P. P. (2013). Representations of posets to generate emerging images. Far east journal of mathematical sciences Special, pp.139-152.
Connolly, M., & Van Essen, D. (1984). The representation of the visual field in parvicellular and magnocellular layers of the lateral geniculate nucleus in the macaque monkey. Journal of Comparative Neurology, 226(4), pp.544-564.
Collier, E. S., & Lawson, R. (2016). Defining filled and empty space: reassessing the filled space illusion for active touch and vision. Experimental brain research, 234(9), 2697-2708.
Goldstein, E. B.(2002). Sensation and perception. (6th ed.) CA:Wadsworth.
Gregory, R. L. (1997). Visual illusions classified. Trends in cognitive sciences, 1(5), pp.190-194.
Kolb, H. (1995). Simple anatomy of the retina. Webvision: The organization of the retina and visual system, pp.1-24.
Knox, H. W. (1894). On the quantitative determination of an optical illusion. The American Journal of Psychology, 6(3), pp.413-421.
Lienhard, D. A. (2017). David H. Hubel and Torsten N. Wiesel’s Research on Optical Development in Kittens. Embryo Project Encyclopedia, ISSN:1940-5030
Livio, M. (2008). The golden ratio: The story of phi, the world's most astonishing number. Broadway Books, pp.85
Malik, A., & Parvez, A. The Gestalt Principles in Contemporary Pakistani Art, pp.03-18.
Mikellidou, K., & Thompson, P. (2014). Crossing the line: Estimations of line length in the Oppel-Kundt illusion. Journal of vision, 14(8), pp.20-20.
Mitra, N. J., Chu, H. K., Lee, T. Y., Wolf, L., Yeshurun, H., & Cohen-Or, D. (2009). Emerging images. ACM Transactions on Graphics (TOG), 28(5), pp.1-8.
Ninio, J. (2001).The science of illusions. London: Cornell University Press.
Ninio, J. (2014). Geometrical illusions are not always where you think they are: a review of some classical and less classical illusions, and ways to describe them. Frontiers in human neuroscience, 8, pp.856.
Pia, L., Neppi-Mòdona, M., Rosselli, F. B., Muscatello, V., Rosato, R., & Ricci, R. (2012). The Oppel-Kundt illusion is effective in modulating horizontal space representation in humans. Perceptual and motor skills, 115(3), pp.729-742.
Rolls, E. T. (2011). David Marr's Vision: floreat computational neuroscience. Brain, 134(3), pp.913-916.
Robinson, J. O. (2013). The psychology of visual illusion. Courier Corporation.
Robinson, J. O. (1972). The psychology of visual illusion (1st ed.) Oxford, England: Hutchinson University Library.
Spear, P. D., Kim, C. B., Ahmad, A., & Tom, B. W. (1996). Relationship between numbers of retinal ganglion cells and lateral geniculate neurons in the rhesus monkey. Visual neuroscience, 13(1), pp.199-203.
Spiegel, H. G. (1937). On the influence of the intermediate field on visually assessed distances. Psychol Forsch, 21, pp.327-383.
Wackermann, J., & Kastner, K. (2010). Determinants of filled/empty optical illusion: Search for the locus of maximal effect. Acta Neurobiol Exp (Wars), 70(4), pp.423-434.
Wackermann, J. (2012). Determinants of filled/empty optical illusion: differential effects of patterning. Acta Neurobiol Exp, 72, pp.89-94.
Wackermann, J. (2012). Determinants of filled/empty optical illusion: Influence of luminance contrast and polarity. Acta Neurobiol Exp (Wars), 72(4), pp.412-20.

中文文獻
Carraher, R. G. , &Thurston, J. B.（1991）,錯視與視覺美術 （Optical illusions and the visual arts蘇茂生譯）。
今井省吾.(1988)，「錯視圖形」(沙興亞譯)，台北:遠流出版社。
王介民.(1994)，工業產品藝術造型設計，北京：清華大學出版社。
林品章.(2000)，視覺傳達設計的理論與實踐，全華科技圖書股份有限公司。
陳上瑜, & 陳一平. (2004)，幾何錯覺的分類：一個心理解剖學的觀點. 交通大學應用藝術研究所視覺傳達組學位論文, 10-11。[Chen.S.Y. & Chen.I.P.(2004). Towards a classification of optical illusions with psychoanatomical criteria.National Chiao Tung University,Taiwan,ROC]
陳姿諭, & 彭立勛. (2013). 服裝視覺設計─ 直線條與橫線條的錯覺應用探討. 設計研究, (9), 頁11-20。
楊清田.(1991)，造型心理學─視覺情報的處理(上)，藝術學報，49期，頁70-71。