Graph Spectral Image Processing

Recent advent of graph signal processing (GSP) has spurred intensive studies of signals that live naturally on irregular data kernels described by graphs (e.g., social networks, wireless sensor networks). Though a digital image contains pixels that reside on a regularly sampled 2D grid, if one can design an appropriate underlying graph connecting pixels with weights that reflect the image structure, then one can interpret the image (or image patch) as a signal on a graph, and apply GSP tools for processing and analysis of the signal in graph spectral domain. In this article, we overview recent graph spectral techniques in GSP specifically for image / video processing. The topics covered include image compression, image restoration, image filtering and image segmentation

Joint Image Reconstruction and Segmentation Using the Potts Model

We propose a new algorithmic approach to the non-smooth and non-convex Potts problem (also called piecewise-constant Mumford-Shah problem) for inverse imaging problems. We derive a suitable splitting into specific subproblems that can all be solved efficiently. Our method does not require a priori knowledge on the gray levels nor on the number of segments of the reconstruction. Further, it avoids anisotropic artifacts such as geometric staircasing. We demonstrate the suitability of our method for joint image reconstruction and segmentation. We focus on Radon data, where we in particular consider limited data situations. For instance, our method is able to recover all segments of the Shepp-Logan phantom from $7$ angular views only. We illustrate the practical applicability on a real PET dataset. As further applications, we consider spherical Radon data as well as blurred data

Facial soft tissue segmentation

The importance of the face for socio-ecological interaction is the cause for a high demand on any surgical intervention on the facial musculo-skeletal system. Bones and soft-tissues are of major importance for any facial surgical treatment to guarantee an optimal, functional and aesthetical result. For this reason, surgeons want to pre-operatively plan, simulate and predict the outcome of the surgery allowing for shorter operation times and improved quality. Accurate simulation requires exact segmentation knowledge of the facial tissues. Thus semi-automatic segmentation techniques are required. This thesis proposes semi-automatic methods for segmentation of the facial soft-tissues, such as muscles, skin and fat, from CT and MRI datasets, using a Markov Random Fields (MRF) framework. Due to image noise, artifacts, weak edges and multiple objects of similar appearance in close proximity, it is difficult to segment the object of interest by using image information alone. Segmentations would leak at weak edges into neighboring structures that have a similar intensity profile. To overcome this problem, additional shape knowledge is incorporated in the energy function which can then be minimized using Graph-Cuts (GC). Incremental approaches by incorporating additional prior shape knowledge are presented. The proposed approaches are not object specific and can be applied to segment any class of objects be that anatomical or non-anatomical from medical or non-medical image datasets, whenever a statistical model is present. In the first approach a 3D mean shape template is used as shape prior, which is integrated into the MRF based energy function. Here, the shape knowledge is encoded into the data and the smoothness terms of the energy function that constrains the segmented parts to a reasonable shape. In the second approach, to improve handling of shape variations naturally found in the population, the fixed shape template is replaced by a more robust 3D statistical shape model based on Probabilistic Principal Component Analysis (PPCA). The advantages of using the Probabilistic PCA are that it allows reconstructing the optimal shape and computing the remaining variance of the statistical model from partial information. By using an iterative method, the statistical shape model is then refined using image based cues to get a better fitting of the statistical model to the patient's muscle anatomy. These image cues are based on the segmented muscle, edge information and intensity likelihood of the muscle. Here, a linear shape update mechanism is used to fit the statistical model to the image based cues. In the third approach, the shape refinement step is further improved by using a non-linear shape update mechanism where vertices of the 3D mesh of the statistical model incur the non-linear penalty depending on the remaining variability of the vertex. The non-linear shape update mechanism provides a more accurate shape update and helps in a finer shape fitting of the statistical model to the image based cues in areas where the shape variability is high. Finally, a unified approach is presented to segment the relevant facial muscles and the remaining facial soft-tissues (skin and fat). One soft-tissue layer is removed at a time such as the head and non-head regions followed by the skin. In the next step, bones are removed from the dataset, followed by the separation of the brain and non-brain regions as well as the removal of air cavities. Afterwards, facial fat is segmented using the standard Graph-Cuts approach. After separating the important anatomical structures, finally, a 3D fixed shape template mesh of the facial muscles is used to segment the relevant facial muscles. The proposed methods are tested on the challenging example of segmenting the masseter muscle. The datasets were noisy with almost all possessing mild to severe imaging artifacts such as high-density artifacts caused by e.g. dental fillings and dental implants. Qualitative and quantitative experimental results show that by incorporating prior shape knowledge leaking can be effectively constrained to obtain better segmentation results

Data-Driven Shape Analysis and Processing

Data-driven methods play an increasingly important role in discovering geometric, structural, and semantic relationships between 3D shapes in collections, and applying this analysis to support intelligent modeling, editing, and visualization of geometric data. In contrast to traditional approaches, a key feature of data-driven approaches is that they aggregate information from a collection of shapes to improve the analysis and processing of individual shapes. In addition, they are able to learn models that reason about properties and relationships of shapes without relying on hard-coded rules or explicitly programmed instructions. We provide an overview of the main concepts and components of these techniques, and discuss their application to shape classification, segmentation, matching, reconstruction, modeling and exploration, as well as scene analysis and synthesis, through reviewing the literature and relating the existing works with both qualitative and numerical comparisons. We conclude our report with ideas that can inspire future research in data-driven shape analysis and processing.Comment: 10 pages, 19 figure