Robust model fitting is a core algorithm in several computer vision applications. Despite being studied for decades, solving this problem efficiently for datasets that are heavily contaminated by outliers is still challenging: due to the underlying computational complexity. A recent focus has been on learning-based algorithms. However, most of these approaches are supervised (which require a large amount of labelled training data). In this paper, we introduce a novel unsupervised learning framework: that learns to directly (without labelled data) solve robust model fitting. Moreover, unlike other learning-based methods, our work is agnostic to the underlying input features, and can be easily generalized to a wide variety of LP-type problems with quasi-convex residuals. We empirically show that our method outperforms existing (un)supervised learning approaches, and also achieves competitive results compared to traditional (non-learning-based) methods. Our approach is designed to try to maximise consensus (MaxCon), similar to the popular RANSAC. The basis of our approach, is to adopt a Reinforcement Learning framework. This requires designing appropriate reward functions, and state encodings. We provide a family of reward functions, tunable by choice of a parameter. We also investigate the application of different basic and enhanced Q-learning components.

We propose a new algorithm for training deep neural networks (DNNs) with binary weights. In particular, we first cast the problem of training binary neural networks (BiNNs) as a bilevel optimization instance and subsequently construct flexible relaxations of this bilevel program. The resulting training method shares its algorithmic simplicity with several existing approaches to train BiNNs, in particular with the straight-through gradient estimator successfully employed in BinaryConnect and subsequent methods. Infact, our proposed method can be interpreted as an adaptive variant of the original straight-through estimator that conditionally (but not always) acts like a linear mapping in the backward pass of error propagation. Experimental results demonstrate that our new algorithm offers favorable performance compared to existing approaches.11This work was partially supported by theWallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundation.

We tackle the problem of large-scale robust fitting using the truncated least squares (TLS) loss. Existing approaches commonly optimize this loss by employing a smooth surrogate, which allows the problem to be solved using well-known methods such as Iteratively Re-weighted Least Squares (IRLS). In this work, we present a new approach to optimize the TLS objective, where we propose to reformulate the original problem as a bi-level program. Then, by applying the Optimal Value Reformulation (OVR) technique to this new formulation, we derive a penalty approach to solve for the best fitting models, where the penalty parameters can be adaptively computed. Our final algorithm can be considered as a special instance of IRLS. As a result, we can incorporate our new algorithm into existing IRLS solvers, where we only need to modify the weight evaluation procedure. Our experimental results show promising results on several instances of large-scale bundle adjustment and non-linear refinement for essential matrix fitting.

Multi-Camera Multiple Object Tracking (MC-MOT) is a significant computer vision problem due to its emerging applicability in several real-world applications. Despite a large number of existing works, solving the data association problem in any MC-MOT pipeline is arguably one of the most challenging tasks. Developing a robust MC-MOT system, however, is still highly challenging due to many practical issues such as inconsistent lighting conditions, varying object movement patterns, or the trajectory occlusions of the objects between the cameras. To address these problems, this work, therefore, proposes a new Dynamic Graph Model with Link Prediction (DyGLIP) approach1to solve the data association task. Compared to existing methods, our new model offers several advantages, including better feature representations and the ability to recover from lost tracks during camera transitions. Moreover, our model works gracefully regardless of the overlapping ratios between the cameras. Experimental results show that we out-perform existing MC-MOT algorithms by a large margin on several practical datasets. Notably, our model works favor-ably on online settings but can be extended to an incremental approach for large-scale datasets.

Robust model fitting is a core algorithm in a large number of computer vision applications. Solving this problem efficiently for datasets highly contaminated with outliers is, however, still challenging due to the underlying computational complexity. Recent literature has focused on learning-based algorithms. However, most approaches are supervised (which require a large amount of labelled training data). In this paper, we introduce a novel unsupervised learning framework that learns to directly solve robust model fitting. Unlike other methods, our work is agnostic to the underlying input features, and can be easily generalized to a wide variety of LP-type problems with quasi-convex residuals. We empirically show that our method out-performs existing unsupervised learning approaches, and achieves competitive results compared to traditional methods on several important computer vision problems1.

