Deformable shape matching

Deformable shape matching has become an important building block in academia as well as in industry. Given two three dimensional shapes A and B the deformation function f aligning A with B has to be found. The function is discretized by a set of corresponding point pairs. Unfortunately, the computation cost of a brute-force search of correspondences is exponential. Additionally, to be of any practical use the algorithm has to be able to deal with data coming directly from 3D scanner devices which suffers from acquisition problems like noise, holes as well as missing any information about topology. This dissertation presents novel solutions for solving shape matching: First, an algorithm estimating correspondences using a randomized search strategy is shown. Additionally, a planning step dramatically reducing the matching costs is incorporated. Using ideas of these both contributions, a method for matching multiple shapes at once is shown. The method facilitates the reconstruction of shape and motion from noisy data acquired with dynamic 3D scanners. Considering shape matching from another perspective a solution is shown using Markov Random Fields (MRF). Formulated as MRF, partial as well as full matches of a shape can be found. Here, belief propagation is utilized for inference computation in the MRF. Finally, an approach significantly reducing the space-time complexity of belief propagation for a wide spectrum of computer vision tasks is presented.Anpassung deformierbarer Formen ist zu einem wichtigen Baustein in der akademischen Welt sowie in der Industrie geworden. Gegeben zwei dreidimensionale Formen A und B, suchen wir nach einer Verformungsfunktion f, die die Deformation von A auf B abbildet. Die Funktion f wird durch eine Menge von korrespondierenden Punktepaaren diskretisiert. Leider sind die Berechnungskosten für eine Brute-Force-Suche dieser Korrespondenzen exponentiell. Um zusätzlich von einem praktischen Nutzen zu sein, muss der Suchalgorithmus in der Lage sein, mit Daten, die direkt aus 3D-Scanner kommen, umzugehen. Bedauerlicherweise leiden diese Daten unter Akquisitionsproblemen wie Rauschen, Löcher sowie fehlender Topologieinformation. In dieser Dissertation werden neue Lösungen für das Problem der Formanpassung präsentiert. Als erstes wird ein Algorithmus gezeigt, der die Korrespondenzen mittels einer randomisierten Suchstrategie schätzt. Zusätzlich wird anhand eines automatisch berechneten Schätzplanes die Geschwindigkeit der Suchstrategie verbessert. Danach wird ein Verfahren gezeigt, dass die Anpassung mehrerer Formen gleichzeitig bewerkstelligen kann. Diese Methode ermöglicht es, die Bewegung, sowie die eigentliche Struktur des Objektes aus verrauschten Daten, die mittels dynamischer 3D-Scanner aufgenommen wurden, zu rekonstruieren. Darauffolgend wird das Problem der Formanpassung aus einer anderen Perspektive betrachtet und als Markov-Netzwerk (MRF) reformuliert. Dieses ermöglicht es, die Formen auch stückweise aufeinander abzubilden. Die eigentliche Lösung wird mittels Belief Propagation berechnet. Schließlich wird ein Ansatz gezeigt, der die Speicher-Zeit-Komplexität von Belief Propagation für ein breites Spektrum von Computer-Vision Problemen erheblich reduziert

