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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.
Linear ScaleSpace has First been Proposed in Japan
, 1999
"... Linear scalespace is considered to be a modern bottomup tool in computer vision. The American and European vision community, however, is unaware of the fact that it has already been axiomatically derived in 1959 in a Japanese paper by Taizo Iijima. This result formed the starting point of vast li ..."
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Cited by 29 (4 self)
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Linear scalespace is considered to be a modern bottomup tool in computer vision. The American and European vision community, however, is unaware of the fact that it has already been axiomatically derived in 1959 in a Japanese paper by Taizo Iijima. This result formed the starting point of vast linear scalespace research in Japan ranging from various axiomatic derivations over deep structure analysis to applications to optical character recognition. Since the outcomes of these activities are unknown to western scalespace researchers, we give an overview of the contribution to the development of linear scalespace theories and analyses. In particular, we review four Japanese axiomatic approaches that substantiate linear scalespace theories proposed between 1959 and 1981. By juxtaposing them to ten American or European axiomatics, we present an overview of the stateoftheart in Gaussian scalespace axiomatics. Furthermore, we show that many techniques for analysing linear scalespace have also been pioneered by Japanese researchers.
ScilImage: A Multilayered Environment for Use and Development of Image Processing Software
, 1994
"... This paper presents an integrated system made up of a portable multilayered interactive environment for software development and use, and a class based infrastructure for image processing. The interactive environment is responsive to different type of users, and consists of a library handler, a C ..."
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Cited by 6 (1 self)
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This paper presents an integrated system made up of a portable multilayered interactive environment for software development and use, and a class based infrastructure for image processing. The interactive environment is responsive to different type of users, and consists of a library handler, a C interpreter, a command expander, a menu and dialog generator, and a visual programming interface. All interface layers are generated from a command description file. The design considerations of each of the interface layers is discussed. The image infrastructure enforces strict image class separation, and takes care of actions common to all image classes. Through the use of an abstraction mechanism based on function overloading, the infrastructure allows image subclassing and the definition of new image classes, which automatically inherit the consistent behavior of the total environment. An overview of the extensive image processing libraries functionality is given, with special attention ...
NonLinear ScaleSpaces Isomorphic to the Linear Case
 Journal of Mathematical Imaging and Vision
, 1999
"... An innite dimensional class of isomorphisms is considered, relating a particular class of nonlinear scalespaces to the wellestablished linear case. The nonlinearity pertains to an invertible mapping of greyvalues, which can be adapted so as to account for external knowledge. This is particularly ..."
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Cited by 5 (2 self)
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An innite dimensional class of isomorphisms is considered, relating a particular class of nonlinear scalespaces to the wellestablished linear case. The nonlinearity pertains to an invertible mapping of greyvalues, which can be adapted so as to account for external knowledge. This is particularly interesting for applications such as segmentation in medical imaging, whereby one is in possession of a model relating tissue types to image greyvalues. It is moreover of interest in dening a consistent scalespace representation of vectorvalued and multispectral images. Keywords: linear/nonlinear/morphological scalespace theory. 1 Introduction We consider an innite dimensional class of pseudolinear scalespace representations, in which the members are isomorphically related to the linear case by a transformation of greyvalues. Although the nonlinearity can be \transformed away" in theory, it may be prudent not to do so in a practical situation whereby one is in possession of a pri...
ScaleSpace has been discovered in Japan
, 1997
"... Gaussian scalespace is considered to be a modern bottomup tool in computer vision. The American and European vision community, however, is unaware of the fact that Gaussian scalespace has already been axiomatically derived in 1959 in a Japanese paper by Taizo Iijima. This result formed the starti ..."
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Cited by 3 (0 self)
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Gaussian scalespace is considered to be a modern bottomup tool in computer vision. The American and European vision community, however, is unaware of the fact that Gaussian scalespace has already been axiomatically derived in 1959 in a Japanese paper by Taizo Iijima. This result formed the starting point of an entire world of linear scalespace research in Japan ranging from various axiomatic derivations over deep structure analysis to applications to optical character recognition (OCR). Since this world is unknown to western scalespace researchers and many papers are written in Japanese, we give an overview of the basic concepts. In particular, we review four Japanese axiomatics for Gaussian scalespace which have been proposed between 1959 and 1981. By juxtaposing them to ten American or European axiomatics, we present an overview of the stateoftheart in Gaussian scalespace axiomatics. Key words: Scalespace, axiomatics, deep structure, OCR. 1 Introduction A rapidly incre...
