Shape from texture is best analyzed in two stages, analogous to stereopsis and structure from motion: (a) Computing the `texture distortion' from the image, and (b) Interpreting the `texture distortion' to infer the orientation and shape of the surface in the scene. We model the texture distortion for a given point and direction on the image plane as an affine transformation and derive the relationship between the parameters of this transformation and the shape parameters. We have developed a technique for estimating affine transforms between nearby image patches which is based on solving a system of linear constraints derived from a differential analysis. One need not explicitly identify texels or make restrictive assumptions about the nature of the texture such as isotropy. We use non-linear minimization of a least squares error criterion to recover the surface orientation (slant and tilt) and shape (principal curvatures and directions) based on the estimated affine transforms in a number of different directions. A simple linear algorithm based on singular value decomposition of the linear parts of the affine transforms provides the initial guess for the minimization procedure. Experimental results on both planar and curved surfaces under perspective projection demonstrate good estimates for both orientation and shape. A sensitivity analysis yields predictions for both computer vision algorithms and human perception of shape from texture.

A unified framework for shape from texture and contour is proposed. It is based on the assumption that the surface markings are not systematically compressed, or formally, that they are weakly isotropic. The weak isotropy principle is based on analysis of the directional statistics of the projected surface markings. It builds on several previous theories, in particular by Witkin [25] and Kanatani [15]. It extends these theories in various ways, most notably to perspective projection. The theory also provides an exact solution to an estimation problem earlier solved approximately by Kanatani. The weak isotropy principle leads to a computationally efficient algorithm, WISP, for estimation of surface orientation. WISP uses simple image observables that are shown to be direct correlates of the surface orientation to compute an initial approximate estimate in a single step. In certain simple cases this first estimate is exact, and in experiments with natural images it is typically within 5...

We address the problem of texture segmentation by using a novel affine invariant model. The introduction of affine invariance as a requirement for texture analysis goes beyond what is known of the human performance and also beyond the psychophysical theories. We propose to compute texture features using affine invariant intrinsic neighborhoods and affine invariant intrinsic orientation matrices. We discuss several possibilities for the definition of the channels and give comparative experimental results where an affine invariant Mumford-Shah type energy functional is used to compute the multichannel affine invariant segmentation. We prove that the method is able to retrieve faithfully the texture regions and to recover the shape from texture information in images where several textures are present. The numerical algorithm is multiscale.

A neural model is presented of how cortical areas V1, V2, and V4 interact to convert a textured 2D image into a representation of curved 3D shape. Two basic problems are solved to achieve this: (1) Patterns of spatially discrete 2D texture elements are transformed into a spatially smooth surface representation of 3D shape. (2) Changes in the statistical properties of texture elements across space induce the perceived 3D shape of this surface representation. This is achieved in the model through multiple-scale filtering of a 2D image, followed by a cooperative-competitive grouping network that coherently binds texture elements into boundary webs at the appropriate depths using a scale-to-depth map and a subsequent depth competition stage. These boundary webs then gate filling-in of surface lightness signals in order to form a smooth 3D surface percept. The model quantitatively simulates challenging psychophysical data about perception of prolate ellipsoids [Todd, J., & Akerstrom, R. (1987). Perception of three-dimensional form from patterns of optical texture. Journal of Experimental Psychology: Human Perception and Performance, 13(2), 242–255]. In particular, the model represents a high degree of 3D curvature for a certain class of images, all of whose texture elements have the same degree of optical compression, in accordance with percepts of human observers. Simulations of 3D percepts of an elliptical cylinder, a slanted plane, and a photo of a golf ball are also presented.

A novel approach is proposed to obtain a record of the patient's occlusion using computer vision. Data acquisition is obtained using intra-oral video cameras. The technique utilizes shape from shading to extract 3D information from 2D views of the jaw, and a novel technique for 3D data registration using genetic algorithms. The resulting 3D model can be used for diagnosis, treatment planning, and implant purposes. The overall purpose of this research is to develop a model-based vision system for orthodontics to replace traditional approaches. This system will be flexible, accurate, and will reduce the cost of orthodontic treatments. Keywords---Image Sequence Analysis, Shape Representation, Registration. I. Introduction O RTHODONTIC treatment involves the application of force systems to teeth over time to correct malocclusions. In order to evaluate tooth movement progress, the orthodontist monitors this movement by means of visual inspection, intra-oral measurements, fabrication of p...

In [12], Witkin proposed a maximum likelihood (ML) estimator of surface orientation based on the observed directional bias of projected texture elements. However, a drawback of this procedure is that the estimate is only defined indirectly in terms of a set of non-linear equations. In this paper we propose an alternative method, which allows an estimate of the surface orientation to be computed directly in a single step from certain simple statistics of the image data. We also show that this direct estimate allows Witkin's ML estimate to be computed to within 0:05 ffi in only two or three iterative steps. The performance of the new estimator is demonstrated experimentally and compared to that of the ML estimator, using both synthetic data and real gray-level images. Index Terms: Shape from texture, surface orientation, foreshortening, isotropy, distributions on the circle, maximum likelihood, method of moments i 1 Introduction Although direct information about depth and three-dim...

In this paper, we propose a new method to estimate the orientations of a planar surface under perspective projection. Texture variations are characterized by the ridges of continuous wavelet transform. The ridges of a continuous wavelet transform mark the places in the spatial frequency where the energy of an image is mostly concentrated. We demonstrate that the ridges contain crucial information in determining the planar surface orientations. An algorithm to determine the ridge points of a textured image is presented. The ridge points are organized into disjoint ridge surfaces. We show that textural information giving the perception of surface orientations can be characterized from a ridge surface of the textured image. The scale in the ridge surface is a parabolic function of the tilt and slant angles. This provides a closed-form solution to determine the surface orientations directly with information only from the restriction of the wavelet transform to the ridge surface. We have us...

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This paper explores the reconstruction of object surfaces from viewed changes in surface texture patterns. Our approach di ers from those in the past in that instead of simply producing local estimates of the surface orientation, our algorithm recovers complete surfaces. Past approaches [1, 16, 4, 9, 8, 11] only found the surface orientation locally and, therefore, did not take advantage of the surface integrability constraint. Unlike [16, 7, 3], our algorithm does not assume that the surface texture pattern is isotropic � and unlike [14, 13], our algorithm does not assume that the viewed surface is at some point fronto-parallel. Furthermore, our algorithm has mechanisms for handling texture boundaries and, consequently, does not produce erratic results in the regions abutting these boundaries. Results on real images are presented demonstrating the potential of our approach. 1

In this paper we propose two techniques to qualitatively estimate disrance in monocular vision. Two kinds of approaches are described, the former based on texture analysis and the latter on histogram inspection. Although both the methods allow only to determine whether a point within an image is nearer or farther than another with respect to the observer, they can be usefully exploited in all those cases where precision is not critical or single images are the only source of information available. Moreover, combined with previously studied techniques, they could be used to provide more accurate results. Step by step algorithms will be presented, along with examples illustrating their application to real images.