Matching deformierbarer Formen

Deformable shape matching has become an important building block in academia as well as in industry. Given two three dimensional shapes A and B the deformation function f aligning A with B has to be found. The function is discretized by a set of corresponding point pairs. Unfortunately, the computation cost of a brute-force search of correspondences is exponential. Additionally, to be of any practical use the algorithm has to be able to deal with data coming directly from 3D scanner devices which suffers from acquisition problems like noise, holes as well as missing any information about topology. This dissertation presents novel solutions for solving shape matching: First, an algorithm estimating correspondences using a randomized search strategy is shown. Additionally, a planning step dramatically reducing the matching costs is incorporated. Using ideas of these both contributions, a method for matching multiple shapes at once is shown. The method facilitates the reconstruction of shape and motion from noisy data acquired with dynamic 3D scanners. Considering shape matching from another perspective a solution is shown using Markov Random Fields (MRF). Formulated as MRF, partial as well as full matches of a shape can be found. Here, belief propagation is utilized for inference computation in the MRF. Finally, an approach significantly reducing the space-time complexity of belief propagation for a wide spectrum of computer vision tasks is presented.Anpassung deformierbarer Formen ist zu einem wichtigen Baustein in der akademischen Welt sowie in der Industrie geworden. Gegeben zwei dreidimensionale Formen A und B, suchen wir nach einer Verformungsfunktion f, die die Deformation von A auf B abbildet. Die Funktion f wird durch eine Menge von korrespondierenden Punktepaaren diskretisiert. Leider sind die Berechnungskosten für eine Brute-Force-Suche dieser Korrespondenzen exponentiell. Um zusätzlich von einem praktischen Nutzen zu sein, muss der Suchalgorithmus in der Lage sein, mit Daten, die direkt aus 3D-Scanner kommen, umzugehen. Bedauerlicherweise leiden diese Daten unter Akquisitionsproblemen wie Rauschen, Löcher sowie fehlender Topologieinformation. In dieser Dissertation werden neue Lösungen für das Problem der Formanpassung präsentiert. Als erstes wird ein Algorithmus gezeigt, der die Korrespondenzen mittels einer randomisierten Suchstrategie schätzt. Zusätzlich wird anhand eines automatisch berechneten Schätzplanes die Geschwindigkeit der Suchstrategie verbessert. Danach wird ein Verfahren gezeigt, dass die Anpassung mehrerer Formen gleichzeitig bewerkstelligen kann. Diese Methode ermöglicht es, die Bewegung, sowie die eigentliche Struktur des Objektes aus verrauschten Daten, die mittels dynamischer 3D-Scanner aufgenommen wurden, zu rekonstruieren. Darauffolgend wird das Problem der Formanpassung aus einer anderen Perspektive betrachtet und als Markov-Netzwerk (MRF) reformuliert. Dieses ermöglicht es, die Formen auch stückweise aufeinander abzubilden. Die eigentliche Lösung wird mittels Belief Propagation berechnet. Schließlich wird ein Ansatz gezeigt, der die Speicher-Zeit-Komplexität von Belief Propagation für ein breites Spektrum von Computer-Vision Problemen erheblich reduziert

Global Depth from Epipolar Volumes - A General Framework for Reconstructing Non-Lambertian Surfaces

Using Epipolar Image Analysis in the context of the correspondence finding problem in depth reconstruction has several advantages. One is the elegant incorporation of prior knowledge about the scene or the surface reflection properties into the reconstruction process. The proposed framework in conjunction with graph cut optimization is able to reconstruct also highly specular surfaces. The use of prior knowledge and multiple images opens new ways to reconstruct surfaces and scenes impossible or error prone with previous methods. Another advantage is improved occlusion handling. Pixels that are partly occluded contribute to the reconstruction results. The proposed shifting of some of the computation to graphics hardware (GPU) results in a significant speed improvement compared to pure CPUbased implementations

Maximum mipmaps for fast, accurate, and scalable dynamic height field rendering

This paper presents a GPU-based, fast, and accurate dynamic height field rendering technique that scales well to large scale height fields. Current real-time rendering algorithms for dynamic height fields employ approximate ray-height field intersection methods, whereas accurate algorithms require pre-computation in the order of seconds to minutes and are thus not suitable for dynamic height field rendering. We alleviate this problem by using maximum mipmaps, a hierarchical data structure supporting accurate and efficient rendering while simultaneously lowering the pre-computation costs to negligible levels. Furthermore, maximum mipmaps allow for view-dependent level-of-detail rendering. In combination with hierarchical ray-stepping this results in an efficient intersection algorithm for large scale height fields

