Local Accuracy and Global Consistency for Efficient SLAM

This thesis is concerned with the problem of Simultaneous Localisation and Mapping (SLAM) using visual data only. Given the video stream of a moving camera, we wish to estimate the structure of the environment and the motion of the device most accurately and in real-time. Two effective approaches were presented in the past. Filtering methods marginalise out past poses and summarise the information gained over time with a probability distribution. Keyframe methods rely on the optimisation approach of bundle adjustment, but computationally must select only a small number of past frames to process. We perform a rigorous comparison between the two approaches for visual SLAM. Especially, we show that accuracy comes from a large number of points, while the number of intermediate frames only has a minor impact. We conclude that keyframe bundle adjustment is superior to ltering due to a smaller computational cost. Based on these experimental results, we develop an efficient framework for large-scale visual SLAM using the keyframe strategy. We demonstrate that SLAM using a single camera does not only drift in rotation and translation, but also in scale. In particular, we perform large-scale loop closure correction using a novel variant of pose-graph optimisation which also takes scale drift into account. Starting from this two stage approach which tackles local motion estimation and loop closures separately, we develop a unified framework for real-time visual SLAM. By employing a novel double window scheme, we present a constant-time approach which enables the local accuracy of bundle adjustment while ensuring global consistency. Furthermore, we suggest a new scheme for local registration using metric loop closures and present several improvements for the visual front-end of SLAM. Our contributions are evaluated exhaustively on a number of synthetic experiments and real-image data-set from single cameras and range imaging devices

Local Accuracy and Global Consistency for Efficient SLAM

This thesis is concerned with the problem of Simultaneous Localisation and Mapping (SLAM) using visual data only. Given the video stream of a moving camera, we wish to estimate the structure of the environment and the motion of the device most accurately and in real-time. Two effective approaches were presented in the past. Filtering methods marginalise out past poses and summarise the information gained over time with a probability distribution. Keyframe methods rely on the optimisation approach of bundle adjustment, but computationally must select only a small number of past frames to process. We perform a rigorous comparison between the two approaches for visual SLAM. Especially, we show that accuracy comes from a large number of points, while the number of intermediate frames only has a minor impact. We conclude that keyframe bundle adjustment is superior to ltering due to a smaller computational cost. Based on these experimental results, we develop an efficient framework for large-scale visual SLAM using the keyframe strategy. We demonstrate that SLAM using a single camera does not only drift in rotation and translation, but also in scale. In particular, we perform large-scale loop closure correction using a novel variant of pose-graph optimisation which also takes scale drift into account. Starting from this two stage approach which tackles local motion estimation and loop closures separately, we develop a unified framework for real-time visual SLAM. By employing a novel double window scheme, we present a constant-time approach which enables the local accuracy of bundle adjustment while ensuring global consistency. Furthermore, we suggest a new scheme for local registration using metric loop closures and present several improvements for the visual front-end of SLAM. Our contributions are evaluated exhaustively on a number of synthetic experiments and real-image data-set from single cameras and range imaging devices

