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66
A geometrical framework for low level vision
 IEEE Trans. on Image Processing
, 1998
"... Abstract—We introduce a new geometrical framework based on which natural flows for image scale space and enhancement are presented. We consider intensity images as surfaces in the space. The image is, thereby, a twodimensional (2D) surface in threedimensional (3D) space for graylevel images, an ..."
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Cited by 221 (35 self)
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Abstract—We introduce a new geometrical framework based on which natural flows for image scale space and enhancement are presented. We consider intensity images as surfaces in the space. The image is, thereby, a twodimensional (2D) surface in threedimensional (3D) space for graylevel images, and 2D surfaces in five dimensions for color images. The new formulation unifies many classical schemes and algorithms via a simple scaling of the intensity contrast, and results in new and efficient schemes. Extensions to multidimensional signals become natural and lead to powerful denoising and scale space algorithms. Index Terms — Color image processing, image enhancement, image smoothing, nonlinear image diffusion, scalespace. I.
A Theoretical Framework for Convex Regularizers in PDEBased Computation of Image Motion
, 2000
"... Many differential methods for the recovery of the optic flow field from an image sequence can be expressed in terms of a variational problem where the optic flow minimizes some energy. Typically, these energy functionals consist of two terms: a data term, which requires e.g. that a brightness consta ..."
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Cited by 99 (25 self)
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Many differential methods for the recovery of the optic flow field from an image sequence can be expressed in terms of a variational problem where the optic flow minimizes some energy. Typically, these energy functionals consist of two terms: a data term, which requires e.g. that a brightness constancy assumption holds, and a regularizer that encourages global or piecewise smoothness of the flow field. In this paper we present a systematic classification of rotation invariant convex regularizers by exploring their connection to diffusion filters for multichannel images. This taxonomy provides a unifying framework for datadriven and flowdriven, isotropic and anisotropic, as well as spatial and spatiotemporal regularizers. While some of these techniques are classic methods from the literature, others are derived here for the first time. We prove that all these methods are wellposed: they posses a unique solution that depends in a continuous way on the initial data. An interesting structural relation between isotropic and anisotropic flowdriven regularizers is identified, and a design criterion is proposed for constructing anisotropic flowdriven regularizers in a simple and direct way from isotropic ones. Its use is illustrated by several examples.
Fast Anisotropic Smoothing of MultiValued Images using CurvaturePreserving PDE’s
 Research Report “Les Cahiers du GREYC”, No 05/01. Equipe IMAGE/GREYC (CNRS UMR 6072), Février
, 2005
"... We are interested in PDE’s (Partial Differential Equations) in order to smooth multivalued images in an anisotropic manner. Starting from a review of existing anisotropic regularization schemes based on diffusion PDE’s, we point out the pros and cons of the different equations proposed in the liter ..."
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Cited by 66 (3 self)
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We are interested in PDE’s (Partial Differential Equations) in order to smooth multivalued images in an anisotropic manner. Starting from a review of existing anisotropic regularization schemes based on diffusion PDE’s, we point out the pros and cons of the different equations proposed in the literature. Then, we introduce a new tensordriven PDE, regularizing images while taking the curvatures of specific integral curves into account. We show that this constraint is particularly well suited for the preservation of thin structures in an image restoration process. A direct link is made between our proposed equation and a continuous formulation of the LIC’s (Line Integral Convolutions by Cabral and Leedom [11]). It leads to the design of a very fast and stable algorithm that implements our regularization method, by successive integrations of pixel values along curved integral lines. Besides, the scheme numerically performs with a subpixel accuracy and preserves then thin image structures better than classical finitedifferences discretizations. Finally, we illustrate the efficiency of our generic curvaturepreserving approach in terms of speed and visual quality with different comparisons and various applications requiring image smoothing: color images denoising, inpainting and image resizing by nonlinear interpolation.
Edge Detection in Multispectral Images
 CVGIP: Graphical Models and Image Processing
, 1989
"... Introduction Edge detection methods based upon differential operators are widely used in the early processing of oneband images, also referred to as graylevel, intensity, monochromatic images, in contrast with multiband, color, multispectral images. In particular, methods based upon the analysis ..."
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Cited by 60 (1 self)
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Introduction Edge detection methods based upon differential operators are widely used in the early processing of oneband images, also referred to as graylevel, intensity, monochromatic images, in contrast with multiband, color, multispectral images. In particular, methods based upon the analysis of zerocrossings of some secondorder differential operator applied to image data have been extensively explored in recent years (see e.g. [1, 4, 5]). The two most popular operators are the Laplacian and the second directional derivative in the direction of gradient; these operators share the nice property of being invariant with respect to translations and rotations in the image plane. Of them, the second directional derivative is the most appealing, due to its connection with the extrema of the gradient magnitude; indeed, the loci of maximal graylevel gradient are a natural definition of edges in intensity images. In contrast, differential methods seem to have received little att
ForwardandBackward Diffusion Processes for Adaptive Image Enhancement and Denoising
 IEEE Transactions on Image Processing
, 2002
"... Signal and image enhancement is considered in the context of a new type of diffusion process that simultaneously enhances, sharpens and denoises images. The nonlinear diffusion coefficient is locally adjusted according to image features such as edges, textures and moments. As such it can switch the ..."
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Cited by 55 (5 self)
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Signal and image enhancement is considered in the context of a new type of diffusion process that simultaneously enhances, sharpens and denoises images. The nonlinear diffusion coefficient is locally adjusted according to image features such as edges, textures and moments. As such it can switch the diffusion process from a forward to a backward (inverse) mode according to a given set of criteria. This results in a forwardandbackward (FAB) adap tive diffusion process that enhances features while locally denoising smoother segments of the signal or image. The proposed method, using the FAB process, is applied in a superresolution scheme.