Maximum consensus estimation plays a critically important role in several robust fitting problems in computer vision. Currently, the most prevalent algorithms for consensus maximization draw from the class of randomized hypothesize-and-verify algorithms, which are cheap but can usually deliver only rough approximate solutions. On the other extreme, there are exact algorithms which are exhaustive search in nature and can be costly for practical-sized inputs. This paper fills the gap between the two extremes by proposing deterministic algorithms to approximately optimize the maximum consensus criterion. Our work begins by reformulating consensus maximization with linear complementarity constraints. Then, we develop two novel algorithms: one based on non-smooth penalty method with a Frank-Wolfe style optimization scheme, the other based on the Alternating Direction Method of Multipliers (ADMM). Both algorithms solve convex subproblems to efficiently perform the optimization. We demonstrate the capability of our algorithms to greatly improve a rough initial estimate, such as those obtained using least squares or a randomized algorithm. Compared to the exact algorithms, our approach is much more practical on realistic input sizes. Further, our approach is naturally applicable to estimation problems with geometric residuals. Matlab code and demo program for our methods can be downloaded from https://goo.gl/FQcxpi.

Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper, we introduce a novel solver for robust estimation that possesses a strong ability to escape poor local minima. Our algorithm is built upon the class of traditional graduated optimization techniques, which are considered state-of-the-art local methods to solve problems having many poor minima. The novelty of our work lies in the introduction of an adaptive kernel (or residual) scaling scheme, which allows us to achieve faster convergence rates. Like other existing methods that aim to return good local minima for robust estimation tasks, our method relaxes the original robust problem, but adapts a filter framework from non-linear constrained optimization to automatically choose the level of relaxation. Experimental results on real large-scale datasets such as bundle adjustment instances demonstrate that our proposed method achieves competitive results.

This paper presents a novel randomized algorithm for robust point cloud registration without correspondences. Most existing registration approaches require a set of putative correspondences obtained by extracting invariant descriptors. However, such descriptors could become unreliable in noisy and contaminated settings. In these settings, methods that directly handle input point sets are preferable. Without correspondences, however, conventional randomized techniques require a very large number of samples in order to reach satisfactory solutions. In this paper, we propose a novel approach to address this problem. In particular, our work enables the use of randomized methods for point cloud registration without the need of putative correspondences. By considering point cloud alignment as a special instance of graph matching and employing an efficient semi-definite relaxation, we propose a novel sampling mechanism, in which the size of the sampled subsets can be larger-than-minimal. Our tight relaxation scheme enables fast rejection of the outliers in the sampled sets, resulting in high quality hypotheses. We conduct extensive experiments to demonstrate that our approach outperforms other state-of-the-art methods. Importantly, our proposed method serves as a generic framework which can be extended to problems with known correspondences.

Learning compact binary codes for image retrieval task using deep neural networks has attracted increasing attention recently. However, training deep hashing networks for the task is challenging due to the binary constraints on the hash codes, the similarity preserving property, and the requirement for a vast amount of labelled images. To the best of our knowledge, none of the existing methods has tackled all of these challenges completely in a unified framework. In this work, we propose a novel end-to-end deep learning approach for the task, in which the network is trained to produce binary codes directly from image pixels without the need o f manual annotation. In particular, to deal with the non-smoothness of binary constraints, we propose a novel pairwise constrained loss function, which simultaneously encodes the distances between pairs of hash codes, and the binary quantization error. In order to train the network with the proposed loss function, we propose an efficient parameter learning algorithm. In addition, to provide similar / dissimilar training images to train the network, we exploit 3D models reconstructed from unlabelled images for automatic generation of enormous training image pairs. The extensive experiments on image retrieval benchmark datasets demonstrate the improvements of the proposed method over the state-of-the-art compact representation methods on the image retrieval problem.

