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104
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 49 (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...
Describing Surfaces
 Computer Vision, Graphics, and Image Processing
, 1985
"... This paper continues ou,' work' on vlsuM representations of threedimensional surfaces [Brady and Yuille 1984b]. The theoretical component o our work is a study of classes of surface curves as a source of constraint on the surface on which they lie, and as a basis for describing it. We analyze bound ..."
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Cited by 48 (3 self)
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This paper continues ou,' work' on vlsuM representations of threedimensional surfaces [Brady and Yuille 1984b]. The theoretical component o our work is a study of classes of surface curves as a source of constraint on the surface on which they lie, and as a basis for describing it. We analyze bounding contours, sin face intersections, lines of cunature, and asymptotes. Our experimental work hives.igates whether the information suggested by our theoretical study can be computed reliably mid efficiently. We demonstrate algorithms that compute lines of curvature of a (Gaussian smoothed) surface; determine planar patches and umbi!ic regions; extract axes of surfaces of revolution and tube surfaces. We report preliminary results on adapting the curvature primM sketch algorithms of Asada and Brady [1984] to detect and describe surface intersections. () Massachusetts Institute of Technology, 1984 This report describes research done at the Artificial Intelligeice Laboratory of the Massachusetts Institute of Technology. Support for the ]aboratory's Artificial Intelligence reseat.oh is provided in par. by the Adwmced Research Projects Agency of the Department of Defense under Office of Naval Research contract N0001480C0505, the Office of Nax'al Research under contract number N000t477C0389, ,and the System Development Foundation. This wcrk was done while Haruo Asada was a visiting scientist at MIT on leave from Toshiba Corporation, Japan, and while Jean Ponce was a visking s.ientist on leave from I.'RIA, Paris, Fro,nee. ' Pr't of (t6:7)
An Extremum Principle for Shape from Contour
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1983
"... An extremum principle is developed that determines threedimensional surface orientation from a twodimensional contour. The principle maximizes the ratio of the area to the square of the perimeter, a measure of the compactness or symmetry of the threedimensional surface. I;he principle interpre ..."
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Cited by 40 (1 self)
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An extremum principle is developed that determines threedimensional surface orientation from a twodimensional contour. The principle maximizes the ratio of the area to the square of the perimeter, a measure of the compactness or symmetry of the threedimensional surface. I;he principle interprets regular figures correctly and it interprets skew symmetries as oriented real symmetries. The maximum likelihood method approximates the principle on irregular figures, but we show that it consistently overestimates the slant of an ellipse.
An OptimizationBased Approach to the Interpretation of Single Line Drawings as 3D Wire Frames
 International Journal of Computer Vision
, 1992
"... Line drawings provide an effective means of communication about the geometry of 3D objects. An understanding of how to duplicate the way humans interpret line drawings is extremely important in enabling manmachine communication with respect to images, diagrams, and spatial constructs. In particula ..."
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Cited by 35 (0 self)
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Line drawings provide an effective means of communication about the geometry of 3D objects. An understanding of how to duplicate the way humans interpret line drawings is extremely important in enabling manmachine communication with respect to images, diagrams, and spatial constructs. In particular, such an understanding could be used to provide the human with the capability to create a linedrawing sketch of a polyhedral object that the machine can automatically convert into the intended 3D model. A recently published paper (Marill 1991) presented a simple optimization procedure supposedly able to duplicate human judgment in recovering the 3D "wire frame" geometry of objects depicted in line drawings. Marill provided some impressive examples, but no theoretical justification for his approach. In this paper we introduce our own work by first critically examining Marill's algorithm. We provide an explanation for why Marill's algorithm was able to perform as well as it did on the exa...
Shape from Texture without Boundaries
 In Proc. ECCV
, 2002
"... We describe a shape from texture method that constructs a maximum a posteriori estimate of surface coe#cients using only the deformation of individual texture elements. Our method does not need to use either the boundary of the observed surface or any assumption about the overall distribution of ..."
