The connection between log.subharmonicity and the integral mean inequality discussed in Armitage and Goldstein [1], Ekonen [2] and Mochizuki [3] will be treated for the exponent p, 1<p<(n+2)⁄n.

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We propose an approach for unsupervised image segmentation based on the Markov random field by using the Bethe approximation. We first derive the Bayesian information criterion under the Bethe approximation and then propose an iterative algorithm to search a model which fits the image data best. For this aim, we derive a criterion for merging two components among several components in terms of a perturbation expansion. Namely, annihilation of components is implemented by merging two components into one component after each convergence of the supervised segmentation with a fixed number of components. We find by numerical experiments that the optimal number of components is selected from the series of local optima with different numbers of components and the best result for segmentation is obtained with good performance.

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Objective: The aim of this study was to reveal the factors that influence the prognosis of esophageal cancer patients, especially from the other causes than esophageal cancer in the follow-up period after esophagectomy.
Method: All of 523 patients with esophageal carcinoma who underwent esophagectomy in a single institute between 1986 and 1999 were followed-up until the end of October 2003. Their prognoses were reviewed and compared by the presence of pre/post-operative radiation, pre/post-operative chemotherapy, surgical procedure, and pathological stages of tumors as well as preoperative general conditions by uni- and multivariate analyses.
Results: Univariate analysis revealed that sex (male against female) (p=0.005), abnormality on ECG (p=0.012), and the presence of preoperative radiation (p=0.016) significantly increased the incidence of non-esophageal cancer death; on the other hand, thoracoscopic approach decreased the incidence of non-esophageal cancer death. Multivariate analyses revealed that the presence of preoperative radiation significantly increased mortality due to non-esophageal cancer causes to a 3.70 hazard ratio (95% CI [95% Confidence Interval]; 1.33–10.61).
Conclusions: This study clearly showed the late effect of preoperative radiation for carcinoma of the esophagus on the postoperative prognosis, especially in terms of later mortality from causes other than esophageal carcinoma.

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Objects represented by anomalous pictures are usually considered unrealizable in a three-dimensional space, but some of them are actually realizable. This paper characterizes a class of realizable anomalous pictures from a mathematical point of view. Distribution of degrees of freedom in the choice of depths of the vertices of a polyhedron represented by a picture is studied, and a decomposition of a polyhedron into components with the minimum degrees of freedom is proposed. According to this decomposition, a class of realizable anomalous pictures is characterized.

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This article addresses qualitative descriptions of image which characterise hierarchy and configuration of image structure. The qualitative descriptions are derived from trajectories of stationary points in the Gaussian scale-space and the gradient field of the scale-space image, which are called respectively “stationary curves” and “figure field”. The stationary curves and figure-field fluxes define the scale-space hierarchy, which is explicitly described as a single tree by introducing a point at infinity. The configuration of image structure at fixed scale is represented by a pseudograph which is obtained from the figure field. The Voronoi tessellation is also employed to extract boundaries of image segments.

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A method for a scale-space analysis of a contour figure based on a crystalline flow is proposed. A crystalline flow is a special family of an evolving polygons, and is a discrete version of a curvature flow. Based on a crystalline flow of a given contour, the proposed method makes a scale-space representation and extracts several sets of dominant facets from the given contour. By changing the shape of the Wulff shape that plays a role of a unit circle for computing the nonlocal curvature of each facet, the method analyzes the contour shape anisotropically.

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The purpose of this paper is to give a new computational model of early visual information processing, and to simulate by using the model the occurrence of visual illusions. The model proposed in this paper is constructed as a maximal overlap biorthogonal wavelet filter bank equipped with a nonlinear processing modeled after “contrast induction” effect (for the definition, see Section 3). This model provides good computer simulations of the occurrence of many lightness illusions such as the Mach band, the Hermann grid, the Chevreul illusion, and other related illusions. Moreover, also the café wall illusion is studied by using the model.

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Given a function y=f(x) in one variable, we consider the problem of computing a k-peaked curve y=φ(x) minimizing the L_p distance between them. In other words, φ(x) has at most k local peaks and minimizes the area bounded by the curves f(x) and φ(x). This gives extension of the authors’ previous work [5] on the unimodal (i.e., single-peaked) approximation for the L₂ distance.

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We consider a constrained gradient system of total variation flow. Our system is often used in color image processing to remove a noise from picture. In this paper, using abstract convergence theory of convex functions, we show the global existence of solutions to our problem with piecewise constant initial data.

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We observe that the resemblance between the integer number system with multiplication & division and the system of convex objects with Minkowski addition & decomposition is really striking. We present an idea of the shape decomposition into prime shapes, which are analogue of the prime numbers and indecomposable ones. Here, we concentrate the discussion on binary images, and present some propositions on the indecomposability problem.

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