A Combinatorial Solution to Non-Rigid 3D Shape-to-Image Matching

We propose a combinatorial solution for the problem of non-rigidly matching a 3D shape to 3D image data. To this end, we model the shape as a triangular mesh and allow each triangle of this mesh to be rigidly transformed to achieve a suitable matching to the image. By penalising the distance and the relative rotation between neighbouring triangles our matching compromises between image and shape information. In this paper, we resolve two major challenges: Firstly, we address the resulting large and NP-hard combinatorial problem with a suitable graph-theoretic approach. Secondly, we propose an efficient discretisation of the unbounded 6-dimensional Lie group SE(3). To our knowledge this is the first combinatorial formulation for non-rigid 3D shape-to-image matching. In contrast to existing local (gradient descent) optimisation methods, we obtain solutions that do not require a good initialisation and that are within a bound of the optimal solution. We evaluate the proposed method on the two problems of non-rigid 3D shape-to-shape and non-rigid 3D shape-to-image registration and demonstrate that it provides promising results.Comment: 10 pages, 7 figure

Level Set Segmentation with Shape and Appearance Models Using Affine Moment Descriptors

We propose a level set based variational approach that incorporates shape priors into edge-based and region-based models. The evolution of the active contour depends on local and global information. It has been implemented using an efficient narrow band technique. For each boundary pixel we calculate its dynamic according to its gray level, the neighborhood and geometric properties established by training shapes. We also propose a criterion for shape aligning based on affine transformation using an image normalization procedure. Finally, we illustrate the benefits of the our approach on the liver segmentation from CT images

Probabilistic and geometric shape based segmentation methods.

Image segmentation is one of the most important problems in image processing, object recognition, computer vision, medical imaging, etc. In general, the objective of the segmentation is to partition the image into the meaningful areas using the existing (low level) information in the image and prior (high level) information which can be obtained using a number of features of an object. As stated in [1,2], the human vision system aims to extract and use as much information as possible in the image including but not limited to the intensity, possible motion of the object (in sequential images), spatial relations (interaction) as the existing information, and the shape of the object which is learnt from the experience as the prior information. The main objective of this dissertation is to couple the prior information with the existing information since the machine vision system cannot predict the prior information unless it is given. To label the image into meaningful areas, the chosen information is modelled to fit progressively in each of the regions by an optimization process. The intensity and spatial interaction (as the existing information) and shape (as the prior information) are modeled to obtain the optimum segmentation in this study. The intensity information is modelled using the Gaussian distribution. Spatial interaction that describes the relation between neighboring pixels/voxels is modelled by assuming that the pixel intensity depends on the intensities of the neighboring pixels. The shape model is obtained using occurrences of histogram of training shape pixels or voxels. The main objective is to capture the shape variation of the object of interest. Each pixel in the image will have three probabilities to be an object and a background class based on the intensity, spatial interaction, and shape models. These probabilistic values will guide the energy (cost) functionals in the optimization process. This dissertation proposes segmentation frameworks which has the following properties: i) original to solve some of the existing problems, ii) robust under various segmentation challenges, and iii) fast enough to be used in the real applications. In this dissertation, the models are integrated into different methods to obtain the optimum segmentation: 1) variational (can be considered as the spatially continuous), and 2) statistical (can be considered as the spatially discrete) methods. The proposed segmentation frameworks start with obtaining the initial segmentation using the intensity / spatial interaction models. The shape model, which is obtained using the training shapes, is registered to the image domain. Finally, the optimal segmentation is obtained using the optimization of the energy functionals. Experiments show that the use of the shape prior improves considerably the accuracy of the alternative methods which use only existing or both information in the image. The proposed methods are tested on the synthetic and clinical images/shapes and they are shown to be robust under various noise levels, occlusions, and missing object information. Vertebral bodies (VBs) in clinical computed tomography (CT) are segmented using the proposed methods to help the bone mineral density measurements and fracture analysis in bones. Experimental results show that the proposed solutions eliminate some of the existing problems in the VB segmentation. One of the most important contributions of this study is to offer a segmentation framework which can be suitable to the clinical works

Local Color Voxel and Spatial Pattern for 3D Textured Recognition

3D textured retrieval including shape, color dan pattern is still a challenging research. Some approaches are proposed, but voxel-based approach has not much been made yet, where by using this approach, it still keeps both geometry and texture information. It also maps all 3D models into the same dimension. Based on this fact, a novel voxel pattern based is proposed by considering local pattern on a voxel called local color voxel pattern (LCVP). Voxels textured is observed by considering voxel to its neighbors. LCVP is computed around each voxel to its neighbors. LCVP value will indicate uniq pattern on each 3D models. LCVP also quantizes color on each voxel to generate a specific pattern. Shift and reflection circular also will be done. In an additional way, inspired by promising recent results from image processing, this paper also implement spatial pattern which utilizing Weber, Oriented Gradient to extract global spatial descriptor. Finally, a combination of local spectra and spatial and established global features approach called multi Fourier descriptor are proposed. For optimal retrieval, the rank combination is performed between local and global approaches. Experiments were performed by using dataset SHREC'13 and SHREC'14 and showed that the proposed method could outperform some performances to state-of-the-art