A morphable model for the synthesis of 3D faces

The rapid increase in the performance of graphics hardware, coupled with recent improvements in its programmability, have made graphics hardware a compelling platform for computationally demanding tasks in a wide variety of application domains. In this report, we describe, summarize, and analyze the latest research in mapping general-purpose computation to graphics hardware. We begin with the technical motivations that underlie general-purpose computation on graphics processors (GPGPU) and describe the hardware and software developments that have led to the recent interest in this field. We then aim the main body of this report at two separate audiences. First, we describe the techniques used in mapping general-purpose computation to graphics hardware. We believe these techniques will be generally useful for researchers who plan to develop the next generation of GPGPU algorithms and techniques. Second, we survey and categorize the latest developments in general-purpose application development on graphics hardware. This survey should be of particular interest to researchers who are interested in using the latest GPGPU applications in their systems of interest.

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A Survey of General-Purpose Computation on Graphics Hardware

Real and Complex Analysis

A Survey of General-Purpose Computation on Graphics Hardware.

General Topology-I

A variational method for nonrigid registration of multimodal image data is presented. A suitable deformation will be determined via the minimization of a morphological, i.e., contrast invariant, matching functional along with an appropriate regularization energy. The aim is to correlate the morphologies of a template and a reference image under the deformation. Mathematically, the morphology of images can be described by the entity of level sets of the image and hence by its Gauss map. A class of morphological matching functionals is presented which measure the defect of the template Gauss map in the deformed state with respect to the deformed Gauss map of the reference image. The problem is regularized by considering a nonlinear elastic regularization energy. Existence of homeomorphic, minimizing deformation is proved under assumptions on the class of admissible deformations. With respect to actual medical applications, suitable generalizations of the matching energies and the boundary conditions are pre...

A Variational Approach to Nonrigid Morphological Image Registration

A level set formulation of Willmore flow is derived using the gradient flow perspective. Starting from single embedded surfaces and the corresponding gradient flow, the metric is generalized to sets of level set surfaces using the identification of normal velocities and variations of the level set function in time via the level set equation. This approach in particular allows one to identify the natural dependent quantities of the derived variational formulation. Furthermore, spatial and temporal discretizations are discussed and some numerical simulations are presented. 2000 Mathematics Subject Classification: 35K55, 53C44, 65M60, 74S05.

https://www.ems-ph.org/journals/show_pdf.php?issn=1463-9963&vol=6&iss=3&rank=6

A level set formulation for Willmore flow

Multimodal image registration significantly benefits from previous denoising and structure segmentation and vice versa. In particular, combined information of different image modalities makes segmentation significantly more robust. Indeed, fundamental tasks in image processing are highly interdependent. A variational approach is presented, which combines the detection of corresponding edges, an edge preserving denoising, and the morphological registration via a nonrigid deformation for a pair of images with structural correspondence. The morphology of an image function is split into a singular part consisting of the edge set and a regular part represented by the field of normals on the ensemble of level sets. A Mumford-Shah type free discontinuity problem is applied to treat the singular morphology and the matching of corresponding edges under the deformation. The matching of the regular morphology is quantified by a second contribution, which compares deformed normals and normals at deformed positions. Finally, a nonlinear elastic energy controls the deformation itself and ensures smoothness and injectivity. A multiscale approach that is based on a phase field approximation leads to an effective and efficient algorithm. Numerical experiments underline the robustness of the presented approach and show applications on medical images.

Multiscale Joint Segmentation and Registration of Image Morphology

An efficient adaptive multigrid level set method for front propagation purposes in three dimensional medical image segmentation is presented. It is able to deal with non sharp segment boundaries. A flexible, interactive modulation of the front speed depending on various boundary and regularization criteria ensure this goal. Efficiency is due to a graded underlying mesh implicitly defined via error or feature indicators. A suitable saturation condition ensures an important regularity condition on the resulting adaptive grid. As a casy study the segmentation of glioma is considered. The clinician interactively selects a few parameters describing the speed function and a few seed points. The automatic process of front propagation then generates a family of segments corresponding to the evolution of the front in time, from which the clinician finally selects an appropriate segment covered by the gliom. Thus, the overall glioma segmentation turns into an efficient, nearly real time process with intuitive and usefully restricted user interaction.

/pdf/an-adaptive-level-set-method-for-medical-image-segmentation-3ehz1k8qyz.pdf

An Adaptive Level Set Method for Medical Image Segmentation

Establishing a correspondence between two surfaces is a basic ingredient in many geometry processing applications. Existing approaches, which attempt to match two meshes directly in 3D, can be cumbersome to implement and it is often hard to produce accurate results in a reasonable amount of time. In this paper, we present a new variational method for matching surfaces that addresses these issues. Instead of matching two surfaces directly in 3D, we apply well-established matching methods from image processing in the parameter domains of the surfaces. A matching energy is introduced that can depend on curvature, feature demarcations or surface textures, and a regularization energy controls length and area changes in the induced non-rigid deformation between the two surfaces. The metric on both surfaces is properly incorporated into the formulation of the energy. This approach reduces all computations to the 2D setting while accounting for the original geometries. Consequently a fast multiresolution numerical algorithm for regular image grids can be used to solve the global optimization problem. The final algorithm is robust, generically much simpler than direct matching methods, and very fast for highly resolved triangle meshes.

Marc Droske

Papers

A Variational Approach to Nonrigid Morphological Image Registration

A level set formulation for Willmore flow

Multiscale Joint Segmentation and Registration of Image Morphology

An Adaptive Level Set Method for Medical Image Segmentation

An image processing approach to surface matching