A probabilistic framework for partial intrinsic symmetries in geometric data

In this paper, we present a novel algorithm for partial intrinsic symmetry detection in 3D geometry. Unlike previous work, our algorithm is based on a conceptually simple and straightforward probabilistic formulation of partial shape matching: based on a Markov random field model, we obtain a probability distribution over all possible intrinsic matches of a shape to itself, which reveals the symmetry structure of the object. Rather than examining this exponentially sized distribution directly, which is infeasible, we approximate marginals of this distribution using sumproduct loopy belief propagation and show how the symmetry information can subsequently be extracted from this condensed representation. Using a parallel implementation on graphics hardware, we are able to extract symmetries of deformable shapes in general poses efficiently. We apply our algorithm on several standard 3D models, demonstrating that a concise probabilistic model yields a practical and general symmetry detection algorithm. 1

through Histogram Pyramids

Image Pyramids, as created during a reduction process of 2D image maps, are frequently used in porting non-local algorithms to graphics hardware. A Histogram pyramid (short: HistoPyramid), a special version of image pyramid, collects the number of active entries in a 2D image. We show how a HistoPyramid can be utilized as an implicit indexing data structure, allowing us to convert a sparse 3D volume into a point cloud entirely on the graphics hardware. In the generalized form, the algorithm reduces a highly sparse matrix with N elements to a list of its M active entries in O(N) + M (log N) steps, despite the restricted graphics hardware architecture. Our method can be used to deliver new and unusual visual effects, such a

IEEE INTERNATIONAL CONFERENCE ON SHAPE MODELING AND APPLICATIONS (SMI) 2009 1 Feature Sensitive Bas Relief Generation

Fig. 1. (a) a real world bas relief; (b) a geometric montage of 3 models; (c) a cubism like relief of the David head model; (d) an original Picasso painting Abstract—Among all forms of sculpture, bas-relief is arguably the closest to painting. Although inherently a two dimensional sculpture, a bas-relief suggests a visual spatial extension of the scene in depth through the combination of composition, perspective, and shading. Most recently, there have been significant results on digital bas-relief generation but many of the existing techniques may wash out high level surface detail during the compression process. The primary goal of this work is to address the problem of fine features by tailoring a filtering technique that achieves good compression without compromising the quality of surface details. As a secondary application we explore the generation of artistic relief which mimic cubism in painting and we show how it could be used for generating Picasso like portraits. Keywords—shape deformation, computer art, sculpture, tone mappin

Real-time Generation of Digital Bas-Reliefs

Bas-relief is a form of sculpture where carved or chiseled forms protrude partially and shallowly from the background. Occupying an intermediate place between painting and full 3D sculpture, bas-relief sculpture exploits properties of human visual perception in order to maintain perceptually salient 3D information. In this paper, we present two methods for automatic bas-relief generation from 3D digital shapes. Both methods are inspired by techniques developed for high dynamic range image compression and have the bilateral filter as the main ingredient. We demonstrate that the methods are capable of preserving fine shape features and achieving good compression without compromising the quality of surface details. For artists, bas-relief generation starts from managing the viewer's point of view and compositing the scene. Therefore we strive in our work to streamline this process by focusing on easy and intuitive user interaction which is paramount to artistic applications. Our algorithms allow for real time computation thanks to our implementation on graphics hardware. Besides interactive production of stills, this work offers the possibility for generating bas-relief animations. Last but not least, we explore the generation of artistic reliefs that mimic cubism in painting

Eikonal rendering: efficient light transport in refractive objects

Figure 1: Real-time renderings of complex refractive objects – (left) glass with red wine casting a colorful caustic, 24.8 fps. (middle) Amberlike bunny with black embeddings showing anisotropic scattering and volume caustics in the surrounding smoke and its interior, 13.0 fps. (right) Rounded cube composed of three differently colored and differently refracting kinds of glass showing scattering effects and caustics in its interior, 6.4 fps. We present a new method for real-time rendering of sophisticated lighting effects in and around refractive objects. It enables us to realistically display refractive objects with complex material properties, such as arbitrarily varying refractive index, inhomogeneous attenuation, as well as spatially-varying anisotropic scattering and reflectance properties. User-controlled changes of lighting positions only require a few seconds of update time. Our method is based on a set of ordinary differential equations derived from the eikonal equation, the main postulate of geometric optics. This set of equations allows for fast casting of bent light rays with the complexity of a particle tracer. Based on this concept, we also propose an efficient light propagation technique using adaptive wavefront tracing. Efficient GPU implementations for our algorithmic concepts enable us to render a combination of visual effects that were previously not reproducible in real-time