For continuous tomography Helgason and Ludwig developed consistency conditions. They were used by others to overcome defects in the measurements. In this paper we introduce a consistency criterion for discrete tomography. We indicate how the consistency criterion can be used to overcome defects in measurements.

In a recent work, we have proposed a novel way to approximate point sets with grids using the LLL algorithm, which operates in polynomial time. Now, we show how this approach can be applied to pattern recognition purposes with interpreting the rate of approximation as a new feature for regularity measurement. Our practical problem is the characterization of pigment networks in skin lesions. For this task we also introduce a novel image processing method for the extraction of the pigment network. Then, we show how our grid approximation framework can be applied with specializing it for the recognition of hexagonal patterns. The classification performance of our approach for the pigment network characterization problem is measured on a database annotated by a clinical expert. Throughout the paper we address several practical issues that may help to apply our general framework to other practical tasks, as well.

Ensemble-based systems are primarily analyzed on how the accuracy of the ensemble depends on that of its members. In this paper, we extend this model with adding a natural constraint regarding a time limit within which the ensemble should make the decision. For this aim, we consider both the execution time and accuracy of each member. Then, we solve the problem on how to find the most accurate ensemble, where the sum of the execution times of its members remains below the limit. As a decision rule, we analyze a majority voting-based one generalized to be applicable in single object detection scenarios. The optimization task leads to a non-separable Knapsack problem, which is addressed using stochastic considerations. The proposed methodology is also validated experimentally for the localization of the optic disc in retinal images.

In earlier papers we have developed an algebraic theory of discrete tomography. In those papers the structure of the functions $f: A \to \{0,1\}$ and $f: A \to \mathbb{Z}$ having given line sums in certain directions have been analyzed. Here $A$ was a block in $\mathbb{Z}^n$ with sides parallel to the axes. In the present paper we assume that there is noise in the measurements and (only) that $A$ is an arbitrary or convex finite set in $\mathbb{Z}^n$. We derive generalizations of earlier results. Furthermore we apply a method of Beck and Fiala to obtain results of the following type: if the line sums in $k$ directions of a function $h: A \to [0,1]$ are known, then there exists a function $f: A \to \{0,1\}$ such that its line sums differ by at most $k$ from the corresponding line sums of $h$.

Generating ensembles from multiple individual classifiers is a popular approach to raise the accuracy of the decision. As a rule for decision making, majority voting is a usually applied model. In this paper, we generalize classical majority voting by incorporating probability terms pn,k to constrain the basic framework. These terms control whether a correct or false decision is made if k correct votes are present among the total number of n. This generalization is motivated by object detection problems, where the members of the ensemble are image processing algorithms giving their votes as pixels in the image domain. In this scenario, the terms pn,k can be specialized by a geometric constraint. Namely, the votes should fall inside a region matching the size and shape of the object to vote together. We give several theoretical results in this new model for both dependent and independent classifiers, whose individual accuracies may also differ. As a real world example, we present our ensemble-based system developed for the detection of the optic disc in retinal images. For this problem, experimental results are shown to demonstrate the characterization capability of this system. We also investigate how the generalized model can help us to improve an ensemble with extending it by adding a new algorithm.