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In the field of 3D head modeling and animation, feature points are often needed to mark important regions of the face and can be used to animate or deform the input model. However, an automatic detection of features remains a challenging task. This paper presents a novel approach to feature detection based on curvature and its derived descriptors, such as shape index, curvedness and Willmore energy. Four important feature regions are detected using the proposed approach - eyes, nose, mouth, ears. For each region, feature points are detected. Results show that the feature points are detected with sufficient accuracy for further use.

While it is usually not difficult to compute principal curvatures of a smooth surface of sufficient differentiability, it is a rather difficult task when only a polygonal approximation of the surface is available, because of the inherent ambiguity of such representation. A number of different approaches has been proposed in the past that tackle this problem using various techniques. Most papers tend to focus on a particular method, while an comprehensive comparison of the different approaches is usually missing.We present results of a large experiment, involving both common and recently proposed curvature estimation techniques, applied to triangle meshes of varying properties. It turns out that none of the approaches provides reliable results under all circumstances. Motivated by this observation, we investigate mesh statistics, which can be computed from vertex positions and mesh connectivity information only, and which can help in deciding which estimator will work best for a particular case. Finally, we propose a meta-estimator, which makes a choice between existing algorithms based on the value of the mesh statistics, and we demonstrate that such meta-estimator, despite its simplicity, provides considerably more robust results than any existing approach.

Simulace eroze je důležitým problémem v oblasti počítačové grafiky. Nejvýznamnějšími erozními procesy v přírodě jsou zvětrávání a hydraulická eroze. Mnoho metod řeší tyto problémy, ale jsou většinou založeny na výškových mapách nebo objemových datech. Výškové mapy neumožňují simulaci komplexních plně 3D scén, zatímco objemová data mají vysoké nároky na paměť. Navrhujeme sjednocený přístup pro zvětrávání a hydraulickou erozi pracující přímo na trojúhelníkových sítích, což zjednodušuje použití metody v široké škále scénářů. Bereme v úvahu fakt, že rychlost eroze v přírodě je ovlivněna lokálním tvarem erodovaného objektu. Pro odhad rychlosti eroze používáme odhad průměrné křivosti, což má za následek vizuálně věrohodnou simulaci erozních procesů. Výsledky metody demonstrujeme na umělých 3D modelech i na reálných datech. The significant properties of the maximum likelihood (ML) estimate are consistency, normality, and efficiency. While it has been proven that these properties are valid when the sample size approaches infinity, the behavior of an ML estimator when working with small sample sizes is largely unknown. However, in real tasks, we usually do not have sufficient data to completely fulfill the conditions of an optimal ML estimate. The question arises as to what amount of data is required to be able to estimate a Gaussian model that provides sufficiently accurate likelihood estimates. This issue is addressed with respect to the number of dimensions of the pattern space.

Although hydraulic erosion modeling on a GIS terrain models has been addressed by a body of previous work, it still remains an open problem. In GIS, raster representation and triangular irregular networks (TIN) are the most commonly used surface models, because they are simple and offer implicit topological information. However, these data structures do not allow the simulation of erosion on concave terrain features, such as caves or overhangs. Other methods, more commonly used in the computational fluid dynamics, use volumetric data representation. They are able to model the 3D features, but they usually have high memory requirements and are computationally demanding. We propose a novel solution to the hydraulic erosion modeling problem that uses a triangular mesh data structure. Our framework allows for adaptive changes of the mesh resolution according to the local complexity of the terrain, which leads to lower memory requirements when compared to the volumetric approaches. Our data structure also supports the visualization of the concave 3D features, allowing the simulation and visualization of erosion on terrain elements such as tunnels or caves.

Triangular meshes are important in many fields in both basic and applied research that rely on their correctness and accuracy. Many operations with meshes can lead to undesirable situations and the resulting models can be damaged and further unusable. Self-intersection and mesh-to-mesh intersection are types of operations that are often present and can cause such problems. We propose an accurate geometry-based method for local repair of intersecting meshes. The state-of-the-art methods either solve the problem inaccurately, or use methods such as arbitrary precision arithmetic or virtual perturbation to deal with the troublesome boundary cases. Our method represents a robust way to repair intersecting meshes accurately without the need to manipulate with the input data or to employ arbitrary precision arithmetic. The correct solution is obtained through a careful classification of the cases that could result from a numerical imprecision of the floating point arithmetic.