Higher-Order Regularization in Computer Vision

At the core of many computer vision models lies the minimization of an objective function consisting of a sum of functions with few arguments. The order of the objective function is defined as the highest number of arguments of any summand. To reduce ambiguity and noise in the solution, regularization terms are included into the objective function, enforcing different properties of the solution. The most commonly used regularization is penalization of boundary length, which requires a second-order objective function. Most of this thesis is devoted to introducing higher-order regularization terms and presenting efficient minimization schemes. One of the topics of the thesis covers a reformulation of a large class of discrete functions into an equivalent form. The reformulation is shown, both in theory and practical experiments, to be advantageous for higher-order regularization models based on curvature and second-order derivatives. Another topic is the parametric max-flow problem. An analysis is given, showing its inherent limitations for large-scale problems which are common in computer vision. The thesis also introduces a segmentation approach for finding thin and elongated structures in 3D volumes. Using a line-graph formulation, it is shown how to efficiently regularize with respect to higher-order differential geometric properties such as curvature and torsion. Furthermore, an efficient optimization approach for a multi-region model is presented which, in addition to standard regularization, is able to enforce geometric constraints such as inclusion or exclusion of different regions. The final part of the thesis deals with dense stereo estimation. A new regularization model is introduced, penalizing the second-order derivatives of a depth or disparity map. Compared to previous second-order approaches to dense stereo estimation, the new regularization model is shown to be more easily optimized

Geocoder: An Efficient Backscatter Map Constructor

The acoustic backscatter acquired by multibeam and sidescan sonars carries important information about the seafloor morphology and physical properties, providing valuable data to aid the difficult task of seafloor characterization, and important auxiliary information for a bathymetric survey. One necessary step towards this characterization is the assemblage of more consistent and more accurate mosaics of acoustic backscatter. For that, it is necessary to radiometrically correct the backscatter intensities registered by these sonars, to geometrically correct and position each acoustic sample in a projection coordinate system and to interpolate properly the intensity values into a final backscatter map. Geocoder is a software tool that implements the ideas discussed above. Initially, the original backscatter time series registered by the sonar is corrected for angle varying gains, for beam pattern and filtered for speckle removal. All samples of the time series are preserved during all the operations, ensuring that the full data resolution is used for the final mosaicking. The time serie s is then slant-range corrected based on a bathymetric model, in the case of sidescan, or based on beam bathymetry, in the case of the multibeam. Subsequently, each backscatter sample of the series is geocoded in a projected coordinate system in accordance to an interpolation scheme that resembles the acquisition geometry. An anti-aliasing algorithm is applied in parallel to the mosaicking procedure, which allows the assemblage of mosaics at any required resolution. Overlap among parallel lines is resolved by a priority table based on the distance of each sample from the ship track; a blending algorithm is applied to minimize the seams between overlapping lines. The final mosaic exhibits low noise, few artifacts, reduced seams between parallel acquisition lines and reduced clutter in the near-nadir region, while still preserving regional data continuity and local seafloor features

Past, Present, and Future of Simultaneous Localization And Mapping: Towards the Robust-Perception Age

Simultaneous Localization and Mapping (SLAM)consists in the concurrent construction of a model of the environment (the map), and the estimation of the state of the robot moving within it. The SLAM community has made astonishing progress over the last 30 years, enabling large-scale real-world applications, and witnessing a steady transition of this technology to industry. We survey the current state of SLAM. We start by presenting what is now the de-facto standard formulation for SLAM. We then review related work, covering a broad set of topics including robustness and scalability in long-term mapping, metric and semantic representations for mapping, theoretical performance guarantees, active SLAM and exploration, and other new frontiers. This paper simultaneously serves as a position paper and tutorial to those who are users of SLAM. By looking at the published research with a critical eye, we delineate open challenges and new research issues, that still deserve careful scientific investigation. The paper also contains the authors' take on two questions that often animate discussions during robotics conferences: Do robots need SLAM? and Is SLAM solved

Probabilistic RGB-D Odometry based on Points, Lines and Planes Under Depth Uncertainty

This work proposes a robust visual odometry method for structured environments that combines point features with line and plane segments, extracted through an RGB-D camera. Noisy depth maps are processed by a probabilistic depth fusion framework based on Mixtures of Gaussians to denoise and derive the depth uncertainty, which is then propagated throughout the visual odometry pipeline. Probabilistic 3D plane and line fitting solutions are used to model the uncertainties of the feature parameters and pose is estimated by combining the three types of primitives based on their uncertainties. Performance evaluation on RGB-D sequences collected in this work and two public RGB-D datasets: TUM and ICL-NUIM show the benefit of using the proposed depth fusion framework and combining the three feature-types, particularly in scenes with low-textured surfaces, dynamic objects and missing depth measurements.Comment: Major update: more results, depth filter released as opensource, 34 page