Jack Valmadre

End-to-End Representation Learning for Correlation Filter Based Tracking

The Correlation Filter is an algorithm that trains a linear template to discriminate between images and their translations. It is well suited to object tracking because its formulation in the Fourier domain provides a fast solution, enabling the detector to be re-trained once per frame. Previous works that use the Correlation Filter, however, have adopted features that were either manually designed or trained for a different task. This work is the first to overcome this limitation by interpreting the Correlation Filter learner, which has a closed-form solution, as a differentiable layer in a deep neural network. This enables learning deep features that are tightly coupled to the Correlation Filter. Experiments illustrate that our method has the important practical benefit of allowing lightweight architectures to achieve state-of-the-art performance at high framerates.

Dense Semantic Correspondence Where Every Pixel is a Classifier

Determining dense semantic correspondences across objects and scenes is a difficult problem that underpins many higher-level computer vision algorithms. Unlike canonical dense correspondence problems which consider images that are spatially or temporally adjacent, semantic correspondence is characterized by images that share similar high-level structures whose exact appearance and geometry may differ. Motivated by object recognition literature and recent work on rapidly estimating linear classifiers, we treat semantic correspondence as a constrained detection problem, where an exemplar LDA classifier is learned for each pixel. LDA classifiers have two distinct benefits: (i) they exhibit higher average precision than similarity metrics typically used in correspondence problems, and (ii) unlike exemplar SVM, can output globally interpretable posterior probabilities without calibration, whilst also being significantly faster to train. We pose the correspondence problem as a graphical model, where the unary potentials are computed via convolution with the set of exemplar classifiers, and the joint potentials enforce smoothly varying correspondence assignment.

General trajectory prior for Non-Rigid reconstruction

Trajectory basis Non-Rigid Structure From Motion (NRSFM) currently faces two problems: the limit of reconstructability and the need to tune the basis size for different sequences. This paper provides a novel theoretical bound on 3D reconstruction error, arguing that the existing definition of reconstructability is fundamentally flawed in that it fails to consider system condition. This insight motivates a novel strategy whereby the trajectorys response to a set of high-pass filters is minimised. The new approach eliminates the need to tune the basis size and is more efficient for long sequences. Additionally, the truncated DCT basis is shown to have a dual interpretation as a high-pass filter. The success of trajectory filter reconstruction is demonstrated quantitatively on synthetic projections of real motion capture sequences and qualitatively on real image sequences.

Separable spatiotemporal priors for convex reconstruction of time-varying 3D point clouds

Reconstructing 3D motion data is highly under-constrained due to several common sources of data loss during measurement, such as projection, occlusion, or miscorrespondence. We present a statistical model of 3D motion data, based on the Kronecker structure of the spatiotemporal covariance of natural motion, as a prior on 3D motion. This prior is expressed as a matrix normal distribution, composed of separable and compact row and column covariances. We relate the marginals of the distribution to the shape, trajectory, and shape-trajectory models of prior art. When the marginal shape distribution is not available from training data, we show how placing a hierarchical prior over shapes results in a convex MAP solution in terms of the trace-norm. The matrix normal distribution, fit to a single sequence, outperforms state-of-the-art methods at reconstructing 3D motion data in the presence of significant data loss, while providing covariance estimates of the imputed points.

Learning Detectors Quickly with Stationary Statistics

Computer vision is increasingly becoming interested in the rapid estimation of object detectors. The canonical strategy of using Hard Negative Mining to train a Support Vector Machine is slow, since the large negative set must be traversed at least once per detector. Recent work has demonstrated that, with an assumption of signal stationarity, Linear Discriminant Analysis is able to learn comparable detectors without ever revisiting the negative set. Even with this insight, the time to learn a detector can still be on the order of minutes. Correlation filters, on the other hand, can produce a detector in under a second. However, this involves the unnatural assumption that the statistics are periodic, and requires the negative set to be re-sampled per detector size. These two methods differ chiefly in the structure which they impose on the covariance matrix of all examples. This paper is a comparative study which develops techniques (i) to assume periodic statistics without needing to revisit the negative set and (ii) to accelerate the estimation of detectors with aperiodic statistics. It is experimentally verified that periodicity is detrimental.

Graph Rigidity for Near-Coplanar Structure from Motion

Recent algorithms for monocular motion capture (MoCap) estimate weak-perspective camera matrices between images using a small subset of approximately-rigid points on the human body (i.e.\ the torso and hip). A problem with this approach, however, is that these points are often close to coplanar, causing canonical linear factorisation algorithms for rigid structure from motion (SFM) to become extremely sensitive to noise. In this paper, we propose an alternative solution to weak-perspective SFM based on a convex relaxation of graph rigidity. We demonstrate the success of our algorithm on both synthetic and real world data, allowing for much improved solutions to marker less MoCap problems on human bodies. Finally, we propose an approach to solve the two-fold ambiguity over bone direction using a k-nearest neighbour kernel density estimator.