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38
Images as embedding maps and minimal surfaces: Movies, color, texture, and volumetric medical images
 INT. J. COMPUT. VIS
, 2000
"... We extend the geometric framework introduced in Sochen et al. (IEEE Trans. on Image Processing, 7(3):310–318, 1998) for image enhancement. We analyze and propose enhancement techniques that selectively smooth images while preserving either the multichannel edges or the orientationdependent textu ..."
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Cited by 103 (23 self)
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We extend the geometric framework introduced in Sochen et al. (IEEE Trans. on Image Processing, 7(3):310–318, 1998) for image enhancement. We analyze and propose enhancement techniques that selectively smooth images while preserving either the multichannel edges or the orientationdependent texture features in them. Images are treated as manifolds in a featurespace. This geometrical interpretation lead to a general way for grey level, color, movies, volumetric medical data, and colortexture image enhancement. We first review our framework in which the Polyakov action from highenergy physics is used to develop a minimization procedure through a geometric flow for images. Here we show that the geometric flow, based on manifold volume minimization, yields a novel enhancement procedure for color images. We apply the geometric framework and the general Beltrami flow to featurepreserving denoising of images in various spaces. Next, we introduce a new method for color and texture enhancement. Motivated by Gabor’s geometric image sharpening method (Gabor, Laboratory Investigation, 14(6):801–807, 1965), we present a geometric sharpening procedure for color images with texture. It is based on inverse diffusion across the multichannel edge, and diffusion along the edge.
Demosaicing: image reconstruction from color ccd samples
 IMAGE PROCESSING, IEEE TRANSACTIONS ON
, 1999
"... A simplified color image formation model is used to construct an algorithm for image reconstruction from CCD sensors samples. The proposed method involves two successive steps. The first is motivated by Cok’s template matching technique, while the second step uses steerable inverse diffusion in co ..."
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Cited by 95 (0 self)
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A simplified color image formation model is used to construct an algorithm for image reconstruction from CCD sensors samples. The proposed method involves two successive steps. The first is motivated by Cok’s template matching technique, while the second step uses steerable inverse diffusion in color. Classical linear signal processing techniques tend to oversmooth the image and result in noticeable color artifacts along edges and sharp features. The question is how should the different color channels support each other to form the best possible reconstruction. Our answer is to let the edges support the color information, and the color channels support the edges, and thereby achieve better perceptual results than those that are bounded by the sampling theoretical limit.
CoherenceEnhancing Diffusion Filtering
, 1999
"... The completion of interrupted lines or the enhancement of flowlike structures is a challenging task in computer vision, human vision, and image processing. We address this problem by presenting a multiscale method in which a nonlinear diffusion filter is steered by the socalled interest operato ..."
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Cited by 91 (2 self)
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The completion of interrupted lines or the enhancement of flowlike structures is a challenging task in computer vision, human vision, and image processing. We address this problem by presenting a multiscale method in which a nonlinear diffusion filter is steered by the socalled interest operator (secondmoment matrix, structure tensor). An mdimensional formulation of this method is analysed with respect to its wellposedness and scalespace properties. An efficient scheme is presented which uses a stabilization by a semiimplicit additive operator splitting (AOS), and the scalespace behaviour of this method is illustrated by applying it to both 2D and 3D images.
A Review of Nonlinear Diffusion Filtering
, 1997
"... . This paper gives an overview of scalespace and image enhancement techniques which are based on parabolic partial differential equations in divergence form. In the nonlinear setting this filter class allows to integrate apriori knowledge into the evolution. We sketch basic ideas behind the differ ..."
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Cited by 88 (8 self)
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. This paper gives an overview of scalespace and image enhancement techniques which are based on parabolic partial differential equations in divergence form. In the nonlinear setting this filter class allows to integrate apriori knowledge into the evolution. We sketch basic ideas behind the different filter models, discuss their theoretical foundations and scalespace properties, discrete aspects, suitable algorithms, generalizations, and applications. 1 Introduction During the last decade nonlinear diffusion filters have become a powerful and wellfounded tool in multiscale image analysis. These models allow to include apriori knowledge into the scalespace evolution, and they lead to an image simplification which simultaneously preserves or even enhances semantically important information such as edges, lines, or flowlike structures. Many papers have appeared proposing different models, investigating their theoretical foundations, and describing interesting applications. For a n...
Image Sequence Analysis via Partial Differential Equations
, 1999
"... This article deals with the problem of restoring and motion segmenting noisy image sequences with a static background. Usually, motion segmentation and image restoration are considered separately in image sequence restoration. Moreover, motion segmentation is often noise sensitive. In this article, ..."
