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Certain defects, such as jagged edges and disappearing detail, have long been an annoyance in digitally generated shaded images. Although increasing the resolution or defocusing the display can alternate them, an understanding of these defects leads to more effective methods. This paper explains the observed defects in terms of the allasing phenomenon inherent in sampled signals and discusses prefiltering as a recognized cure. A method for evaluating filters is presented, the application of prefiltering to hidden-surface algorithms is discussed, and an implementation of a filtering tiler is shown accompanied by examples of its effectiveness. [ABSTRACT FROM AUTHOR]

Abstract: Formal models can be useful in computer graphics as a conceptual framework supporting representation systems. This allows to formally derive properties and algorithms and proof their correctness and validity. This paper describes a formal model based on a geometric algebra. This algebra has been used to obtain specific representation systems and study their equivalence. The representation systems derived in a natural way from this model are based on simplicial coverings and can be applied to non-manifold solids and to solids with holes. Representations have been developed for polyhedral and free-form solids. Algorithms described and proved include boolean operations and representation conversion. The paper covers the three abstraction levels: theoretical model, representations and derived algorithms. As a practical application an experimental modeller for free-form solid has been developed (ESC-MOD system: “Extended Simplicial Chains MOdeller”). [Copyright &y& Elsevier]

Abstract: Thinning is a critical pre-processing step to obtain skeletons for pattern analysis. Quadtree and octree are hierarchical data representations in image processing and computer graphics. In this paper, we present new 2-D area-based and 3-D surface-based thinning algorithms for directly converting quadtree and octree representations to skeletons. The computational complexity of our thinning algorithm for a 2-D or a 3-D image with each length N is respectively O(N 2) or O(N 3), which is more efficient than the existing algorithms of O(N 3) or O(N 4). Furthermore, our thinning algorithms can lessen boundary noise spurs and are suited for parallel implementation. [Copyright &y& Elsevier]

In this paper, adaptive mathematical morphology and its application to edge linking are presented to fill in the gaps between edge segments. Broken edges are extended along their slope directions by using the adaptive dilation operation with the suitable sized elliptical structuring elements. The size and orientation of the structuring element are adjusted according to the local properties, such as slope and curvature. Post-processes of thinning and pruning are also applied. The edge-linking operation is performed in an iterative manner, so that the broken edges can be linked up gradually and smoothly while the details of the object shape are preserved. [ABSTRACT FROM AUTHOR]

• Novel adaptive version of Bogdanov chaotic map is introduced and investigated. • General scheme for the hash generation based on the proposed novel chaotic map is presented. • Statistical analysis proves that the confusion and diffusion property of the proposed hash function is strong and stable. • The obtained generation scheme is able to resist the birthday attack and the probability of collisions is small. • The use of different values of adaptive coefficients for the construction of piecewise functions based on adaptive maps allows to adjust the key space of the hash function arbitrarily. Chaotic hash functions are a prospective branch of modern cryptography. Being compared with traditional hashing algorithms, an approach based on deterministic chaos allows achieving diffusion and confusion with less computational costs. Most of the recently proposed chaotic hash functions use piecewise maps. Cryptosystems based on such maps are not vulnerable to attack by the reconstruction of phase space but their key spaces depend on maps parameters and therefore can be insufficient. In this paper, we propose an approach for the construction of piecewise hash functions from adaptive chaotic maps. The idea is to match different values of the adaptive coefficient to several sub-domains of the chaotic map. Thus, the adaptive coefficient values are part of the hash function key. Therefore, an increase in the sub-functions number potentially enhances the cryptographic strength of the algorithm. Thus, hash functions based on novel adaptive maps have larger key space compared to conventional piecewise maps. We explicitly show that the proposed hash generation technique allows obtaining digests with the required statistical properties. Moreover, we run a collision test to prove that the collision probability is small. The obtained results can be useful in chaos-based cryptography as well for the various simulations of real processes and phenomena with chaotic behavior, in computer graphics and multimedia. [ABSTRACT FROM AUTHOR]