Catálogo de publicaciones - libros

Defuzzification of fuzzy spatial sets by feature distance minimization, recently proposed as an alternative to crisp segmentation, is studied further. Fully utilizing information available in a fuzzy (discrete) representation of a continuous shape, we present an improved defuzzification method, such that the crisp discrete representation of a fuzzy set is generated at an increased spatial resolution, compared to the resolution of the fuzzy set. The correspondence between a fuzzy and a crisp set is established through a distance between their representations based on selected features, where the different resolutions of the images to compare are taken into account. The performance of the method is tested on both synthetic and real images.

We present an extended Mumford-Shah regularization for blind image deconvolution and segmentation in the context of Bayesian estimation for blurred, noisy images or video sequences. The Mumford-Shah functional is extended to have cost terms for the estimation of blur kernels via a newly introduced prior solution space. This functional is minimized using Γ-convergence approximation in an embedded alternating minimization within Neumann conditions. Accurate blur identification is the basis of edge-preserving image restoration in the extended Mumford-Shah regularization. One output of the finite set of curves and object boundaries are grouped and partitioned via a graph theoretical approach for the segmentation of blurred objects. The chosen regularization parameters using the L-curve method is presented. Numerical experiments show that the proposed algorithm is efficiency and robust in that it can handle images that are formed in different environments with different types and amounts of blur and noise.

Our domain of interest is polygonal (and polyhedral) approximation of point sets. Neither the order of data points nor the number of needed line segments (surface patches) are known. In particular, point sets can be obtained by laser range scanner mounted on a moving robot or given as edge pixels/voxels in digital images. Polygonal approximation of edge pixels can also be interpreted as grouping of edge pixels to parts of object contours. The presented approach is described in the statistical framework of Expectation Maximization (EM) and in cognitively motivated geometric framework. We use local support estimation motivated by human visual perception to evaluate support in data points of EM components after each EM step. Consequently, we are able to recognize a locally optimal solution that is not globally optimal, and modify the number of model components and their parameters. We will show experimentally that the proposed approach has much stronger global convergence properties than the EM approach. In particular, the proposed approach is able to converge to a globally optimal solution independent of the initial number of model components and their initial parameters.

A new efficient standard discrete line recognition method is presented. This algorithm incrementally computes in linear time all straight lines which cross a given set of pixels. Moreover, pixels can be considered in any order and do not need to be connected. A new invertible 2D discrete curve reconstruction algorithm based on the proposed recognition method completes this paper. This algorithm computes a polygonal line so that its standard digitization is equal to the discrete curve. These two methods are based on the definition of a new generalized preimage and the framework is the discrete analytical geometry.

The recognition of discrete primitives as digital straight segments (DSS) is a deeply studied problem in digital geometry (see a review in [6]). One characterization of the DSS is purely geometrical: all the points must lie between two lines whose distance (relative to the infinite norm) is less than 1. A common approach used to solve this question is to compute the convex hull of the given points. Recent papers explain how to update the minimum distance when a point is inserted during an online (incremental) recognition in O (log n ) time in the general case [2] or in O (1) time with assumption [2, 4]. Nevertheless, for other cases like insertions mixed with deletions or the union of two DSS, we have no optimal method to compute the resulting width. Thus, we propose a unified, simple and optimal approach applicable for any configuration. Moreover, our function is called independently from the convex hull processing. This allows to reuse any existing library without any modification. Thereby, we offer an efficient tool that opens a new horizon for the applications.

A discrete rotation algorithm can be apprehended as a parametric map f _ α from $\mathbb Z[i]$ to $\mathbb Z[i]$ , whose resulting permutation “looks like” the map induced by an Euclidean rotation. For this kind of algorithm, to be incremental means to compute successively all the intermediate rotated copies of an image for angles in-between 0 and a destination angle. The discretized rotation consists in the composition of an Euclidean rotation with a discretization; the aim of this article is to describe an algorithm which computes incrementally a discretized rotation. The suggested method uses only integer arithmetic and does not compute any sine nor any cosine. More precisely, its design relies on the analysis of the discretized rotation as a step function: the precise description of the discontinuities turns to be the key ingredient that makes the resulting procedure optimally fast and exact. A complete description of the incremental rotation process is provided, also this result may be useful in the specification of a consistent set of definitions for discrete geometry.

Let $SC_{k_i}^{n_i, l_i}$ be a simple closed k _ i -curve in ${\bf Z}^{n_i}$ with l _ i elements, i ∈ {1, 2}. After doing a $(3^{n_1+n_2}-1)$ -homotopic thinning of $SC_{k_1}^{n_1, l_1}\times SC_{k_2}^{n_2, l_2}$ to obtain a closed $(3^{n_1+n_2}-1)$ -surface, we calculate the $(3^{n_1+n_2}-1)$ -fundamental group of $SC_{k_1}^{n_1, l_1}\times SC_{k_2}^{n_2, l_2}$ by the use of some properties of an $(8, 3^{n_1+n_2}-1)$ -covering. AMS Classification: 52XX, 52B05, 52Cxx, 57M05, 55P10, 57M10.

In digitizing 3D objects one wants as much as possible object properties to be preserved in its digital reconstruction. One of the most fundamental properties is topology. Only recently a sampling theorem for cubic grids could be proved which guarantees topology preservation [1]. The drawback of this theorem is that it requires more complicated reconstruction methods than the direct representation with voxels. In this paper we show that face centered cubic (fcc) and body centered cubic (bcc) grids can be used as an alternative. The fcc and bcc voxel representations can directly be used for a topologically correct reconstruction. Moreover this is possible with coarser grid resolutions than in the case of a cubic grid. The new sampling theorems for fcc and bcc grids also give absolute bounds for the geometric error.

Dimension is a fundamental concept in topology. Mylopoulos and Pavlidis [17] provided a definition for discrete spaces. In the present paper we propose an alternative one for the case of planar digital objects. It makes up certain shortcomings of the definition from [17] and implies dimensionality properties analogous to those familiar from classical topology. We also establish relations between dimension of digital objects and their Euler characteristic.

This paper presents an image analysis measurement algorithm – best-fit rectangle for particle size and shape. The best-fit rectangle approach is a combination of the Ferret method and the least 2^nd moments minimization, only requiring calculation of three moments about the center of gravity, and maximum and minimum co-ordinates in a co-ordinate system oriented in the direction of the axis of least 2nd moments, and a simple area ratio. It is a simple rotation-invariance method, reflecting shape (Elongation and angularity). The algorithm is introduced theoretically in details, analyzed and compared to other widely used methods, and has been tested by a large number of solid particle samples in a laboratory. The test results show that by using this method, the results are very close to manual measurements.