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Cited by 46 (3 self)
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This article deals with the problem of restoring and motion segmenting noisy image sequences with a static background. Usually, motion segmentation and image restoration are considered separately in image sequence restoration. Moreover, motion segmentation is often noise sensitive. In this article, the motion segmentation and the image restoration parts are performed in a coupled way, allowing the motion segmentation part to positively influence the restoration part and viceversa. This is the key of our approach that allows to deal simultaneously with the problem of restoration and motion segmentation. To this end, we propose a theoretically justified optimization problem that permits to take into account both requirements. The model is theoretically justified. Existence and unicity are proved in the space of bounded variations. A suitable numerical scheme based on half quadratic minimization is then proposed and its convergence and stability demonstrated. Experimental results obtaine...
An Adaptive Finite Element Method for Large Scale Image Processing
 INTERNATIONAL CONFERENCE ON SCALESPACE THEORIES IN COMPUTER VISION
, 1999
"... Nonlinear diffusion methods have proved to be powerful methods in the processing of 2D and 3D images. They allow a denoising and smoothing of image intensities while retaining and enhancing edges. As time evolves in the corresponding process, a scale of successively coarser image details is generate ..."
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Cited by 45 (20 self)
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Nonlinear diffusion methods have proved to be powerful methods in the processing of 2D and 3D images. They allow a denoising and smoothing of image intensities while retaining and enhancing edges. As time evolves in the corresponding process, a scale of successively coarser image details is generated. Certain features, however, remain highly resolved and sharp. On the other hand, compression is an important topic in image processing as well. Here a method is presented which combines the two aspects in an efficient way. It is based on a semi–implicit Finite Element implementation of nonlinear diffusion. Error indicators guide a successive coarsening process. This leads to locally coarse grids in areas of resulting smooth image intensity, while enhanced edges are still resolved on fine grid levels. Special emphasis has been put on algorithmical aspects such as storage requirements and efficiency. Furthermore, a new nonlinear anisotropic diffusion method for vector field visualization is presented.
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 40 (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.
Orthonormal Vector Sets Regularization with PDE's and Applications
, 2001
"... We are interested in regularizing fields of orthonormal vector sets, using constraintpreserving anisotropic diffusion PDE's. Each point of such a field is defined by multiple orthogonal and unitary vectors and can indeed represent a lot of interesting orientation features such as direction vec ..."
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Cited by 38 (3 self)
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We are interested in regularizing fields of orthonormal vector sets, using constraintpreserving anisotropic diffusion PDE's. Each point of such a field is defined by multiple orthogonal and unitary vectors and can indeed represent a lot of interesting orientation features such as direction vectors or orthogonal matrices (among other examples). We first develop a general variational framework that solves this regularization problem, thanks to a constrained minimization of phifunctionals. This leads to a set of coupled vectorvalued PDE's preserving the orthonormal constraints. Then, we focus on particular applications of this general framework, including the restoration of noisy direction fields, noisy chromaticity color images, estimated camera motions and DTMRI (Diffusion Tensor MRI) datasets.
A Scheme for CoherenceEnhancing Diffusion Filtering with Optimized Rotation Invariance
, 2000
"... For strongly undirected anisotropic processes such as coherenceenhancing diffusion... ..."
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Cited by 35 (5 self)
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For strongly undirected anisotropic processes such as coherenceenhancing diffusion...
Anisotropic Diffusion for Monte Carlo Noise Reduction
"... Monte Carlo sampling can be used to estimate solutions to global light transport and other rendering problems. However, a large number of observations may be needed to reduce the variance to acceptable levels. Rather than computing more observations within each pixel, if spatial coherence exists in ..."
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Cited by 23 (0 self)
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Monte Carlo sampling can be used to estimate solutions to global light transport and other rendering problems. However, a large number of observations may be needed to reduce the variance to acceptable levels. Rather than computing more observations within each pixel, if spatial coherence exists in image space it can be used to reduce visual error by averaging estimators in adjacent pixels. Anisotropic diffusion is a spacevariant noise reduction technique that can selectively preserve texture, edges, and other details using a map of image coherence. The coherence map can be estimated from depth and normal information as well as interpixel colour distances. Incremental estimation of the reduction in variance, in conjunction with statistical normalization of interpixel colour distances, yields an energypreserving algorithm that converges to a spatially nonconstant steady state.