Sparse image approximation with application to flexible image coding

Natural images are often modeled through piecewise-smooth regions. Region edges, which correspond to the contours of the objects, become, in this model, the main information of the signal. Contours have the property of being smooth functions along the direction of the edge, and irregularities on the perpendicular direction. Modeling edges with the minimum possible number of terms is of key importance for numerous applications, such as image coding, segmentation or denoising. Standard separable basis fail to provide sparse enough representation of contours, due to the fact that this kind of basis do not see the regularity of edges. In order to be able to detect this regularity, a new method based on (possibly redundant) sets of basis functions able to capture the geometry of images is needed. This thesis presents, in a first stage, a study about the features that basis functions should have in order to provide sparse representations of a piecewise-smooth image. This study emphasizes the need for edge-adapted basis functions, capable to accurately capture local orientation and anisotropic scaling of image structures. The need of different anisotropy degrees and orientations in the basis function set leads to the use of redundant dictionaries. However, redundant dictionaries have the inconvenience of giving no unique sparse image decompositions, and from all the possible decompositions of a signal in a redundant dictionary, just the sparsest is needed. There are several algorithms that allow to find sparse decompositions over redundant dictionaries, but most of these algorithms do not always guarantee that the optimal approximation has been recovered. To cope with this problem, a mathematical study about the properties of sparse approximations is performed. From this, a test to check whether a given sparse approximation is the sparsest is provided. The second part of this thesis presents a novel image approximation scheme, based on the use of a redundant dictionary. This scheme allows to have a good approximation of an image with a number of terms much smaller than the dimension of the signal. This novel approximation scheme is based on a dictionary formed by a combination of anisotropically refined and rotated wavelet-like mother functions and Gaussians. An efficient Full Search Matching Pursuit algorithm to perform the image decomposition in such a dictionary is designed. Finally, a geometric image coding scheme based on the image approximated over the anisotropic and rotated dictionary of basis functions is designed. The coding performances of this dictionary are studied. Coefficient quantization appears to be of crucial importance in the design of a Matching Pursuit based coding scheme. Thus, a quantization scheme for the MP coefficients has been designed, based on the theoretical energy upper bound of the MP algorithm and the empirical observations of the coefficient distribution and evolution. Thanks to this quantization, our image coder provides low to medium bit-rate image approximations, while it allows for on the fly resolution switching and several other affine image transformations to be performed directly in the transformed domain

Probabilistic and Deep Learning Algorithms for the Analysis of Imagery Data

Accurate object classification is a challenging problem for various low to high resolution imagery data. This applies to both natural as well as synthetic image datasets. However, each object recognition dataset poses its own distinct set of domain-specific problems. In order to address these issues, we need to devise intelligent learning algorithms which require a deep understanding and careful analysis of the feature space. In this thesis, we introduce three new learning frameworks for the analysis of both airborne images (NAIP dataset) and handwritten digit datasets without and with noise (MNIST and n-MNIST respectively). First, we propose a probabilistic framework for the analysis of the NAIP dataset which includes (1) an unsupervised segmentation module based on the Statistical Region Merging algorithm, (2) a feature extraction module that extracts a set of standard hand-crafted texture features from the images, (3) a supervised classification algorithm based on Feedforward Backpropagation Neural Networks, and (4) a structured prediction framework using Conditional Random Fields that integrates the results of the segmentation and classification modules into a single composite model to generate the final class labels. Next, we introduce two new datasets SAT-4 and SAT-6 sampled from the NAIP imagery and use them to evaluate a multitude of Deep Learning algorithms including Deep Belief Networks (DBN), Convolutional Neural Networks (CNN) and Stacked Autoencoders (SAE) for generating class labels. Finally, we propose a learning framework by integrating hand-crafted texture features with a DBN. A DBN uses an unsupervised pre-training phase to perform initialization of the parameters of a Feedforward Backpropagation Neural Network to a global error basin which can then be improved using a round of supervised fine-tuning using Feedforward Backpropagation Neural Networks. These networks can subsequently be used for classification. In the following discussion, we show that the integration of hand-crafted features with DBN shows significant improvement in performance as compared to traditional DBN models which take raw image pixels as input. We also investigate why this integration proves to be particularly useful for aerial datasets using a statistical analysis based on Distribution Separability Criterion. Then we introduce a new dataset called noisy-MNIST (n-MNIST) by adding (1) additive white gaussian noise (AWGN), (2) motion blur and (3) Reduced contrast and AWGN to the MNIST dataset and present a learning algorithm by combining probabilistic quadtrees and Deep Belief Networks. This dynamic integration of the Deep Belief Network with the probabilistic quadtrees provide significant improvement over traditional DBN models on both the MNIST and the n-MNIST datasets. Finally, we extend our experiments on aerial imagery to the class of general texture images and present a theoretical analysis of Deep Neural Networks applied to texture classification. We derive the size of the feature space of textural features and also derive the Vapnik-Chervonenkis dimension of certain classes of Neural Networks. We also derive some useful results on intrinsic dimension and relative contrast of texture datasets and use these to highlight the differences between texture datasets and general object recognition datasets

