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52
Computing Local Surface Orientation and Shape from Texture for Curved Surfaces
, 1997
"... 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 di ..."
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Cited by 106 (4 self)
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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 nonlinear 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.
Shapeadapted smoothing in estimation of 3D shape cues from affine distortions of local 2D brightness structure
, 2001
"... This article describes a method for reducing the shape distortions due to scalespace smoothing that arise in the computation of 3D shape cues using operators (derivatives) de ned from scalespace representation. More precisely, we are concerned with a general class of methods for deriving 3D shap ..."
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Cited by 71 (3 self)
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This article describes a method for reducing the shape distortions due to scalespace smoothing that arise in the computation of 3D shape cues using operators (derivatives) de ned from scalespace representation. More precisely, we are concerned with a general class of methods for deriving 3D shape cues from 2D image data based on the estimation of locally linearized deformations of brightness patterns. This class
Canonical Frames for Planar Object Recognition
, 1992
"... We present a canonical frame construction for determining projectively invariant indexing functions for nonalgebraic smooth plane curves. These invariants are semilocal rather than global, which promotes tolerance to occlusion. Two applications are demonstrated. Firstly, we report preliminary work ..."
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Cited by 69 (11 self)
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We present a canonical frame construction for determining projectively invariant indexing functions for nonalgebraic smooth plane curves. These invariants are semilocal rather than global, which promotes tolerance to occlusion. Two applications are demonstrated. Firstly, we report preliminary work on building a model based recognition system for planar objects. We demonstrate that the invariant measures, derived from the canonical frame, provide sufficient discrimination between objects to be useful for recognition. Recognition is of partially occluded objects in cluttered scenes. Secondly, jigsaw puzzles are assembled and rendered from a single strongly perspective view of the separate pieces. Both applications require no camera calibration or pose information, and models are generated and verified directly from images.
Shape From Texture for Smooth Curved Surfaces in Perspective Projection
 Journal of Mathematical Imaging and Vision
, 1992
"... Projective distortion of surface texture observed in a perspective image can provide direct information about the shape of the underlying surface. Previous theories have generally concerned planar surfaces; in this paper we present a systematic analysis of first and secondorder texture distortion ..."
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Cited by 60 (6 self)
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Projective distortion of surface texture observed in a perspective image can provide direct information about the shape of the underlying surface. Previous theories have generally concerned planar surfaces; in this paper we present a systematic analysis of first and secondorder texture distortion cues for the case of a smooth curved surface. In particular, we analyze several kinds of texture gradients and relate them to surface orientation and surface curvature. The local estimates obtained from these cues can be integrated to obtain a global surface shape, and we show that the two surfaces resulting from the wellknown tilt ambiguity in the local foreshortening cue typically have qualitatively different shapes. As an example of a practical application of the analysis, a shape from texture algorithm based on local orientationselective filtering is described, and some experimental results are shown. i Figure 1: This image of a slanting plane covered with circles illustrates several...
Shape from texture from a multiscale perspective
 Fourth Int. Conf. Comp. Vision
, 1993
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The texture gradient equation for recovering shape from texture
 IEEE Trans. on Pattern Analysis and Machine Intelligence
"... AbstractÐThis paper studies the recovery of shape from texture under perspective projection. We regard Shape from Texture as a statistical estimation problem, the texture being the realization of a stochastic process. We introduce warplets, which generalize wavelets over the 2D affine group. At fine ..."
