Ryszard Kozera

Computer Vision and Graphics

Since most of even recently proposed image quality assessment metrics are typically applied for a single color channel in both compared images, a reliable color image quality assessment is still a challenging task for researchers. One of the major drawbacks limiting the progress in this field is the lack of image datasets containing the subjective scores for images contaminated by color specific distortions. After the publication of the TID2013 dataset, containing i.a. images with 6 types of color distortions, this situation has changed, however there is still a need of validation of some recently proposed grayscale metrics in view of their applicability for color specific distortions. In this paper some results obtained using different approaches to color to grayscale conversion for some well-known metrics as well as for recently proposed combined ones, are presented and discussed, leading to meaningful increase of the prediction accuracy of image quality for color distortions.

Existence and uniqueness in photometric stereo

We analyze the problem of recovering the shape of a smooth Lambertian surface from two images obtained by consecutive illumination of the surface by distant point light sources from two different directions. We discuss the issues of existence and uniqueness for the corresponding system of two first-order nonlinear partial differential equations. We show that generically this system has, up to a constant, a unique solution. We also examine exceptional cases for which there is no such uniqueness.

Impossible and ambiguous shading patterns

A smooth object depicted in a monochrome image will often exhibit brightness variation, or shading. A problem much studied in computer vision has been that of how object shape may be recovered from image shading. When the imaging conditions are such that an overhead point-source illuminates a smooth Lambertian surface, the problem may be formulated as that of finding a solution to an eikonal equation. This article will focus on the existence and uniqueness of such solutions, reporting recent results obtained. With regard to existence, shading patterns are exhibited for which there is no corresponding object shape. Specifically, a necessary and sufficient condition is presented for a circularly symmetric eikonal equation to admit exclusively unbounded solutions; additionally, a sufficient condition is given for an eikonal equation to have no solution whatsoever. In connection with uniqueness, we consider eikonal equations, defined over a disc, such that the Euclidean norm of the gradient of any solution is circularly symmetric, vanishes exactly at the disc center, and diverges to infinity as the circumference of the disc is approached. Contrary to earlier influential work, a class of such eikonal equations is shown to possess simultaneously circularly symmetric and noncircularly symmetric bounded smooth solutions.

Uniqueness in Shape from Shading Revisited

We analyse the problem of representing solutions of first-orderpartial differential equations in terms of complete integrals and envelopes. In this context, we revisit the uniqueness results alreadyexisting in the shape-from-shading literature that concern eikonalequations corresponding to the images of a Lambertian hemi-sphere and aLambertian plane. We show that the approach adopted by Brooks in [2, 3] isincomplete and subsequently re-establish its uniqueness claims.

Nonlinearities and Noise Reduction in 3-Source Photometric Stereo

Abstract1-D Leap-Frog (L. Noakes, J. Math. Australian Soc. A, Vol. 64, pp. 37–50, 1999) is an iterative scheme for solving a class of nonquadratic optimization problems. In this paper a 2-D version of Leap-Frog is applied to a non optimization problem in computer vision, namely the recovery (so far as possible) of an unknown surface from 3 noisy camera images. This contrasts with previous work on photometric stereo, in which noise is added to the gradient of the height function rather than camera images. Given a suitable initial guess, 2-D Leap-Frog is proved to converge to the maximum-likelihood estimate for the vision problem. Performance is illustrated by examples.

On shape recovery from two shading patterns

In this paper, we analyze the problem of recovering the shape of a smooth Lambertian surface from two images obtained by consecutive illumination of the surface by distant point light-sources from two different directions. We discuss the issues of existence and uniqueness of solutions to the corresponding system of two first-order non-linear partial differential equations. We show that generically this system has, up to a constant, a unique solution. We also examine exceptional cases for which there is no such uniqueness.

Geometric Properties for Incomplete Data

Contributors. Preface. I Continuous Geometry: Representation of Free-form Objects. Spheres and Conics. Algorithms for Spatial Pythagoreanhodograph Curves. Cumulative Chords, Piecewise-Quadratics and Piecewise-Cubics. Spherical Splines. Graph-Spectral Methods for Surface Height Recovery from Gauss Maps.- II Discrete Geometry: Segmentation of Boundaries into Convex and Concave Parts. Convex and Concave Parts of Digital Curves. Polygonalisation and Polyhedralisation by Optimisation. Binary Tomography by Iterating Linear Programs. Cascade of dual LDA Operators for Face Recognition. Precision of Geometric Moments in Picture Analysis. Shape-from-Shading by Iterative Fast Marching for Vertical and Oblique Light Sources. Shape from Shadows.- III Approximation and Regularization: A Confidence Measure for Variational Optic Flow Methods. Video Image Sequence Analysis: Estimating Missing Data and Segmenting Multiple Motions. Robust Local Approximation of Scattered Data. On Robust Estimation and Smoothing with Spatial and Tonal Kernels. Subspace Estimation with Uncertain and Correlated Data. On the use of Dual Norms in Bounded Variation Type Regularization.- Index.

Circularly symmetric eikonal equations and non-uniqueness in computer vision

which arises naturally in wavefront analysis and in the development of special methods for integrating Hamilton’s equations (the Jacobi-Hamilton method), has long attracted the attention of physicists and mathematicians. More recently, there has been a resurgence of interest in the eikonal equation as a result of its applicability in an area of computer vision. One of the issues considered in the latter context has been that of determining whether or not a particular eikonal equation exhibits many solutions defined over a given domain. In this paper, we shall offer insight into this issue by presenting a non-uniqueness result of significance for the foundations of computer vision. A monochrome photograph of a smooth object will typically exhibit brightness variation, or shading. Of interest to researchers in computer vision is the problem of how object shape may be extracted from image shading. This shape-from-shading problem has been shown by Horn ([6]; 192 0022-241X/92

Length estimation for curves with different samplings

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2D leapfrog algorithm for optimal surface reconstruction

This paper* looks at the problem of approximating the length of the unknown parametric curve ?: [0, 1] ? IRn from points qi = ?(ti), where the parameters ti are not given. When the ti are uniformly distributed Lagrange interpolation by piecewise polynomials provides efficient length estimates, but in other cases this method can behave very badly [15]. In the present paper we apply this simple algorithm when the ti are sampled in what we call an ?-uniform fashion, where 0 ? ? ? 1. Convergence of length estimates using Lagrange interpolants is not as rapid as for uniform sampling, but better than for some of the examples of [15]. As a side-issue we also consider the task of approximating ? up to parameterization, and numerical experiments are carried out to investigate sharpness of our theoretical results. The results may be of interest in computer vision, computer graphics, approximation and complexity theory, digital and computational geometry, and digital image analysis.