Yes / Point set registration has been actively studied in computer vision and graphics. Optimization algorithms are at the core of solving registration problems. Traditional optimization approaches are mainly based on the gradient of objective functions. The derivation of objective functions makes it challenging to find optimal solutions for complex optimization models, especially for those applications where accuracy is critical. Learning-based optimization is a novel approach to address this problem, which learns the gradient direction from datasets. However, many learning-based optimization algorithms learn gradient directions via a single feature extracted from the dataset, which will cause the updating direction to be vulnerable to perturbations around the data, thus falling into a bad stationary point. This paper proposes the General Discriminative Optimization (GDO) method that updates a gradient path automatically through the trade-off among contributions of different features on updating gradients. We illustrate the benefits of GDO with tasks of 3D point set registrations and show that GDO outperforms the state-of-the-art registration methods in terms of accuracy and robustness to perturbations.

Point set registration is a well-researched yet still not a very exploited area in computer vision. As the field of machine learning grows, the possibilities of application expand. This thesis investigates the possibility to expand an already implemented probabilistic machine learning approach to point set registration to more complex, larger datasets gathered in a forest environment. The system used as a starting point was created by Järemo Lawin et. al. [10]. The aim of the thesis was to investigate the possibility to register the forest data with the existing system, without ground-truth poses, with different optimizers, and to implement a SLAM pipeline. Also, older methods were used as a benchmark for evaluation, more specifically iterative closest point(ICP) and fast global registration(FGR).To enable the gathered data to be processed by the registration algorithms, preprocessing was required. Transforming the data points from the coordinate system of the sensor to world relative coordinates via LiDAR base coordinates. Subsequently, the registration was performed with different approaches. Both the KITTI odometry dataset, which RLLReg originally was evaluated with[10], and the gathered forest data were used. Data augmentation was utilized to enable ground-truth-independent training and to increase diversity in the data. In addition, the registration results were used to create a SLAM-pipeline, enabling mapping and localization in the scanned areas. The results showed great potential for using RLLReg to register forest scenes compared to other, older, approaches. Especially, the lack of ground-truth was manageable using data augmentation to create training data. Moreover, there was no evidence that AdaBound improves the system when replacing the Adam-optimizer. Finally, forest models with sensor paths plotted were generated with decent results. However, a potential for post-processing with further refinement is possible. Nevertheless, the possibility of point set registration and LiDAR-SLAM using machine learning has been confirmed.

In this thesis a novel approach in generating 3D IGP is applied using shape grammar, an effective pattern generation method. The particular emphasis here is to generate the motifs (repeat unit) in 3D using parameterization, which can then be manipulated within 3D space to construct architectural structures. Three unique distinctive shape grammar algorithms were developed in 3D; Parameterized Shape Grammar (PSG), Auto-Parameterized Shape Grammar (APSG) and Volumetric Shell Shape Grammar (VSSG). Firstly, the PSG generates the motifs in 3D. It allows one to use a single changeable regular 3D polygon, and forms a motif by given grammar rules including, Euclidean transformations and Boolean operations. Next, APSG was used to construct the architectural structures that manipulates the motif by automating the grammar rules. The APSG forms a wall, a column, a self-similarity star and a dome, the main features of Islamic architecture. However, applying Euclidean transformations to create non-Euclidean surfaces resulted in gaps and or overlaps which does not form a perfect tessellation. This is improved upon by the VSSM, which integrates two key methods, shell mapping and coherent point drift, to map an aesthetically accurate 3D IGM on a given surface. This work has successfully presented methods for creating complex intricate 3D Islamic Geometric Motifs (IGM), and provided an efficient mapping technique to form visually appealing decorated structures. / Partially funded by the Centre of Visual Computing (CVC)