New feature points based on geometric invariants for 3D image registration

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M\"obius Invariants of Shapes and Images

Identifying when different images are of the same object despite changes caused by imaging technologies, or processes such as growth, has many applications in fields such as computer vision and biological image analysis. One approach to this problem is to identify the group of possible transformations of the object and to find invariants to the action of that group, meaning that the object has the same values of the invariants despite the action of the group. In this paper we study the invariants of planar shapes and images under the M\"obius group $\mathrm{PSL}(2,\mathbb{C})$, which arises in the conformal camera model of vision and may also correspond to neurological aspects of vision, such as grouping of lines and circles. We survey properties of invariants that are important in applications, and the known M\"obius invariants, and then develop an algorithm by which shapes can be recognised that is M\"obius- and reparametrization-invariant, numerically stable, and robust to noise. We demonstrate the efficacy of this new invariant approach on sets of curves, and then develop a M\"obius-invariant signature of grey-scale images

A Kind of Affine Weighted Moment Invariants

A new kind of geometric invariants is proposed in this paper, which is called affine weighted moment invariant (AWMI). By combination of local affine differential invariants and a framework of global integral, they can more effectively extract features of images and help to increase the number of low-order invariants and to decrease the calculating cost. The experimental results show that AWMIs have good stability and distinguishability and achieve better results in image retrieval than traditional moment invariants. An extension to 3D is straightforward

Anatomical landmark based registration of contrast enhanced T1-weighted MR images

In many problems involving multiple image analysis, an im- age registration step is required. One such problem appears in brain tumor imaging, where baseline and follow-up image volumes from a tu- mor patient are often to-be compared. Nature of the registration for a change detection problem in brain tumor growth analysis is usually rigid or affine. Contrast enhanced T1-weighted MR images are widely used in clinical practice for monitoring brain tumors. Over this modality, con- tours of the active tumor cells and whole tumor borders and margins are visually enhanced. In this study, a new technique to register serial contrast enhanced T1 weighted MR images is presented. The proposed fully-automated method is based on five anatomical landmarks: eye balls, nose, confluence of sagittal sinus, and apex of superior sagittal sinus. Af- ter extraction of anatomical landmarks from fixed and moving volumes, an affine transformation is estimated by minimizing the sum of squared distances between the landmark coordinates. Final result is refined with a surface registration, which is based on head masks confined to the sur- face of the scalp, as well as to a plane constructed from three of the extracted features. The overall registration is not intensity based, and it depends only on the invariant structures. Validation studies using both synthetically transformed MRI data, and real MRI scans, which included several markers over the head of the patient were performed. In addition, comparison studies against manual landmarks marked by a radiologist, as well as against the results obtained from a typical mutual information based method were carried out to demonstrate the effectiveness of the proposed method

Automated Fragmentary Bone Matching

Identification, reconstruction and matching of fragmentary bones are basic tasks required to accomplish quantification and analysis of fragmentary human remains derived from forensic contexts. Appropriate techniques for three-dimensional surface matching have received great attention in computer vision literature, and various methods have been proposed for matching fragmentary meshes; however, many of these methods lack automation, speed and/or suffer from high sensitivity to noise. In addition, reconstruction of fragementary bones along with identification in the presence of reference model to compare with in an automatic scheme have not been addressed. In order to address these issues, we used a multi-stage technique for fragment identification, matching and registration. The study introduces an automated technique for matching of fragmentary human skeletal remains for improving forensic anthropology practice and policy. The proposed technique involves creation of surfaces models for the fragmentary elements which can be done using computerized tomographic scans followed by segmentation. Upon creation of the fragmentary elements models, the models go through feature extraction technique where the surface roughness map of each model is measured using local shape analysis measures. Adaptive thesholding is then used to extract model features. A multi-stage technique is then used to identify, match and register bone fragments to their corresponding template bone model. First, extracted features are used for matching with different template bone models using iterative closest point algorithm with different positions and orientations. The best match score, in terms of minimum root-mean-square error, is used along with the position and orientation and the resulting transformation to register the fragment bone model with the corresponding template bone model using iterative closest point algorithm

Geometric and photometric affine invariant image registration

This thesis aims to present a solution to the correspondence problem for the registration of wide-baseline images taken from uncalibrated cameras. We propose an affine invariant descriptor that combines the geometry and photometry of the scene to find correspondences between both views. The geometric affine invariant component of the descriptor is based on the affine arc-length metric, whereas the photometry is analysed by invariant colour moments. A graph structure represents the spatial distribution of the primitive features; i.e. nodes correspond to detected high-curvature points, whereas arcs represent connectivities by extracted contours. After matching, we refine the search for correspondences by using a maximum likelihood robust algorithm. We have evaluated the system over synthetic and real data. The method is endemic to propagation of errors introduced by approximations in the system.BAE SystemsSelex Sensors and Airborne System