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Multiresolution markov models for signal and image processing
 Proceedings of the IEEE
, 2002
"... This paper reviews a significant component of the rich field of statistical multiresolution (MR) modeling and processing. These MR methods have found application and permeated the literature of a widely scattered set of disciplines, and one of our principal objectives is to present a single, coheren ..."
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Cited by 153 (17 self)
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This paper reviews a significant component of the rich field of statistical multiresolution (MR) modeling and processing. These MR methods have found application and permeated the literature of a widely scattered set of disciplines, and one of our principal objectives is to present a single, coherent picture of this framework. A second goal is to describe how this topic fits into the even larger field of MR methods and concepts–in particular making ties to topics such as wavelets and multigrid methods. A third is to provide several alternate viewpoints for this body of work, as the methods and concepts we describe intersect with a number of other fields. The principle focus of our presentation is the class of MR Markov processes defined on pyramidally organized trees. The attractiveness of these models stems from both the very efficient algorithms they admit and their expressive power and broad applicability. We show how a variety of methods and models relate to this framework including models for selfsimilar and 1/f processes. We also illustrate how these methods have been used in practice. We discuss the construction of MR models on trees and show how questions that arise in this context make contact with wavelets, state space modeling of time series, system and parameter identification, and hidden
ObjectCentered Surface Reconstruction: Combining MultiImage Stereo and Shading
 International Journal of Computer Vision
, 1995
"... Our goal is to reconstruct both the shape and reflectance properties of surfaces from multiple images. We argue that an objectcentered representation is most appropriate for this purpose because it naturally accommodates multiple sources of data, multiple images (including motion sequences of a rig ..."
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Cited by 131 (20 self)
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Our goal is to reconstruct both the shape and reflectance properties of surfaces from multiple images. We argue that an objectcentered representation is most appropriate for this purpose because it naturally accommodates multiple sources of data, multiple images (including motion sequences of a rigid object), and selfocclusions. We then present a specific objectcentered reconstruction method and its implementation. The method begins with an initial estimate of surface shape provided, for example, by triangulating the result of conventional stereo. The surface shape and reflectance properties are then iteratively adjusted to minimize an objective function that combines information from multiple input images. The objective function is a weighted sum of stereo, shading, and smoothness components, where the weight varies over the surface. For example, the stereo component is weighted more strongly where the surface projects onto highly textured areas in the images, and less strongly othe...
Optimal Algorithm for Shape from Shading and Path Planning
, 2001
"... An optimal algorithm for the reconstruction of a surface from its shading image is presented. The algorithm solves the 3D reconstruction from a single shading image problem. The shading image is treated as a penalty function and the height of the reconstructed surface is a weighted distance. A cons ..."
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Cited by 80 (2 self)
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An optimal algorithm for the reconstruction of a surface from its shading image is presented. The algorithm solves the 3D reconstruction from a single shading image problem. The shading image is treated as a penalty function and the height of the reconstructed surface is a weighted distance. A consistent numerical scheme based on Sethian’s fast marching method is used to compute the reconstructed surface. The surface is a viscosity solution of an Eikonal equation for the vertical light source case. For the oblique light source case, the reconstructed surface is the viscosity solution to a different partial differential equation. A modification of the fast marching method yields a numerically consistent, computationally optimal, and practically fast algorithm for the classical shape from shading problem. Next, the fast marching method coupled with a back tracking via gradient descent along the reconstructed surface is shown to solve the path planning problem in robot navigation.
A Simple Algorithm for Shape from Shading
, 1992
"... In this paper we describe a simple shape from shading algorithm which recovers depth from a brightness image, typically in fewer than ten iterations. This algorithm, which is a simplification of the algorithm of Oliensis and Dupuis, is based on a minimum downhill principle which guarantees continuou ..."
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Cited by 72 (3 self)
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In this paper we describe a simple shape from shading algorithm which recovers depth from a brightness image, typically in fewer than ten iterations. This algorithm, which is a simplification of the algorithm of Oliensis and Dupuis, is based on a minimum downhill principle which guarantees continuous surfaces and stable results. The algorithm is applicable to a broad variety of objects and reflectance maps. 1 Introduction Until the recent publications of Oliensis and Dupuis [[5],[6],[7]] most researchers in shape from shading were convinced that recovering depth from a brightness image necessarily required some regularization technique in order to guarantee a physically plausible surface [4]. It also seemed evident that only an iterative process with typically several thousand iterations would lead to a good approximation of the true surface. Linear methods [8] with an elegant solution in the Fourier domain form an exception to that rule, but they can only be applied to a limited numb...
Single View Modeling of FreeForm Scenes
 IN PROC. OF CVPR
, 2002
"... This paper presents a novel approach for reconstructing freeform, texturemapped, 3D scene models from a single painting or photograph. Given a sparse set of userspecified constraints on the local shape of the scene, a smooth 3D surface that satisfies the constraints is generated. This problem is ..."
