Explanation Of Ponzo Illusion From The Viewpoint Of Solving Inverse Problems

Visuall illusion can reflect the basic principles of the visual processing mechanisms,which is a useful tool to understand the processing mechanism of the human visual system.The Ponzo illusion is one of the typical geometric illusions,which refers to that there are two parallel horizontal lines of equal length in the middle of the two converging lines and the observers perceive that the upper horizontal line is longer than the lower one subjectively.Since the Ponzo illusion was proposed by Italy psychologist Mario Ponzo,it has attracted attentions of researchers all over the world.Various theories have been proposed to explain the illusion,such as The Inappropriate Constancy Scaling,the Two Factors Theory,Assimilation Theory,The Tilt-constancy Theory,etc.These qualitative analysis can explain some of the aspects of the illusion effectively.However,these theories failed to explain the Ponzo illusion in a quantitative and computational manner.In this paper,after a thorough investigation to exising theories and projective geometry,a quantitative mathematic model is proposed to analyze and explain the Ponzo illusion.The model is based on the geometric relationships of a human being observing a scene.Compared with existing qualitative models,the proposed one can provide a scheme for quantitative analysis.To validate the proposed mathematical model,on the basis of surveying the concepts and solving methods of ill-posed inverse problems,we analyze the factors that could cause Ponzo illusion from the viewpoint of solving an inverse problem.Based on the analysis,some key factors are chosen to design visual subjective experiments.At the mean time,the proposed model also provides a way to generative accurate graphics for testing and verifying the Ponzo illusion.An internet based platform is developed to collect mass data of the subjective visual experiment.These data are used to verify the proposed mathematic model.Neural network regression is performed on the collected data.The regression results are then compared with the theoretical values computed from the geometric model.The distribution difference are taken as performance measurement,in order to verify the correctness of the proposed model.This paper proposes a geometric model to the Ponzo illusion qauntitatively.The model could be useful for in-depth invesigation on visual illusion.It also may accelerate the research of the field and can be used in potential applications.