GreyScale Images
, 1995
"... Despite the fact that images constitute the main objects in machine vision, there is remarkably little concern about their actual definition. We propose a definition beyond machinespecific technicalities. Such a definition is of interest in the design of applications for which the details of the ..."
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Cited by 2 (1 self)
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Despite the fact that images constitute the main objects in machine vision, there is remarkably little concern about their actual definition. We propose a definition beyond machinespecific technicalities. Such a definition is of interest in the design of applications for which the details of the storage medium are not crucially important (the usual case). It provides a unified conceptual framework for various existing theories and techniques, such as scalespace theory and mathematical morphology. Its relevance is, above all, computational. Everything is formulated in terms of machine concepts. Keywords: image structure, linear image processing, mathematical morphology, linear/morphological scalespace. 1 Introduction Despite the fact that images constitute the pivot of computer vision and image analysis, there exists remarkably little debate about their actual definition. Typically an image is represented as a (discrete or continuous) point mapping f : IR n ! IR of space...
Duality Principles in Image Processing and Analysis
 IVCNZ
, 1998
"... Duality is a wellestablished concept in quantum physics. It formalises the fact that what one observes is not nature in itself, butin Heisenberg's words"nature exposed to our method of questioning". In the context of image analysis "question" pertains to some task whi ..."
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Cited by 2 (0 self)
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Duality is a wellestablished concept in quantum physics. It formalises the fact that what one observes is not nature in itself, butin Heisenberg's words"nature exposed to our method of questioning". In the context of image analysis "question" pertains to some task while "nature" (empirical facts and natural laws) could be taken as the totality of image data supplemented with relevant external factors (knowledge or hypotheses). However, the analogy with quantum physics falls short in at least one fundamental aspect. Whereas the physicist studies nature for nature's sake, endeavouring to reveal natural laws, the image scientist pursues a certain task. This implies a shift of paradigm from the retrospect to the prospect. It will be argued that this leads to a subtle but important difference in the role duality plays in image processing and analysis as compared to the technically similar "bracket" formalism in quantum physics. Duality in the context of image processing and analysis ...
PseudoLinear ScaleSpace Theory  Towards The Integration of Linear and. . .
 International Journal of Computer Vision
, 1997
"... It has been observed that linear, Gaussian scalespace, and nonlinear, morphological erosion and dilation scalespaces generated by a quadratic structuring function have a lot in common. Indeed, farreaching analogies have been reported, which seems to suggest the existence of an underlying isomorph ..."
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Cited by 1 (1 self)
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It has been observed that linear, Gaussian scalespace, and nonlinear, morphological erosion and dilation scalespaces generated by a quadratic structuring function have a lot in common. Indeed, farreaching analogies have been reported, which seems to suggest the existence of an underlying isomorphism. However, an actual mapping appears to be missing. In the present work a oneparameter isomorphism is constructed in closedform, which encompasses linear and both types of morphological scalespaces as (nonuniform) limiting cases. Apart from establishing such a formal connection, the unfolding of the family provides a means to transfer known results from one domain to the other. Moreover, for any fixed and nondegenerate parameter value one obtains a novel type of "pseudolinear" multiscale representation that is, in a precise way, "inbetween" the familiar ones, and may be of interest in its own right. 1 Introduction Both morphological as well as linear scalespace representations ha...
DECOMPOSITION OF SEPARABLE CONCAVE STRUCTURING FUNCTIONS
"... This paper presents a decomposition scheme for a large class of greyscale structuring elements from mathematical morphology. In contrast with many existing decomposition schemes, our method is valid in the continuous domain. Conditions are given under which this continuous method can be properly di ..."
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This paper presents a decomposition scheme for a large class of greyscale structuring elements from mathematical morphology. In contrast with many existing decomposition schemes, our method is valid in the continuous domain. Conditions are given under which this continuous method can be properly discretized. The class of functions that can be decomposed with our method contains the class of quadratic functions, that are of major importance in, for instance, distance transforms and morphological scale space. In the continuous domain, the size of the structuring elements resulting from the decomposition, can be chosen arbitrarily small. For functions from the mentioned class, that can be separated along the standard image axes, a discrete decomposition in 3 × 3 elements can be guaranteed.