Attila Kuba

A 3D 6-subiteration thinning algorithm for extracting medial lines

Thinning is a frequently used method for extracting skeletons in discrete spaces. This paper presents an efficient parallel thinning algorithm that directly extracts medial lines from elongated 3D binary objects (i.e., without creating medial surface). Our algorithm provides good results, preserves topology and it is easy to implement.

Advances in Discrete Tomography and Its Applications

ANHA Series Preface Preface List of Contributors Introduction / A. Kuba and G.T. Herman Part I. Foundations of Discrete Tomography An Introduction to Discrete Point X-Rays / P. Dulio, R.J. Gardner, and C. Peri Reconstruction of Q-Convex Lattice Sets / S. Brunetti and A. Daurat Algebraic Discrete Tomography / L. Hajdu and R. Tijdeman Uniqueness and Additivity for n-Dimensional Binary Matrices with Respect to Their 1-Marginals / E. Vallejo Constructing (0, 1)-Matrices with Given Line Sums and Certain Fixed Zeros / R.A. Brualdi and G. Dahl Reconstruction of Binary Matrices under Adjacency Constraints / S. Brunetti, M.C. Costa, A. Frosini, F. Jarray, and C. Picouleau Part II. Discrete Tomography Reconstruction Algorithms Decomposition Algorithms for Reconstructing Discrete Sets with Disjoint Components / P. Balazs Network Flow Algorithms for Discrete Tomography / K.J. Batenburg A Convex Programming Algorithm for Noisy Discrete Tomography / T.D. Capricelli and P.L. Combettes Variational Reconstruction with DC-Programming / C. Schnorr, T. Schule, and S. Weber Part III. Applications of Discrete Tomography Direct Image Reconstruction-Segmentation, as Motivated by Electron Microscopy / Hstau Y. Liao and Gabor T. Herman Discrete Tomography for Generating Grain Maps of Polycrystals / A. Alpers, L. Rodek, H.F. Poulsen, E. Knudsen, G.T. Herman Discrete Tomography Methods for Nondestructive Testing / J. Baumann, Z. Kiss, S. Krimmel, A. Kuba, A. Nagy, L. Rodek, B. Schillinger, and J. Stephan Emission Discrete Tomography / E. Barcucci, A. Frosini, A. Kuba, A. Nagy, S. Rinaldi, M. Samal, and S. Zopf Application of a Discrete Tomography Approach to Computerized Tomography / Y. Gerard and F. Feschet Index

A parallel 3D 12-subiteration thinning algorithm

Abstract Thinning on binary images is an iterative layer by layer erosion until only the “skeletons” of the objects are left. This paper presents an efficient parallel thinning algorithm which produces either curve skeletons or surface skeletons from 3D binary objects. It is important that a curve skeleton is extracted directly (i.e., without creating a surface skeleton). The strategy which is used is called directional: each iteration step is composed of a number of subiterations each of which can be executed in parallel. One iteration step of the proposed algorithm contains 12 subiterations instead of the usual six. The algorithm makes easy implementation possible, since deletable points are given by 3×3×3 matching templates. The topological correctness for (26, 6) binary pictures is proved.

A Sequential 3D Thinning Algorithm and Its Medical Applications

Skeleton is a frequently applied shape feature to represent the general form of an object. Thinning is an iterative object reduction technique for producing a reasonable approximation to the skeleton in a topology preserving way. This paper describes a sequential 3D thinning algorithm for extracting medial lines of objects in (26, 6) pictures. Our algorithm has been successfully applied in medical image analysis. Three of the emerged applications (analysing airways, blood vessels, and colons) are also presented.

