Shape Generation using Spatially Partitioned Point Clouds

We propose a method to generate 3D shapes using point clouds. Given a point-cloud representation of a 3D shape, our method builds a kd-tree to spatially partition the points. This orders them consistently across all shapes, resulting in reasonably good correspondences across all shapes. We then use PCA analysis to derive a linear shape basis across the spatially partitioned points, and optimize the point ordering by iteratively minimizing the PCA reconstruction error. Even with the spatial sorting, the point clouds are inherently noisy and the resulting distribution over the shape coefficients can be highly multi-modal. We propose to use the expressive power of neural networks to learn a distribution over the shape coefficients in a generative-adversarial framework. Compared to 3D shape generative models trained on voxel-representations, our point-based method is considerably more light-weight and scalable, with little loss of quality. It also outperforms simpler linear factor models such as Probabilistic PCA, both qualitatively and quantitatively, on a number of categories from the ShapeNet dataset. Furthermore, our method can easily incorporate other point attributes such as normal and color information, an additional advantage over voxel-based representations.Comment: To appear at BMVC 201

Map-Based Localization for Unmanned Aerial Vehicle Navigation

Unmanned Aerial Vehicles (UAVs) require precise pose estimation when navigating in indoor and GNSS-denied / GNSS-degraded outdoor environments. The possibility of crashing in these environments is high, as spaces are confined, with many moving obstacles. There are many solutions for localization in GNSS-denied environments, and many different technologies are used. Common solutions involve setting up or using existing infrastructure, such as beacons, Wi-Fi, or surveyed targets. These solutions were avoided because the cost should be proportional to the number of users, not the coverage area. Heavy and expensive sensors, for example a high-end IMU, were also avoided. Given these requirements, a camera-based localization solution was selected for the sensor pose estimation. Several camera-based localization approaches were investigated. Map-based localization methods were shown to be the most efficient because they close loops using a pre-existing map, thus the amount of data and the amount of time spent collecting data are reduced as there is no need to re-observe the same areas multiple times. This dissertation proposes a solution to address the task of fully localizing a monocular camera onboard a UAV with respect to a known environment (i.e., it is assumed that a 3D model of the environment is available) for the purpose of navigation for UAVs in structured environments. Incremental map-based localization involves tracking a map through an image sequence. When the map is a 3D model, this task is referred to as model-based tracking. A by-product of the tracker is the relative 3D pose (position and orientation) between the camera and the object being tracked. State-of-the-art solutions advocate that tracking geometry is more robust than tracking image texture because edges are more invariant to changes in object appearance and lighting. However, model-based trackers have been limited to tracking small simple objects in small environments. An assessment was performed in tracking larger, more complex building models, in larger environments. A state-of-the art model-based tracker called ViSP (Visual Servoing Platform) was applied in tracking outdoor and indoor buildings using a UAVs low-cost camera. The assessment revealed weaknesses at large scales. Specifically, ViSP failed when tracking was lost, and needed to be manually re-initialized. Failure occurred when there was a lack of model features in the cameras field of view, and because of rapid camera motion. Experiments revealed that ViSP achieved positional accuracies similar to single point positioning solutions obtained from single-frequency (L1) GPS observations standard deviations around 10 metres. These errors were considered to be large, considering the geometric accuracy of the 3D model used in the experiments was 10 to 40 cm. The first contribution of this dissertation proposes to increase the performance of the localization system by combining ViSP with map-building incremental localization, also referred to as simultaneous localization and mapping (SLAM). Experimental results in both indoor and outdoor environments show sub-metre positional accuracies were achieved, while reducing the number of tracking losses throughout the image sequence. It is shown that by integrating model-based tracking with SLAM, not only does SLAM improve model tracking performance, but the model-based tracker alleviates the computational expense of SLAMs loop closing procedure to improve runtime performance. Experiments also revealed that ViSP was unable to handle occlusions when a complete 3D building model was used, resulting in large errors in its pose estimates. The second contribution of this dissertation is a novel map-based incremental localization algorithm that improves tracking performance, and increases pose estimation accuracies from ViSP. The novelty of this algorithm is the implementation of an efficient matching process that identifies corresponding linear features from the UAVs RGB image data and a large, complex, and untextured 3D model. The proposed model-based tracker improved positional accuracies from 10 m (obtained with ViSP) to 46 cm in outdoor environments, and improved from an unattainable result using VISP to 2 cm positional accuracies in large indoor environments. The main disadvantage of any incremental algorithm is that it requires the camera pose of the first frame. Initialization is often a manual process. The third contribution of this dissertation is a map-based absolute localization algorithm that automatically estimates the camera pose when no prior pose information is available. The method benefits from vertical line matching to accomplish a registration procedure of the reference model views with a set of initial input images via geometric hashing. Results demonstrate that sub-metre positional accuracies were achieved and a proposed enhancement of conventional geometric hashing produced more correct matches - 75% of the correct matches were identified, compared to 11%. Further the number of incorrect matches was reduced by 80%

Geometric deep learning

The goal of these course notes is to describe the main mathematical ideas behind geometric deep learning and to provide implementation details for several applications in shape analysis and synthesis, computer vision and computer graphics. The text in the course materials is primarily based on previously published work. With these notes we gather and provide a clear picture of the key concepts and techniques that fall under the umbrella of geometric deep learning, and illustrate the applications they enable. We also aim to provide practical implementation details for the methods presented in these works, as well as suggest further readings and extensions of these ideas

Automatic visual recognition using parallel machines

Invariant features and quick matching algorithms are two major concerns in the area of automatic visual recognition. The former reduces the size of an established model database, and the latter shortens the computation time. This dissertation, will discussed both line invariants under perspective projection and parallel implementation of a dynamic programming technique for shape recognition. The feasibility of using parallel machines can be demonstrated through the dramatically reduced time complexity. In this dissertation, our algorithms are implemented on the AP1000 MIMD parallel machines. For processing an object with a features, the time complexity of the proposed parallel algorithm is O(n), while that of a uniprocessor is O(n2). The two applications, one for shape matching and the other for chain-code extraction, are used in order to demonstrate the usefulness of our methods. Invariants from four general lines under perspective projection are also discussed in here. In contrast to the approach which uses the epipolar geometry, we investigate the invariants under isotropy subgroups. Theoretically speaking, two independent invariants can be found for four general lines in 3D space. In practice, we show how to obtain these two invariants from the projective images of four general lines without the need of camera calibration. A projective invariant recognition system based on a hypothesis-generation-testing scheme is run on the hypercube parallel architecture. Object recognition is achieved by matching the scene projective invariants to the model projective invariants, called transfer. Then a hypothesis-generation-testing scheme is implemented on the hypercube parallel architecture

Nested Invariance Pooling and RBM Hashing for Image Instance Retrieval

The goal of this work is the computation of very compact binary hashes for image instance retrieval. Our approach has two novel contributions. The first one is Nested Invariance Pooling (NIP), a method inspired from i-theory, a mathematical theory for computing group invariant transformations with feed-forward neural networks. NIP is able to produce compact and well-performing descriptors with visual representations extracted from convolutional neural networks. We specifically incorporate scale, translation and rotation invariances but the scheme can be extended to any arbitrary sets of transformations. We also show that using moments of increasing order throughout nesting is important. The NIP descriptors are then hashed to the target code size (32-256 bits) with a Restricted Boltzmann Machine with a novel batch-level reg-ularization scheme specifically designed for the purpose of hashing (RBMH). A thorough empirical evaluation with state-of-the-art shows that the results obtained both with the NIP descriptors and the NIP+RBMH hashes are consistently outstanding across a wide range of datasets