Just Noticeable Difference
Weber’s Law and Weberized TV Restoration
Jianhong Shen School of Mathematics University of Minnesota Minneapolis, MN 55455, USA
Abstract Most conventional image processors consider little the influence of human vision psychology. Weber’s Law in psychology and psychophysics claims that human’s perception and response to the intensity fluctuation of visual signals are weighted by the background stimulus , instead of being plainly uniform. This paper attempts to integrate this well known perceptual law into the classical total variation (TV) image restoration model of Rudin, Osher, and Fatemi [Physica D, 60:259-268, 1992]. We study the issues of existence and uniqueness for the proposed Weberized nonlinear TV restoration model, making use of the direct method in the space of functions with bounded variations. We also propose an iterative algorithm based on the linearization technique for the associated nonlinear EulerLagrange equation. PACS (2001): 87.19.Dd (information processing in vision and hearing); 87.57.Nk (image analysis). Keywords: Weber’s Law; Vision; Psychophysics; Image restoration.
1 Introduction: Weber’s Law
As information carriers, all images are eventually perceived and interpreted by the human visual system. As a result, human vision psychology and psychophysics play an important role in the successful communication of image information. From the imaging science point of view, this fact implies that any ideal image processor should take into account the consequences of vision psychology and psychophysics. The current paper makes an attempt in this direction. We develop an image restoration model that intends to incorporate one of the most well known and influential psychological results - Weber’s Law for sound and light perception. We study its major mathematical properties (e.g., existence and uniqueness), as well as the computational strategy for the associated nonlinear PDE.
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Email: jhshen@math.umn.edu. Tel: (612) 625-3570. Fax: (612)
Jianhong Shen School of Mathematics University of Minnesota Minneapolis, MN 55455, USA
Abstract Most conventional image processors consider little the influence of human vision psychology. Weber’s Law in psychology and psychophysics claims that human’s perception and response to the intensity fluctuation of visual signals are weighted by the background stimulus , instead of being plainly uniform. This paper attempts to integrate this well known perceptual law into the classical total variation (TV) image restoration model of Rudin, Osher, and Fatemi [Physica D, 60:259-268, 1992]. We study the issues of existence and uniqueness for the proposed Weberized nonlinear TV restoration model, making use of the direct method in the space of functions with bounded variations. We also propose an iterative algorithm based on the linearization technique for the associated nonlinear EulerLagrange equation. PACS (2001): 87.19.Dd (information processing in vision and hearing); 87.57.Nk (image analysis). Keywords: Weber’s Law; Vision; Psychophysics; Image restoration.
1 Introduction: Weber’s Law
As information carriers, all images are eventually perceived and interpreted by the human visual system. As a result, human vision psychology and psychophysics play an important role in the successful communication of image information. From the imaging science point of view, this fact implies that any ideal image processor should take into account the consequences of vision psychology and psychophysics. The current paper makes an attempt in this direction. We develop an image restoration model that intends to incorporate one of the most well known and influential psychological results - Weber’s Law for sound and light perception. We study its major mathematical properties (e.g., existence and uniqueness), as well as the computational strategy for the associated nonlinear PDE.
¤
Email: jhshen@math.umn.edu. Tel: (612) 625-3570. Fax: (612)
References: [Web34] E. H. Weber. De pulsu, resorptione, audita et tactu. Annotationes anatomicae et physiologicae, Leipzig: Koehler, 1834.