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.

In spite of its lack of theoretical justification, nonlinear diffusion filtering has become a powerful image enhancement tool in recent years. The goal of the present paper is to provide a mathematical foundation for continuous nonlinear diffusion filtering as a scale-space transformation which is flexible enough to simplify images without loosing the capability of enhancing edges. By studying the Lyapunov functionals, it is shown that nonlinear diffusion reduces L p norms and central moments and increases the entropy of images. The proposed anisotropic class utilizes a diffusion tensor which may be adapted to the image structure. It permits existence, uniqueness and regularity results, the solution depends continuously on the initial image, and it satisfies an extremum principle. All considerations include linear and certain nonlinear isotropic models and apply to m- dimensional vector-valued images. The results are juxtaposed to linear and morphological scale-spaces. . Keywords....

We present a new multiscale contour #tting process which combines information about the image and the contour of the object at di#erent levels of scale. The algorithm is based on energy minimizing deformable models but avoids some of the problems associated with these models. The segmentation algorithm starts by constructing a linear scale-space of an image through convolution of the original image with a Gaussian kernel at di#erent levels of scale, where the scale corresponds to the standard deviation of the Gaussian kernel. At high levels of scale large scale features of the objects are preserved while small scale features, like object details as well as noise, are suppressed. In order to maximize the accuracy of the segmentation, the contour of the object of interest is then tracked in scale-space from coarse to #ne scales. We propose a hybrid Multi-Temperature Simulated Annealing optimization to minimize the energy of the deformable model. At high levels of scale the SA optimizatio...

Abstract: We study the unique affine invariant morphological scale space in 3D. We discuss its properties and we show that it improves the Dynamic Shape model. We explain the algorithms and we display the first numerical experiments.

Visualization of medical data requires the extraction of surfaces that represent the boundaries of objects of interest. This paper describes a method that combines finding these boundaries accurately and ensuring that this surface consists of high quality triangles. The latter is important for subsequent visualization and simulation. We show that the surfaces created using this method are both accurate and have good quality triangles.

Deformable contour is an image segmentation technique in which a contour is deformed until it fits around the target object. Many researches reported that deformable contour is a feasible technique for image segmentation. Several searching techniques such as Greedy Algorithm, Hill Climbing, and Simulated Annealing are often used in the target object contour fitting process. However, these techniques often cause a stuck in the searching process and hence resulting in local maxima# In this paper, Genet ic Algorithm (GA) is introduced to be applied with deformable contour to segment brain in MR images depending on the fitness function at different image scales. The segmentation algorithm starts by constructing images at several different scales depending on the standard deviation of the Gaussian kernel. At coarse scale, draft target contour is encountered because local maxima are eliminated since there are less noise and lower small gradients in the image. This draft contour is then used ...

We present a fast and reliable algorithm, based on iso-surface techniques, to extract differential invariant features at increasing scales. We show that it automatically finds the connection order of singularities, hence it is easy to follow features across scales. As an example, we visualize the orbits of corner points, and compare some criterions to measure their significance.

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...

A method is presented to extract space curves, defined by differential invariants, at increasing scales. The curves are considered as the intersection of two iso-surfaces in 3D, so their moving paths or orbits can be explicitly obtained in scale space as the intersection of two iso-surfaces in 4D. This method is based on a novel algorithm to search for iso-surfaces and their intersections in nD. The algorithm is a significant extension of the 3D Marching Lines algorithm with new orientation and implementation considerations. As a result of these considerations, the reconstructed iso-surfaces and their intersections can be proved to have good topological properties; moreover the implementation is quite straightforward. Specifically, a 4D extension has been implemented to follow spatial curves efficiently via scale. The algorithm automatically finds the connection order of singularities, so tracking remains reliable even if scale is not densely sampled. As an example, the develo...

For automatic registration of medical images, we must search for geometric features that are invariant both with respect to rigid transformations and to smooth changes of resolution. Beginning with Witkin's seminal paper, scale space theory provides an elegant framework for studying the multiscale behavior of these characteristics. However, a natural scale-space representation of features, useful for practical applications, is still missing. We address here the problem of multiscale extraction and representation of characteristic points based on iso-surface techniques. Our main concern is with 2D images: we analyze corner points at increasing scales using the Marching Lines algorithm. Since we can exploit the intrinsic nature of intensity of medical images, segmentation of components or parameterization of curves is not needed, in contrast with other methods. Due to the direct use of the coordinates of points, we get a representation of orbits, which is very convenient both for det...