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Cited by 34 (4 self)
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We describe a shape from texture method that constructs a maximum a posteriori estimate of surface coe#cients using only the deformation of individual texture elements. Our method does not need to use either the boundary of the observed surface or any assumption about the overall distribution of elements. The method assumes that texture elements are of a limited number of types of fixed shape. We show that, with this assumption and assuming generic view and texture, each texture element yields the surface gradient unique up to a twofold ambiguity.
Observer biases in the 3D interpretation of line drawings
, 1998
"... Line drawings produced by contours traced on a surface can produce a vivid impression of the surface shape. The stability of this perception is notable considering that the information provided by the surface contours is quite ambiguous. We have studied the stability of line drawing perception from ..."
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Cited by 29 (7 self)
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Line drawings produced by contours traced on a surface can produce a vivid impression of the surface shape. The stability of this perception is notable considering that the information provided by the surface contours is quite ambiguous. We have studied the stability of line drawing perception from psychophysical and computational standpoints. For a given family of simple line drawings, human observers could perceive the drawings as depicting either an elliptic (eggshaped) or hyperbolic (saddleshaped) smooth surface patch. Rotation of the image along the line of sight and change in aspect ratio of the line drawing could bias the observer toward either interpretation. The results were modeled by a simple Bayesian observer that computes the probability to choose either interpretation given the information in the image and prior preferences. The model's decision rule is noncommitting: for a given input image its responses are still probabilistic, reflecting variability in the modeled observers' judgements. A good fit to the data was obtained when three observer assumptions were introduced: a preference for convex surfaces, a preference for surface contours aligned with the principal lines of curvature, and a preference for a surface orientation consistent with an object viewed from above. We discuss how these assumptions might reflect regularities of the visual world. 1998 Elsevier Science Ltd. All rights reserved.
PLANAR SURFACE ORIENTATION FROM TEXTURE SPATIAL FREQUENCIES
, 1995
"... This paper presents a computational model and a practical algorithm for determining the threedimensional orientation of a planar surface from visual texture information. The model consists of three parts: (1) a local spatial frequency based texture representation; (2) a model describing the projec ..."
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Cited by 28 (1 self)
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This paper presents a computational model and a practical algorithm for determining the threedimensional orientation of a planar surface from visual texture information. The model consists of three parts: (1) a local spatial frequency based texture representation; (2) a model describing the projection of surface texture to image texture; and (3) a solution of the texture projection model for the surface orientation under an assumption of surface texture homogeneity. The algorithm first measures the dominant frequency at each image point using three waveletlike transforms, and then finds the surface orientation that minimizes the variance of the image frequencies' backprojections. The algorithm is tested on photographs of realworld surfaces, exhibiting an average accuracy of better than 3 ° in slant and 4 ° in tilt. The current model and algorithm are more accurate, yet substantially simpler, than earlier versions of this approach.
Appendix  Projective Geometry for Machine Vision
, 1992
"... Introduction The idea for this Appendix arose from our perception of a frustrating situation faced by vision researchers. For example, one is interested in some aspect of the theory of perspective image formation such as the epipolar line. The interested party goes to the library to check out a boo ..."
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Cited by 27 (0 self)
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Introduction The idea for this Appendix arose from our perception of a frustrating situation faced by vision researchers. For example, one is interested in some aspect of the theory of perspective image formation such as the epipolar line. The interested party goes to the library to check out a book on projective geometry filled with hope that the necessary mathematical machinery will be directly at hand. These expectations are quickly dashed. Upon opening the book, the expectant reader finds the presentation dominated by endless observations about harmonic relations and a few chapters which explore the minutiae of Pappus' theorem. Finally, as a last cruel twist of irony, the book ends in triumph with a rather exhilarating discourse on the conic pencil. All of the material is presented in the form of theorems defined on points, lines and conics without the use of coordinates, except perhaps for a quick pause to define barycentric coordinates just to taunt the reader. Dejected, the vis
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 26 (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 Texture and Contour by Weak Isotropy
 J. of Artificial Intelligence
, 1993
"... 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 ..."
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Cited by 25 (6 self)
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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...