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We give here the basis for a general theory of flat morphological operators for functions defined on a space E and taking their values in an arbitrary complete lattice V . Contrarily to Heijmans [4], [6], we make no assumption on the complete lattice V , and in contrast with Serra [18], we rely exclusively on the usual construction of flat operators by thresholding and stacking. Some known...
We introduce two features to quantify distributions of line figures in the three-dimensional (3D) space. One of these is the Concentrationindex and the other is a feature based on the extended Voronoi tessellation. The former quantifies the degree of concentration, and the latter the difference of density. We explain the two features with their applications to the benign/malignant discrimination...
A fan cloud is a set of triangles that can be used to visualize and work with point clouds. It is fast to compute and can replace a triangular mesh representation: We discuss visualization, multiresolution reduction, refinement, and selective refinement. Algorithms for triangular meshes can also be applied to fan clouds. They become even simpler, because fans are not interrelated. This localness of...
Digital halftoning is a technique to convert a continuoustone image into a binary image consisting of black and white dots. It is an important technique for printing machines and printers to output an image with few intensity levels or colors which looks similar to an input image. The purposes of this paper are to reveal that there are a number of problems related to combinatorial and computational...
This paper addresses the problem of motion parameter recovery. A novel paradigm is offered to this problem, which computes a maximum likelihood (ML) estimate. The main novelty is that all domain-range point combinations are considered, as opposed to a single “optimal” combination. While this involves the optimization of nontrivial cost functions, the results are superior to those of the so-called...
Distance maps have many applications in computer vision, pattern recognition, morphology and robotics. In this paper, an approach of Distance Map based Image Enhancement (DMIE) is proposed for improving the quality of interpolated images. In DMIE, edge detection is performed after images are interpolated by conventional interpolation schemes. A unidied linear-time algorithm for the distance transform...
Surface area of discrete objects is an important feature for model-based image analysis. In this article, we present a theoretical framework in order to prove multigrid convergence of surface area estimators based on discrete normal vector field integration. The paper details an algorithm which is optimal in time and multigrid convergent to estimate the surface area and a very efficient algorithm...
Gibbs random field models describe image textures in terms of geometric structure and energy of pixel interactions. The interaction means statistical interdependence of signals, the structure is given by characteristic pixel neighbourhoods, and the energy depends on signal co- occurrences over the neighbourhoods. In translation invariant textures all the neighbourhoods have the same relative geometry...
This paper proposes a method of texture analysis using morphological size distribution. Our framework is based on the concept that a texture is described by estimation of primitive, size distribution of grains derived from the primitive, and spatial distribution of the grains. We concentrate on estimation of primitive using an assumption on grain size distribution. We assume a model that grains are...
One of the powerful features of mathematical morphology lies in its strong algebraic structure, that finds equivalents in set theoretical terms, fuzzy sets theory and logics. Moreover this theory is able to deal with global and structural information since several spatial relationships can be expressed in terms of morphological operations. The aim of this paper is to show that the framework of mathematical...
We study nonlinear multiresolution signal decomposition based on morphological pyramids. Motivated by a problem arising in multiresolution volume visualization, we introduce a new class of morphological pyramids. In this class the pyramidal synthesis operator always has the same form, i.e. a dilation by a structuring element A, preceded by upsampling, while the pyramidal analysis operator is a certain...
Median filters are frequently used in signal analysis because they are robust edge-preserving smoothing filters. Since median filters are nonlinear filters, the tools of linear theory are not applicable to them. One approach to deal with nonlinear filters consists in investigating their root images (fixed elements or signals transparent to the filter). Whereas for one-dimensional median filters the...
In this paper, we aim to develop an algorithm for the extraction of a medial set of a random point set in two-an d three-dimensional spaces. Using the medial set of a random point, we define the topology of a random point set. The algorithm for the extraction of a median set is based on the principal surface analysis.
We propose a scale-based method for extracting corners from a given polygonal contour figure. A crystalline flow is introduced to represent geometric features in a scale-space. It is an extension of a usual curvature flow. A special class of polygonal contours is evolved based on the nonlocal curvature. The nonlocal curvature is determined for each facet by its length. In the crystalline flow, a given...
This paper proposes a new formulation of the Minkowski algebra for figures. In the conventional Minkowski algebra, the sum operation was always defined, but its inverse was not necessarily defined. On the other hand, the proposed algebra forms a group, and hence every element has its inverse, and the sum and the inverse operation can be taken freely. In this new algebraic system, some of the elements...
We propose a novel type of decomposition for polygonal shapes. It is thought that, for the task of object recognition, the human visual system uses a part-based representation. Decompositions based on skeletons have been previously proposed in computer vision. Our method is the first one, however, based on the straight line skeleton. Compared to the medial axis, the straight line skeleton has a few...
In uncertain geometry in the 2D plane, points are replaced by uncertainty regions. By allowing uncertainty several geometric notions such as parallelism and concurrency become inconsistent with Euclidean geometry. In previous work we explained how consistency can be partially restored by graph-theoretical grouping algorithms. In this paper we study inconsistencies at a higher-level, e.g., the violation...
In this paper, we introduce a resolution-conversion method for two- and three-dimensional discrete objects. We first derive a method for boundary extraction, second, introduce a method for the estimation of a smooth boundary, and third, construct an algorithm for resolution conversion.
Digital halftoning is a problem of computing a binary image approximating an input gray (or color) image. We consider two problems on digital halftoning: mathematical evaluation of a halftoning image and design of optimization-based halftoning algorithms. We propose an efficient automatic evaluation system of halftoning images by using quality evaluation functions based on discrepancy measures. Our...
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