Extreme Learning Machine (ELM) is a training algorithm for Single-Layer Feed-forward Neural Network (SLFN). The difference in theory of ELM from other training algorithms is in the existence of explicitly-given solution due to the immutability of initialed weights. In practice, ELMs achieve performance similar to that of other state-of-the-art training techniques, while taking much less time to train a model. Experiments show that the speedup of training ELM is up to the 5 orders of magnitude comparing to standard Error Back-propagation algorithm. ELM is a recently discovered technique that has proved its efficiency in classic regression and classification tasks, including multi-class cases. In this thesis, extensions of ELMs for non-typical for Artificial Neural Networks (ANNs) problems are presented. The first extension, described in the third chapter, allows to use ELMs to get probabilistic outputs for multi-class classification problems. The standard way of solving this type of problems is based 'majority vote' of classifier's raw outputs. This approach can rise issues if the penalty for misclassification is different for different classes. In this case, having probability outputs would be more useful. In the scope of this extension, two methods are proposed. Additionally, an alternative way of interpreting probabilistic outputs is proposed. ELM method prove useful for non-linear dimensionality reduction and visualization, based on repetitive re-training and re-evaluation of model. The forth chapter introduces adaptations of ELM-based visualization for classification and regression tasks. A set of experiments has been conducted to prove that these adaptations provide better visualization results that can then be used for perform classification or regression on previously unseen samples. Shape registration of 3D models with non-isometric distortion is an open problem in 3D Computer Graphics and Computational Geometry. The fifth chapter discusses a novel approach for solving this problem by introducing a similarity metric for spectral descriptors. Practically, this approach has been implemented in two methods. The first one utilizes Siamese Neural Network to embed original spectral descriptors into a lower dimensional metric space, for which the Euclidean distance provides a good measure of similarity. The second method uses Extreme Learning Machines to learn similarity metric directly for original spectral descriptors. Over a set of experiments, the consistency of the proposed approach for solving deformable registration problem has been proven.

Registration means to bring two or more shapes into a suitable relative configuration (position and orientation). In its major applications like 3D scan alignment, the aim is to coalesce data and regions originating from the same physical region have similar local form. So, the correspondence between shapes is discoverable from the shapes themselves, and the registration makes corresponding regions coincide. This work concerns the registration of shapes to satisfy a purpose or intent, not involving data integration. Regions relevant to the purpose are marked as patches correspondingly on two input 3D meshes of objects. Then, a method of registration is used to obtain the suitable configuration. Three methods of registration are explored in the present work. The first method of registration is to align intrinsic co-ordinate frames defined on the shapes. This is used in a scenario of comparison of shapes with dissimilar local form, which are to be aligned as an expert requires, as in the comparison of dental casts and apple bitemarks in forensics. Regions recognized in dentistry are marked as patches on the cast and bitemark shapes by a dentist. From these, an intrinsic frame is defined and aligned to bring the shapes close. The alignment is used to calculate distortion of a deteriorated bitemark. Another application of frame alignment is the analysis of shape variation of contours in a population for wearable product design. A frame based on anthropometric landmarks is used to construct the contours of the product's interface with the body-part, analyze its spread through a 2D grid-statistics method, and construct the interface shape. The frame helps assess the fit of the constructed shape on an individual. The method is demonstrated with respirator masks. Frame-based alignment is seen to give unsatisfactory results with head shapes for motorcycle-helmet interior design, as it does not adequately describe the helmet-head interaction. This inspires the second method of registration. The second method of registration is the biased minimization of distance between corresponding patches on the shapes, by weighting patches to indicate their importance in the registration. The method is used to assess the small deviation of precisely-known quantities in shapes, such as in manufactured part inspection. Here, the patches marked are grouped, and the part and model shapes registered at patches in the combinations of groups, by giving a binary weighting of 1 to these patches and 0 to others. The deviation of every patch across the registrations at multiple datum systems is tabulated and analyzed to infer errors. The method is exemplified with welded bars and bent-pipes. In the analysis of head-shape variation in a population to create headforms for wearable products, the deviations are large and not precisely known. So, the head shapes are registered at patches on regions pertinent to the product's functioning, with a relatively higher weight for a reference patch. A 3D grid-statistics method is used to analyze the shapes' spread and arrive at the headform shapes. The selection of head form for a given head shape is also treated. The method is demonstrated with motorcycle helmets and respirator masks. Biased distance-minimization is applied to obtain the mechanical assembly of part meshes. Different schemes of marking patches are tested as cases. The method leads to both intended and unintended final configurations, prompting for a better objective in registration. Thus, the third method of registration, that of normals is proposed; this happens in a transformed space. By analyzing the nature of assembly in CAD systems, the face-normals of the mesh are used to obtain the intended orientation of parts. The normals of corresponding patches are registered using three methods of registration, namely on a unit-sphere, of unit-normals, and spherical co-ordinates of normals. In each method, the optimal transformation is suitably converted to be applied on the actual part shape in 3D. Unit-normal alignment gives sensible results, while the other two lead to skewed final orientations. This is attributed to the nature of the space of registration. The methods are applied to examples involving different assembly relations, such as alignment of holes. On the whole, it is shown that correspondence embodies the knowledge of importance of regions on shapes for a purpose. The registration method should lead to an apt shape placement, which need not always mean coincidence. In essence, correspondence denotes 'what' regions are of relevance, and registration, 'how' to get the relative configuration satisfying a purpose or intent.

The primary goal of this dissertation is to develop point-based rigid and non-rigid image registration methods that have better accuracy than existing methods. We first present point-based PoIRe, which provides the framework for point-based global rigid registrations. It allows a choice of different search strategies including (a) branch-and-bound, (b) probabilistic hill-climbing, and (c) a novel hybrid method that takes advantage of the best characteristics of the other two methods. We use a robust similarity measure that is insensitive to noise, which is often introduced during feature extraction. We show the robustness of PoIRe using it to register images obtained with an electronic portal imaging device (EPID), which have large amounts of scatter and low contrast. To evaluate PoIRe we used (a) simulated images and (b) images with fiducial markers; PoIRe was extensively tested with 2D EPID images and images generated by 3D Computer Tomography (CT) and Magnetic Resonance (MR) images. PoIRe was also evaluated using benchmark data sets from the blind retrospective evaluation project (RIRE). We show that PoIRe is better than existing methods such as Iterative Closest Point (ICP) and methods based on mutual information. We also present a novel point-based local non-rigid shape registration algorithm. We extend the robust similarity measure used in PoIRe to non-rigid registrations adapting it to a free form deformation (FFD) model and making it robust to local minima, which is a drawback common to existing non-rigid point-based methods. For non-rigid registrations we show that it performs better than existing methods and that is less sensitive to starting conditions. We test our non-rigid registration method using available benchmark data sets for shape registration. Finally, we also explore the extraction of features invariant to changes in perspective and illumination, and explore how they can help improve the accuracy of multi-modal registration. For multimodal registration of EPID-DRR images we present a method based on a local descriptor defined by a vector of complex responses to a circular Gabor filter.