Structure Characterization Using Mathematical Morphology

This thesis deals with the application of mathematical morphology to images of some kind of structure, with the intention of characterizing (or describing) that structure. The emphasis is placed on measuring properties of the real-world scene, rather than measuring properties of the digital image. That is, we require that the measurement tools are sampling-invariant, or at least produce a sampling-related error that is as small as possible. Filters defined by mathematical morphology can be defined both in the continuous space and the sampled space, but will produce different results in both spaces. We term these differences "discretization errors". Many of the results presented in this thesis decrease the discretization errors of morphological filters.Applied Science

Morphological scale-space to differentiate microstructures of food products

Applied Science

Qualitative comparison of contraction-based curve skeletonization methods

In recent years, many new methods have been proposed for extracting curve skeletons of 3D shapes, using a mesh-contraction principle. However, it is still unclear how these methods perform with respect to each other, and with respect to earlier voxel-based skeletonization methods, from the viewpoint of certain quality criteria known from the literature. In this study, we compare six recent contraction-based curve-skeletonization methods that use a mesh representation against six accepted quality criteria, on a set of complex 3D shapes. Our results reveal previously unknown limitations of the compared methods, and link these limitations to algorithmic aspects of the studied methods. Keywords: Curve skeletons; shape analysis; shape representatio

Performance of optimal registration estimators

This paper derives a theoretical limit for image registration and presents an iterative estimator that achieves the limit. The variance of any parametric registration is bounded by the Cramer-Rao bound (CRB). This bound is signal-dependent and is proportional to the variance of input noise. Since most available registration techniques are biased, they are not optimal. The bias, however, can be reduced to practically zero by an iterative gradientbased estimator. In the proximity of a solution, this estimator converges to the CRB with a quadratic rate. Images can be brought close to each other, thus speedup the registration process, by a coarse-to-fine multi-scale registration. The performance of iterative registration is finally shown to significantly increase image resolution from multiple low resolution images under translational motions.Quantitative Imaging GroupApplied Science

Discrete Morphology with Line Structuring Elements

Discrete morphological operations with line segments are notoriously hard to implement. In this paper we study different possible implementations of the line structuring element, compare them, and examine their rotation and translation invariance in the continuous-domain sense. That is, we are interested in obtaining a morphological operator that is invariant to rotations and translations of the image before sampling

Tubular structure filtering by ranking orientation responses of path operators

National audienceThin objects in 3D volumes, for instance vascular networks in medical imaging or various kinds of fibres in materials science, have been of interest for some time to computer vision. Particularly, tubular objects are everywhere elongated in one principal direction –which varies spatially– and are thin in the other two perpendicular di- rections. Filters for detecting such structures use for instance an analysis of the three principal directions of the Hessian, which is a local feature. In this article, we present a low-level tubular structure detection filter. This filter relies on paths, which are semi-global features that avoid any blurring effect induced by scale-space convolution. More precisely, our filter is based on recently developed morphological path operators. These require sampling only in a few principal directions, are robust to noise and do not assume feature regularity. We show that by ranking the directional response of this operator, we are further able to efficiently distinguish between blob, thin planar and tubular structures. We validate this approach on several applications, both from a qualitative and a quantitative point of view, demonstrating an efficient response on tubular structures