Diffusion and Regularization of Vector and MatrixValued Images
, 2002
"... The goal of this paper is to present a unified description of diffusion and regularization techniques for vectorvalued as well as matrixvalued data fields. In the vectorvalued setting, we first review a number of existing methods and classify them into linear and nonlinear as well as isotropic an ..."
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Cited by 55 (16 self)
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The goal of this paper is to present a unified description of diffusion and regularization techniques for vectorvalued as well as matrixvalued data fields. In the vectorvalued setting, we first review a number of existing methods and classify them into linear and nonlinear as well as isotropic and anisotropic methods. For these approaches we present corresponding regularization methods. This taxonomy is applied to the design of regularization methods for variational motion analysis in image sequences. Our vectorvalued framework is then extended to the smoothing of positive semidefinite matrix fields. In this context a novel class of anisotropic di usion and regularization methods is derived and it is shown that suitable algorithmic realizations preserve the positive semidefiniteness of the matrix field without any additional constraints. As an application, we present an anisotropic nonlinear structure tensor and illustrate its advantages over the linear structure tensor.
Rags: Regionaided geometric snake
 IEEE Transactions on Image Processing
, 2004
"... Abstract—An enhanced, regionaided, geometric active contour that is more tolerant toward weak edges and noise in images is introduced. The proposed method integrates gradient flow forces with region constraints, composed of image region vector flow forces obtained through the diffusion of the regio ..."
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Cited by 38 (13 self)
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Abstract—An enhanced, regionaided, geometric active contour that is more tolerant toward weak edges and noise in images is introduced. The proposed method integrates gradient flow forces with region constraints, composed of image region vector flow forces obtained through the diffusion of the region segmentation map. We refer to this as the Regionaided Geometric Snake or RAGS. The diffused region forces can be generated from any reliable region segmentation technique, greylevel or color. This extra region force gives the snake a global complementary view of the boundary information within the image which, along with the local gradient flow, helps detect fuzzy boundaries and overcome noisy regions. The partial differential equation (PDE) resulting from this integration of image gradient flow and diffused region flow is implemented using a level set approach. We present various examples and also evaluate and compare the performance of RAGS on weak boundaries and noisy images. Index Terms—Color snakes, deformable contours, geometric snakes, region segmentation, regionaided snakes, weakedge leakage. I.
Analysing superimposed oriented patterns
 Image Analysis and Interpretation, 6th IEEE Southwest Symposium on Volume, Pages
, 2004
"... journal = {IEEE Transactions on Image Processing}, publisher = {IEEE}, volume = {15}, number = {12}, year = {2006}, pages = {36903700}} © 2006 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for cre ..."
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Cited by 36 (8 self)
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journal = {IEEE Transactions on Image Processing}, publisher = {IEEE}, volume = {15}, number = {12}, year = {2006}, pages = {36903700}} © 2006 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Multiscale gradient watersheds of color images
 Transactions on Image Processing
"... Abstract—We present a new framework for the hierarchical segmentation of color images. The proposed scheme comprises a nonlinear scalespace with vectorvalued gradient watersheds. Our aim is to produce a meaningful hierarchy among the objects in the image using three image components of distinct pe ..."
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Cited by 24 (3 self)
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Abstract—We present a new framework for the hierarchical segmentation of color images. The proposed scheme comprises a nonlinear scalespace with vectorvalued gradient watersheds. Our aim is to produce a meaningful hierarchy among the objects in the image using three image components of distinct perceptual significance for a human observer, namely strong edges, smooth segments and detailed segments. The scalespace is based on a vectorvalued diffusion that uses the Additive Operator Splitting numerical scheme. Furthermore, we introduce the principle of the dynamics of contours in scalespace that combines scale and contrast information. The performance of the proposed segmentation scheme is presented via experimental results obtained with a wide range of images including natural and artificial scenes. Index Terms—Anisotropic diffusion, color segmentation, dynamics of contours, scalespace, vectorvalued gradient, watershed segmentation. I.
Selection and Fusion of Color Models for Image Feature Detection
"... Abstract—The choice of a color model is of great importance for many computer vision algorithms (e.g., feature detection, object recognition, and tracking) as the chosen color model induces the equivalence classes to the actual algorithms. As there are many color models available, the inherent diffi ..."
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Cited by 23 (1 self)
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Abstract—The choice of a color model is of great importance for many computer vision algorithms (e.g., feature detection, object recognition, and tracking) as the chosen color model induces the equivalence classes to the actual algorithms. As there are many color models available, the inherent difficulty is how to automatically select a single color model or, alternatively, a weighted subset of color models producing the best result for a particular task. The subsequent hurdle is how to obtain a proper fusion scheme for the algorithms so that the results are combined in an optimal setting. To achieve proper color model selection and fusion of feature detection algorithms, in this paper, we propose a method that exploits nonperfect correlation between color models or feature detection algorithms derived from the principles of diversification. As a consequence, a proper balance is obtained between repeatability and distinctiveness. The result is a weighting scheme which yields maximal feature discrimination. The method is verified experimentally for three different image feature detectors. The experimental results show that the fusion method provides feature detection results having a higher discriminative power than the standard weighting scheme. Further, it is experimentally shown that the color model selection scheme provides a proper balance between color invariance (repeatability) and discriminative power (distinctiveness). Index Terms—Color, learning, feature detection, scene analysis. 1