POSE: Pseudo Object Space Error for Initialization-Free Bundle Adjustment

Bundle adjustment is a nonlinear refinement method for camera poses and 3D structure requiring sufficiently good initialization. In recent years, it was experimentally observed that useful minima can be reached even from arbitrary initialization for affine bundle adjustment problems (and fixed-rank matrix factorization instances in general). The key success factor lies in the use of the variable projection (VarPro) method, which is known to have a wide basin of convergence for such problems. In this paper, we propose the Pseudo Object Space Error (pOSE), which is an objective with cameras represented as a hybrid between the affine and projective models. This formulation allows us to obtain 3D reconstructions that are close to the true projective reconstructions while retaining a bilinear problem structure suitable for the VarPro method. Experimental results show that using pOSE has a high success rate to yield faithful 3D reconstructions from random initializations, taking one step towards initialization-free structure from motion

Graph matching with a dual-step EM algorithm

This paper describes a new approach to matching geometric structure in 2D point-sets. The novel feature is to unify the tasks of estimating transformation geometry and identifying point-correspondence matches. Unification is realized by constructing a mixture model over the bipartite graph representing the correspondence match and by affecting optimization using the EM algorithm. According to our EM framework, the probabilities of structural correspondence gate contributions to the expected likelihood function used to estimate maximum likelihood transformation parameters. These gating probabilities measure the consistency of the matched neighborhoods in the graphs. The recovery of transformational geometry and hard correspondence matches are interleaved and are realized by applying coupled update operations to the expected log-likelihood function. In this way, the two processes bootstrap one another. This provides a means of rejecting structural outliers. We evaluate the technique on two real-world problems. The first involves the matching of different perspective views of 3.5-inch floppy discs. The second example is furnished by the matching of a digital map against aerial images that are subject to severe barrel distortion due to a line-scan sampling process. We complement these experiments with a sensitivity study based on synthetic data

Multi-resolution dental image registration based on genetic algorithm

The Automated Dental Identification System (ADIS) is a Post Mortem Dental Identification System. This thesis presents dental image registration, required for the preprocessing steps of the image comparison component of ADIS. We proposed a multi resolution dental image registration based on genetic algorithms. The main objective of this research is to develop techniques for registration of extracted subject regions of interest with corresponding reference regions of interest.;We investigated and implemented registration using two multi resolution techniques namely image sub sampling and wavelet decomposition. Multi resolution techniques help in the reduction of search data since initial registration is carried at lower levels and results are updated as the levels of resolutions increase. We adopted edges as image features that needed to be aligned. Affine transformations were selected to transform the subject dental region of interest to achieve better alignment with the reference region of interest. These transformations are known to capture complex image distortions. The similarity between subject and reference image has been computed using Oriented Hausdorff Similarity measure that is robust to severe noise and image degradations. A genetic algorithm was adopted to search for the best transformation parameters that give maximum similarity score.;Testing results show that the developed registration algorithm yielded reasonable results in accuracy for dental test cases that contained slight misalignments. The relative percentage errors between the known and estimated transformation parameters were less than 20% with a termination criterion of a ten minute time limit. Further research is needed for dental cases that contain high degree of misalignment, noise and distortions

Equivariance and Invariance for Robust Unsupervised and Semi-Supervised Learning

Although there is a great success of applying deep learning on a wide variety of tasks, it heavily relies on a large amount of labeled training data, which could be hard to obtain in many real scenarios. To address this problem, unsupervised and semi-supervised learning emerge to take advantage of the plenty of cheap unlabeled data to improve the model generalization. In this dissertation, we claim that equivariant and invariance are two critical criteria to approach robust unsupervised and semi-supervised learning. The idea is as follows: the features of a robust model ought to be sufficiently informative and equivariant to transformations on the input data, and the classifiers should be resilient and invariant to small perturbations on the data manifold and model parameters. Specifically, features are learnt via auto-encoding the transformations on the input data, and models are regularized through minimizing the effects of perturbations on features or model parameters. Experiments on several benchmarks show the proposed methods outperform many state-of-the-art approaches on unsupervised and semi-supervised learning, proving importance of the equivariance and invariance rules for robust feature representation learning

Shape/image registration for medical imaging : novel algorithms and applications.

This dissertation looks at two different categories of the registration approaches: Shape registration, and Image registration. It also considers the applications of these approaches into the medical imaging field. Shape registration is an important problem in computer vision, computer graphics and medical imaging. It has been handled in different manners in many applications like shapebased segmentation, shape recognition, and tracking. Image registration is the process of overlaying two or more images of the same scene taken at different times, from different viewpoints, and/or by different sensors. Many image processing applications like remote sensing, fusion of medical images, and computer-aided surgery need image registration. This study deals with two different applications in the field of medical image analysis. The first one is related to shape-based segmentation of the human vertebral bodies (VBs). The vertebra consists of the VB, spinous, and other anatomical regions. Spinous pedicles, and ribs should not be included in the bone mineral density (BMD) measurements. The VB segmentation is not an easy task since the ribs have similar gray level information. This dissertation investigates two different segmentation approaches. Both of them are obeying the variational shape-based segmentation frameworks. The first approach deals with two dimensional (2D) case. This segmentation approach starts with obtaining the initial segmentation using the intensity/spatial interaction models. Then, shape model is registered to the image domain. Finally, the optimal segmentation is obtained using the optimization of an energy functional which integrating the shape model with the intensity information. The second one is a 3D simultaneous segmentation and registration approach. The information of the intensity is handled by embedding a Willmore flow into the level set segmentation framework. Then the shape variations are estimated using a new distance probabilistic model. The experimental results show that the segmentation accuracy of the framework are much higher than other alternatives. Applications on BMD measurements of vertebral body are given to illustrate the accuracy of the proposed segmentation approach. The second application is related to the field of computer-aided surgery, specifically on ankle fusion surgery. The long-term goal of this work is to apply this technique to ankle fusion surgery to determine the proper size and orientation of the screws that are used for fusing the bones together. In addition, we try to localize the best bone region to fix these screws. To achieve these goals, the 2D-3D registration is introduced. The role of 2D-3D registration is to enhance the quality of the surgical procedure in terms of time and accuracy, and would greatly reduce the need for repeated surgeries; thus, saving the patients time, expense, and trauma