Robust Subspace Estimation via Low-Rank and Sparse Decomposition and Applications in Computer Vision

PhDRecent advances in robust subspace estimation have made dimensionality reduction and noise and outlier suppression an area of interest for research, along with continuous improvements in computer vision applications. Due to the nature of image and video signals that need a high dimensional representation, often storage, processing, transmission, and analysis of such signals is a difficult task. It is therefore desirable to obtain a low-dimensional representation for such signals, and at the same time correct for corruptions, errors, and outliers, so that the signals could be readily used for later processing. Major recent advances in low-rank modelling in this context were initiated by the work of Cand`es et al. [17] where the authors provided a solution for the long-standing problem of decomposing a matrix into low-rank and sparse components in a Robust Principal Component Analysis (RPCA) framework. However, for computer vision applications RPCA is often too complex, and/or may not yield desirable results. The low-rank component obtained by the RPCA has usually an unnecessarily high rank, while in certain tasks lower dimensional representations are required. The RPCA has the ability to robustly estimate noise and outliers and separate them from the low-rank component, by a sparse part. But, it has no mechanism of providing an insight into the structure of the sparse solution, nor a way to further decompose the sparse part into a random noise and a structured sparse component that would be advantageous in many computer vision tasks. As videos signals are usually captured by a camera that is moving, obtaining a low-rank component by RPCA becomes impossible. In this thesis, novel Approximated RPCA algorithms are presented, targeting different shortcomings of the RPCA. The Approximated RPCA was analysed to identify the most time consuming RPCA solutions, and replace them with simpler yet tractable alternative solutions. The proposed method is able to obtain the exact desired rank for the low-rank component while estimating a global transformation to describe camera-induced motion. Furthermore, it is able to decompose the sparse part into a foreground sparse component, and a random noise part that contains no useful information for computer vision processing. The foreground sparse component is obtained by several novel structured sparsity-inducing norms, that better encapsulate the needed pixel structure in visual signals. Moreover, algorithms for reducing complexity of low-rank estimation have been proposed that achieve significant complexity reduction without sacrificing the visual representation of video and image information. The proposed algorithms are applied to several fundamental computer vision tasks, namely, high efficiency video coding, batch image alignment, inpainting, and recovery, video stabilisation, background modelling and foreground segmentation, robust subspace clustering and motion estimation, face recognition, and ultra high definition image and video super-resolution. The algorithms proposed in this thesis including batch image alignment and recovery, background modelling and foreground segmentation, robust subspace clustering and motion segmentation, and ultra high definition image and video super-resolution achieve either state-of-the-art or comparable results to existing methods

Image compression with anisotropic diffusion

Compression is an important field of digital image processing where well-engineered methods with high performance exist. Partial differential equations (PDEs), however, have not much been explored in this context so far. In our paper we introduce a novel framework for image compression that makes use of the interpolation qualities of edge-enhancing diffusion. Although this anisotropic diffusion equation with a diffusion tensor was originally proposed for image denoising, we show that it outperforms many other PDEs when sparse scattered data must be interpolated. To exploit this property for image compression, we consider an adaptive triangulation method for removing less significant pixels from the image. The remaining points serve as scattered interpolation data for the diffusion process. They can be coded in a compact way that reflects the B-tree structure of the triangulation. We supplement the coding step with a number of amendments such as error threshold adaptation, diffusion-based point selection, and specific quantisation strategies. Our experiments illustrate the usefulness of each of these modifications. They demonstrate that for high compression rates, our PDE-based approach does not only give far better results than the widely-used JPEG standard, but can even come close to the quality of the highly optimised JPEG2000 codec