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33
Efficient and Reliable Schemes for Nonlinear Diffusion Filtering
 IEEE Transactions on Image Processing
, 1998
"... Nonlinear diffusion filtering is usually performed with explicit schemes. They are only stable for very small time steps, which leads to poor efficiency and limits their practical use. Based on a recent discrete nonlinear diffusion scalespace framework we present semiimplicit schemes which are sta ..."
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Cited by 185 (20 self)
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Nonlinear diffusion filtering is usually performed with explicit schemes. They are only stable for very small time steps, which leads to poor efficiency and limits their practical use. Based on a recent discrete nonlinear diffusion scalespace framework we present semiimplicit schemes which are stable for all time steps. These novel schemes use an additive operator splitting (AOS) which guarantees equal treatment of all coordinate axes. They can be implemented easily in arbitrary dimensions, have good rotational invariance and reveal a computational complexity and memory requirement which is linear in the number of pixels. Examples demonstrate that, under typical accuracy requirements, AOS schemes are at least ten times more efficient than the widelyused explicit schemes.
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...
The Topological Structure of ScaleSpace Images
, 1998
"... We investigate the "deep structure" of a scalespace image. The emphasis is on topology, i.e. we concentrate on critical pointspoints with vanishing gradientand toppointscritical points with degenerate Hessianand monitor their displacements, respectively generic morsifications ..."
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Cited by 40 (21 self)
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We investigate the "deep structure" of a scalespace image. The emphasis is on topology, i.e. we concentrate on critical pointspoints with vanishing gradientand toppointscritical points with degenerate Hessianand monitor their displacements, respectively generic morsifications in scalespace. Relevant parts of catastrophe theory in the context of the scalespace paradigm are briefly reviewed, and subsequently rewritten into coordinate independent form. This enables one to implement topological descriptors using a conveniently defined, global coordinate system. 1 Introduction 1.1 Historical Background A fairly well understood way to endow an image with a topology is to embed it into a oneparameter family of images known as a "scalespace image". The parameter encodes "scale" or "resolution" (coarse/fine scale means low/high resolution, respectively). Among the simplest is the linear or Gaussian scalespace model. Proposed by Iijima [13] in the context of pattern recogniti...
A scale space approach for automatically segmenting words from historical handwritten documents
 IEEE Trans. on Pat
, 2005
"... Abstract—Many libraries, museums, and other organizations contain large collections of handwritten historical documents, for example, the papers of early presidents like George Washington at the Library of Congress. The first step in providing recognition/ retrieval tools is to automatically segment ..."
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Cited by 39 (2 self)
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Abstract—Many libraries, museums, and other organizations contain large collections of handwritten historical documents, for example, the papers of early presidents like George Washington at the Library of Congress. The first step in providing recognition/ retrieval tools is to automatically segment handwritten pages into words. State of the art segmentation techniques like the gap metrics algorithm have been mostly developed and tested on highly constrained documents like bank checks and postal addresses. There has been little work on full handwritten pages and this work has usually involved testing on clean artificial documents created for the purpose of research. Historical manuscript images, on the other hand, contain a great deal of noise and are much more challenging. Here, a novel scale space algorithm for automatically segmenting handwritten (historical) documents into words is described. First, the page is cleaned to remove margins. This is followed by a graylevel projection profile algorithm for finding lines in images. Each line image is then filtered with an anisotropic Laplacian at several scales. This procedure produces blobs which correspond to portions of characters at small scales and to words at larger scales. Crucial to the algorithm is scale selection, that is, finding the optimum scale at which blobs correspond to words. This is done by finding the maximum over scale of the extent or area of the blobs. This scale maximum is estimated using three different approaches. The blobs recovered at the optimum scale are then bounded with a rectangular box to recover the words. A postprocessing filtering step is performed to eliminate boxes of unusual size which are unlikely to correspond to words. The approach is tested on a number of different data sets and it is shown that, on 100 sampled documents from the George Washington corpus of handwritten document images, a total error rate of 17 percent is observed. The technique
Information Measures in ScaleSpaces
 IEEE TRANS. INFORMATION THEORY
, 1999
"... This paper investigates Rényi's generalized entropies under linear and nonlinear scalespace evolutions of images. Scalespaces are useful computer vision concepts for both scale analysis and image restoration. We regard images as densities and prove monotony and smoothness properties for the g ..."