Representing images by compact hash codes is an attractive approach for large-scale content-based image retrieval. In most state-of-the-art hashing-based image retrieval systems, for each image, local descriptors are first aggregated as a global representation vector. This global vector is then subjected to a hashing function to generate a binary hash code. In previous works, the aggregating and the hashing processes are designed independently. Hence, these frameworks may generate suboptimal hash codes. In this paper, we first propose a novel unsupervised hashing framework in which feature aggregating and hashing are designed simultaneously and optimized jointly. Specifically, our joint optimization generates aggregated representations that can be better reconstructed by some binary codes. This leads to more discriminative binary hash codes and improved retrieval accuracy. In addition, the proposed method is flexible. It can be extended for supervised hashing. When the data label is available, the framework can be adapted to learn binary codes which minimize the reconstruction loss with respect to label vectors. Furthermore, we also propose a fast version of the state-of-the-art hashing method Binary Autoencoder to be used in our proposed frameworks. Extensive experiments on benchmark datasets under various settings show that the proposed methods outperform the state-of-the-art unsupervised and supervised hashing methods.

In the large-scale image retrieval task, the two most important requirements are the discriminability of image representations and the efficiency in computation and storage of representations. Regarding the former requirement, Convolutional Neural Network is proven to be a very powerful tool to extract highly discriminative local descriptors for effective image search. Additionally, to further improve the discriminative power of the descriptors, recent works adopt fine-tuned strategies. In this article, taking a different approach, we propose a novel, computationally efficient, and competitive framework. Specifically, we first propose various strategies to compute masks, namely, SIFT-masks , SUM-mask , and MAX-mask , to select a representative subset of local convolutional features and eliminate redundant features. Our in-depth analyses demonstrate that proposed masking schemes are effective to address the burstiness drawback and improve retrieval accuracy. Second, we propose to employ recent embedding and aggregating methods that can significantly boost the feature discriminability. Regarding the computation and storage efficiency, we include a hashing module to produce very compact binary image representations. Extensive experiments on six image retrieval benchmarks demonstrate that our proposed framework achieves the state-of-the-art retrieval performances.

The known rotation problem refers to a special case of structure-from-motion where the absolute orientations of the cameras are known. When formulated as a minimax (ℓ∞) problem on reprojection errors, the problem is an instance of pseudo-convex programming. Though theoretically tractable, solving the known rotation problem on large-scale data (1,000's of views, 10,000's scene points) using existing methods can be very time-consuming. In this paper, we devise a fast algorithm for the known rotation problem. Our approach alternates between pose estimation and triangulation (i.e., resection-intersection) to break the problem into multiple simpler instances of pseudo-convex programming. The key to the vastly superior performance of our method lies in using a novel minimum enclosing ball (MEB) technique for the calculation of updating steps, which obviates the need for convex optimisation routines and greatly reduces memory footprint. We demonstrate the practicality of our method on large-scale problem instances which easily overwhelm current state-of-the-art algorithms.

Maximum consensus estimation plays a critically important role in computer vision. Currently, the most prevalent approach draws from the class of non-deterministic hypothesize-and-verify algorithms, which are cheap but do not guarantee solution quality. On the other extreme, there are global algorithms which are exhaustive search in nature and can be costly for practical-sized inputs. This paper aims to fill the gap between the two extremes by proposing a locally convergent maximum consensus algorithm. Our method is based on a formulating the problem with linear complementarity constraints, then defining a penalized version which is provably equivalent to the original problem. Based on the penalty problem, we develop a Frank-Wolfe algorithm that can deterministically solve the maximum consensus problem. Compared to the randomized techniques, our method is deterministic and locally convergent, relative to the global algorithms, our method is much more practical on realistic input sizes. Further, our approach is naturally applicable to problems with geometric residuals.

Deformations of surfaces with the same intrinsic shape can often be described accurately by a conformal model. A major focus of computational conformal geometry is the estimation of the conformal mapping that aligns a given pair of object surfaces. The uniformization theorem enables this task to be acccomplished in a canonical 2D domain, wherein the surfaces can be aligned using a Möbius transformation. Current algorithms for estimating Möbius transformations, however, often cannot provide satisfactory alignment or are computationally too costly. This paper introduces a novel globally optimal algorithm for estimating Möbius transformations to align surfaces that are topological discs. Unlike previous methods, the proposed algorithm deterministically calculates the best transformation, without requiring good initializations. Further, our algorithm is also much faster than previous techniques in practice. We demonstrate the efficacy of our algorithm on data commonly used in computational conformal geometry.