The completion of interrupted lines or the enhancement of flow-like 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 so-called interest operator (second-moment matrix, structure tensor). An m-dimensional formulation of this method is analysed with respect to its well-posedness and scale-space properties. An efficient scheme is presented which uses a stabilization by a semi-implicit additive operator splitting (AOS), and the scale-space behaviour of this method is illustrated by applying it to both 2-D and 3-D images.

An innite dimensional class of isomorphisms is considered, relating a particular class of nonlinear scale-spaces to the well-established linear case. The nonlinearity pertains to an invertible mapping of grey-values, 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 grey-values. It is moreover of interest in dening a consistent scale-space representation of vector-valued and multispectral images. Keywords: linear/nonlinear/morphological scale-space theory. 1 Introduction We consider an innite dimensional class of pseudo-linear scale-space representations, in which the members are isomorphically related to the linear case by a transformation of grey-values. 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...

This paper presents an integrated system made up of a portable multi-layered 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 sub-classing 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 ...

Duality is a well-established concept in quantum physics. It formalises the fact that what one observes is not nature in itself, but---in 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 ...

Gaussian scale-space is considered to be a modern bottom-up tool in computer vision. The American and European vision community, however, is unaware of the fact that Gaussian scale-space 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 scale-space 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 scale-space 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 scale-space which have been proposed between 1959 and 1981. By juxtaposing them to ten American or European axiomatics, we present an overview of the state-of-the-art in Gaussian scale-space axiomatics. Key words: Scale-space, axiomatics, deep structure, OCR. 1 Introduction A rapidly incre...

It has been observed that linear, Gaussian scale-space, and nonlinear, morphological erosion and dilation scale-spaces generated by a quadratic structuring function have a lot in common. Indeed, far-reaching 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 one-parameter isomorphism is constructed in closed-form, which encompasses linear and both types of morphological scale-spaces as (non-uniform) 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 non-degenerate parameter value one obtains a novel type of "pseudo-linear" multiscale representation that is, in a precise way, "in-between" the familiar ones, and may be of interest in its own right. 1 Introduction Both morphological as well as linear scale-space representations ha...

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 machine-specific 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 scale-space 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 scale-space. 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...

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.