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Cited by 61 (0 self)
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This paper presents a novel approach for reconstructing freeform, texturemapped, 3D scene models from a single painting or photograph. Given a sparse set of userspecified constraints on the local shape of the scene, a smooth 3D surface that satisfies the constraints is generated. This problem is formulated as a constrained variational optimization problem. In contrast to previous work in single view reconstruction, our technique enables high quality reconstructions of freeform curved surfaces with arbitrary reflectance properties. A key feature of the approach is a novel hierarchical transformation technique for accelerating convergence on a nonuniform, piecewise continuous grid. The technique is interactive and updates the model in real time as constraints are added, allowing fast reconstruction of photorealistic scene models. The approach is shown to yield high quality results on a large variety of images.
The Direct Computation of Height from Shading
 In Conference on Computer Vision and Pattern Recognition
, 1991
"... We present a method of recovering shape from shading that solves directly for the surface height. By using a discrete formulation of the problem, we are able to achieve good convergence behavior by employing numerical solution techniques more powerful than gradient descent methods derived from varia ..."
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Cited by 60 (1 self)
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We present a method of recovering shape from shading that solves directly for the surface height. By using a discrete formulation of the problem, we are able to achieve good convergence behavior by employing numerical solution techniques more powerful than gradient descent methods derived from variational calculus. Because we directly solve for height, we avoid the problem of finding an integrable surface maximally consistent with surface orientation. Furthermore, since we do not need additional constraints to make the problem well posed, we use a smoothness constraint only to drive the system towards a good solution; the weight of the smoothness term is eventually reduced to near zero. Also, by solving directly for height, we can use stereo processing to provide initial and boundary conditions. Our shape from shading technique, as well as its relation to stereo, is demonstrated on both synthetic and real imagery. 1 Introduction The problem of extracting shape from the shaded image of...
Numerical Methods for Shapefromshading: A New Survey with Benchmarks
, 2007
"... Many algorithms have been suggested for the shapefromshading problem, and some years have passed since the publication of the survey paper by Zhang et al. [1]. In this new survey paper, we try to update their presentation including some recent methods which seem to be particularly representative o ..."
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Cited by 52 (4 self)
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Many algorithms have been suggested for the shapefromshading problem, and some years have passed since the publication of the survey paper by Zhang et al. [1]. In this new survey paper, we try to update their presentation including some recent methods which seem to be particularly representative of three classes of methods: methods based on partial differential equations, methods using optimization, and methods approximating the image irradiance equation. One of the goals of this paper is to set the comparison of these methods on a firm basis. To this end, we provide a brief description of each method, highlighting its basic assumptions and mathematical properties. Moreover, we propose some numerical benchmarks in order to compare the methods in terms of their efficiency and accuracy in the reconstruction of surfaces corresponding to synthetic, as well as to real images.
Analysis of Shape from Shading Techniques
 PROC IEEE CVPR
, 1994
"... Since the first shapefromshading technique was developed by Horn in the early 1970s, different approaches have been continuously emerging in the past two decades. Some of them improve existing techniques, while others are completely new approaches. However, there is no literature on the comparison ..."
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Cited by 45 (0 self)
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Since the first shapefromshading technique was developed by Horn in the early 1970s, different approaches have been continuously emerging in the past two decades. Some of them improve existing techniques, while others are completely new approaches. However, there is no literature on the comparison and performance analysis of these techniques. This is exactly what is addressed in this paper.
Shapelets correlated with surface normals produce surfaces
 In ICCV05
, 2005
"... This paper addresses the problem of deducing the surface shape of an object given just the surface normals. Many shape measurement algorithms such as shape from shading and shape from texture only return the surface normals of an object, often with an ambiguity of π in the surface tilt. The surface ..."
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Cited by 44 (0 self)
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This paper addresses the problem of deducing the surface shape of an object given just the surface normals. Many shape measurement algorithms such as shape from shading and shape from texture only return the surface normals of an object, often with an ambiguity of π in the surface tilt. The surface shape has to be inferred from these normals, typically via some integration process. However, reconstruction through the integration of surface gradients is sensitive to noise and the choice of integration paths across the surface. In addition, existing techniques cannot accommodate ambiguities in tilt. This paper presents a new approach to the reconstruction of surfaces from surface normals using basis functions, referred to here as shapelets. The surface gradients of the shapelets are correlated with the gradients of the surface and the correlations summed to form the reconstruction. This results in a simple reconstruction process that is very robust to noise. Where there is an ambiguity of π in the surface tilt, reconstructions of reduced quality are still possible up to a positive/negative shape ambiguity. Intriguingly, some form of reconstruction is also possible using just slant information. 1.