Reconstruction of 4- and 8-connected convex discrete sets from row and column projections

In this paper we examine the problem of reconstructing a discrete two-dimensional set from its two orthogonal projection (H,V) when the set satisfies some convexity conditions. We show that the algorithm of the paper [Int. J. Imaging Systems and Technol. 9 (1998) 69] is a good heuristic algorithm but it does not solve the problem for all (H,V) instances. We propose a modification of this algorithm solving the problem for all (H,V) instances, by starting to build the “spine”. The complexity of our reconstruction algorithm is O(mn·log(mn)·min{m2,n2}) in the worst case. However, according to our experimental results, in 99% of the studied cases the algorithm is able to reconstruct a solution without using the newly introduced operation. In such cases the upper bound of the complexity of the algorithm is O(mn·log(mn)). A systematic comparison of this algorithm was done and the results show that this algorithm has the better average complexity than other published algorithms. The way of comparison and the results are given in a separate paper [Linear Algebra Appl. (submitted)]. Finally we prove that the problem can be solved in polynomial time also in a class of discrete sets which is larger than the class of convex polyominoes, namely, in the class of 8-connected convex sets.

A comparison of lossless compression methods for medical images

In this work, lossless grayscale image compression methods are compared on a medical image database. The database contains 10 different types of images with bit rates varying from 8 to 16 bits per pixel. The total number of test images was about 3000, originating from 125 different patient studies. Methods used for compressing the images include seven methods designed for grayscale images and 18 ordinary general-purpose compression programs. Furthermore, four compressed image file formats were used. The results show that the compression ratios strongly depend on the type of the image. The best methods turned out to be TMW, CALIC and JPEG-LS. The analysis step in TMW is very time-consuming. CALIC gives high compression ratios in a reasonable time, whereas JPEG-LS is nearly as effective and very fast.

Discrete Tomography: A Historical Overview

In this chapter we introduce the topic of discrete tomography and give a brief historical survey of the relevant contributions. After discussing the nature of the basic theoretical problems (those of consistency, uniqueness, and reconstruction) that arise in discrete tomography, we give the details of the classical special case (namely, two-dimensional discrete sets — i.e.,binary matrices — and two orthogonal projections) including a polynomial time reconstruction algorithm. We conclude the chapter with a summary of some of the applications of discrete tomography.

Discrete tomography in medical imaging

Discrete tomography (DT) deals with the reconstruction of a function from its projections, when the function has a known discrete range. The knowledge of the discrete range, possibly together with some prior information, can significantly reduce the number of projections required for a high-quality reconstruction. The reconstruction methods used in DT applications are usually based on some formulation as an optimization problem. This paper presents methods and results of DT based on problems of angiography, emission tomography, and electron microscopy (EM).

Reconstruction of convex 2D discrete sets in polynomial time

The reconstruction problem is considered in those classes of discrete sets where the reconstruction can be performed from two projections in polynomial time. The reconstruction algorithms and complexity results are summarized in the case of hv-convex sets, hv-convex 8-connected sets, hv-convex polyominoes, and directed h-convex sets. As new results some properties of the feet and spines of the hv-convex 8-connected sets are proven and it is shown that the spine of such a set can be determined from the projections in linear time. Two algorithms are given to reconstruct hv-convex 8-connected sets. Finally, it is shown that the directed h-convex sets are uniquely reconstructible with respect to their row and column sum vectors.

Comparison of algorithms for reconstructing hv-convex discrete sets

Three reconstruction algorithms to be used for reconstructing hv-convex discrete sets from their row and column sums are compared. All these algorithms have two versions: one for reconstructing hv-convex polyominoes and another one for reconstructing hv-convex 8-connected discrete sets. In both classes of discrete sets the algorithms are compared from the viewpoints of average execution time and memory complexities. Discrete sets with given sizes are generated with uniform distribution, and then reconstructed from their row and column sums. First we have implemented two previously published algorithms. According to our comparisons, the algorithm which was better from the viewpoint of worst time complexity was the worse from the viewpoint of average time complexity and memory requirements. Then, as a new method, a combination of the two algorithms was also implemented and it is shown that it inherits the best properties of the other two methods.