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Cited by 36 (1 self)
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AbstractÐThis paper studies the recovery of shape from texture under perspective projection. We regard Shape from Texture as a statistical estimation problem, the texture being the realization of a stochastic process. We introduce warplets, which generalize wavelets over the 2D affine group. At fine scales, the warpogram of the image obeys a transport equation, called Texture Gradient Equation. In order to recover the 3D shape of the surface, one must estimate the deformation gradient, which measures metric changes in the image. This is made possible by imposing a notion of homogeneity for the original texture, according to which the deformation gradient is equal to the velocity of the Texture Gradient Equation. By measuring the warplet transform of the image at different scales, we obtain a deformation gradient estimator. Index TermsÐShape from texture, texture gradient, warplets, wavelets. æ 1
Surface orientation from texture: Ideal observers, generic observers and the information content of texture cues
, 1998
"... Perspective views of textured, planar surfaces provide a number of cues about the orientations of the surfaces. These include the information created by perspective scaling of texture elements (scaling), the information created by perspective foreshortening of texels (foreshortening) and, for textur ..."
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Cited by 29 (2 self)
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Perspective views of textured, planar surfaces provide a number of cues about the orientations of the surfaces. These include the information created by perspective scaling of texture elements (scaling), the information created by perspective foreshortening of texels (foreshortening) and, for textures composed of discrete elements, the information created by the effects of both scaling and foreshortening on the relative positions of texels (position). We derive a general form for ideal observers for each of these cues as they appear in images of spatially extended textures, (e.g. those composed of solid 2D figures). As an application of the formulation, we derive a set of ‘generic ’ observers which we show perform near optimally for images of a broad range of surface textures, without special prior knowledge about the statistics of the textures. Using simulations of ideal observers, we analyze the informational structure of texture cues, including a quantification of lower bounds on reliability for the three different cues, how cue reliability varies with slant angle and how it varies with field of view. We also quantify how strongly the reliability of the foreshortening cue depends on a prior assumption of isotropy. Finally, we extend the analysis to a naturalistic class of textures, showing that the information content of textures particularly suited to psychophysical investigation can be quantified, at least to a firstorder approximation. The results provide an important computational foundation for psychophysical work on perceiving
Affine Invariant Texture Segmentation and Shape From Texture by Variational Methods
, 1998
"... 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 u ..."
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Cited by 27 (0 self)
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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 MumfordShah 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.
Shape from nonhomogeneous, nonstationary, anisotropic, perspective texture
 In BMVC
, 2005
"... We present a method for ShapefromTexture in one of its most general forms. Previous ShapefromTexture papers assume that the texture is constrained by one or more of the following properties: homogeneity, isotropy, stationarity, or viewed orthographically. We make none of these assumptions. We do ..."
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Cited by 15 (0 self)
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We present a method for ShapefromTexture in one of its most general forms. Previous ShapefromTexture papers assume that the texture is constrained by one or more of the following properties: homogeneity, isotropy, stationarity, or viewed orthographically. We make none of these assumptions. We do not presume that the frontal texture is known a priori, or from a known set, or even present in the image. Instead, surface smoothness is assumed, and the surface is recovered via a consistency constraint. The key idea is that the frontal texture is estimated, and a correct estimation leads to the most consistent surface. In addition to surface shape, a frontal view of the texture is also recovered. Results are given for synthetic and real examples. 1
Shape From Texture: Homogeneity Revisited
 IN PROC. 11TH BRITISH MACHINE VISION CONFERENCE
, 2000
"... The objective of this paper is to estimate the orientation of a scene plane from an uncalibrated perspective image under the assumption that the scene is coated with a homogeneous (but unknown) texture. We make the following novel contributions: first, we show that the problem is equivalent to es ..."
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Cited by 12 (2 self)
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The objective of this paper is to estimate the orientation of a scene plane from an uncalibrated perspective image under the assumption that the scene is coated with a homogeneous (but unknown) texture. We make the following novel contributions: first, we show that the problem is equivalent to estimating the vanishing line of the plane; second, we show that estimating the two degrees of freedom of this line can be decomposed into two searches each for one parameter; third, we give an algorithm for this estimation which is applicable to both regular and irregular textures. The algorithms do not require that texels are identified explicitly. But once the plane vanishing line has been obtained, then texels locations can be determined, and the geometry of the scene plane computed up to an affine transformation. We give examples of these computations on real images.