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Cited by 22 (3 self)
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This paper investigates Rényi's generalized entropies under linear and nonlinear scalespace evolutions of images. Scalespaces are useful computer vision concepts for both scale analysis and image restoration. We regard images as densities and prove monotony and smoothness properties for the generalized entropies. The scalespace extended generalized entropies are applied to global scale selection and size estimations. Finally, we introduce an entropybased fingerprint description for textures.
Deformable Solid Modeling via Medial Sampling and Displacement Subdivision
, 2004
"... Discrete mreps use tolerancebased, sampled medial skeleta as an underlying framework for boundaries defined by displaced subdivision surfaces. They provide local and global shape information, combining the strengths of multiscale skeletal modeling with the multiresolution, deformation and shading ..."
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Cited by 14 (0 self)
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Discrete mreps use tolerancebased, sampled medial skeleta as an underlying framework for boundaries defined by displaced subdivision surfaces. They provide local and global shape information, combining the strengths of multiscale skeletal modeling with the multiresolution, deformation and shading properties afforded by subdivision surfaces. Hierarchically linked medial figures allow figural, objectbased deformation, and their stability of object representation with respect to boundary perturbation shows advantages of tolerancebased medial representations over Blum axis and Voronoibased skeletal models. Mrep models provide new approaches to traditional computer graphics modeling, to physically based modeling and simulation, and to imageanalysis, segmentation and display, by combining local and objectlevel deformability and by explicitly including objectscale, tolerance and hierarchical levelofdetail. Sampled medial representations combine the solid modeling capabilities of constructive solid geometry with the flexibility of traditional breps, to which they add multiscale medial and boundary
Recursive Separable Schemes for Nonlinear Diffusion Filters
, 1997
"... Poor efficiency is a typical problem of nonlinear diffusion filtering, when the simple and popular explicit (Eulerforward) scheme is used: for stability reasons very small time step sizes are necessary. In order to overcome this shortcoming, a novel type of semiimplicit schemes is studied, socall ..."
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Cited by 12 (4 self)
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Poor efficiency is a typical problem of nonlinear diffusion filtering, when the simple and popular explicit (Eulerforward) scheme is used: for stability reasons very small time step sizes are necessary. In order to overcome this shortcoming, a novel type of semiimplicit schemes is studied, socalled additive operator splitting (AOS) methods. They share the advantages of explicit and (semi)implicit schemes by combining simplicity with absolute stability. They are reliable, since they satisfy recently established criteria for discrete nonlinear diffusion scalespaces. Their efficiency is due to the fact that they can be separated into onedimensional processes, for which a fast recursive algorithm with linear complexity is available. AOS schemes reveal good rotational invariance and they are symmetric with respect to all axes. Examples demonstrate that, under typical accuracy requirements, they are at least ten times more efficient than explicit schemes.
Scale Space Hierarchy
 JOURNAL OF MATHEMATICAL IMAGING AND VISION
, 2001
"... We investigate the deep structure of a scale space image. We concentrate on scale space critical points  points with vanishing gradient with respect to both spatial and scale direction. We show that these points are always saddle points. They turn ..."
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Cited by 12 (7 self)
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We investigate the deep structure of a scale space image. We concentrate on scale space critical points  points with vanishing gradient with respect to both spatial and scale direction. We show that these points are always saddle points. They turn
Calculations on critical points under gaussian blurring
 In Nielsen et al
, 1999
"... Abstract. The behaviour of critical points of Gaussian scalespace images is mainly described by their creation and annihilation. In existing literature these events are determined in socalled canonical coordinates. A description in a userdefined Cartesian coordinate system is stated, as well as t ..."
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Cited by 10 (8 self)
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Abstract. The behaviour of critical points of Gaussian scalespace images is mainly described by their creation and annihilation. In existing literature these events are determined in socalled canonical coordinates. A description in a userdefined Cartesian coordinate system is stated, as well as the results of a straightforward implementation. The location of a catastrophe can be predicted with subpixel accuracy. An example of an annihilation is given. Also an upper bound is derived for the area where critical points can be created. Experimental data of an MR, a CT, and an artificial noise image satisfy this result. 1