The space of essential matrices as a Riemannian quotient manifold

The essential matrix, which encodes the epipolar constraint between points in two projective views, is a cornerstone of modern computer vision. Previous works have proposed different characterizations of the space of essential matrices as a Riemannian manifold. However, they either do not consider the symmetric role played by the two views, or do not fully take into account the geometric peculiarities of the epipolar constraint. We address these limitations with a characterization as a quotient manifold which can be easily interpreted in terms of camera poses. While our main focus in on theoretical aspects, we include applications to optimization problems in computer vision.This work was supported by grants NSF-IIP-0742304, NSF-OIA-1028009, ARL MAST-CTA W911NF-08-2-0004, and ARL RCTA W911NF-10-2-0016, NSF-DGE-0966142, and NSF-IIS-1317788

Flowing ConvNets for Human Pose Estimation in Videos

The objective of this work is human pose estimation in videos, where multiple frames are available. We investigate a ConvNet architecture that is able to benefit from temporal context by combining information across the multiple frames using optical flow. To this end we propose a network architecture with the following novelties: (i) a deeper network than previously investigated for regressing heatmaps; (ii) spatial fusion layers that learn an implicit spatial model; (iii) optical flow is used to align heatmap predictions from neighbouring frames; and (iv) a final parametric pooling layer which learns to combine the aligned heatmaps into a pooled confidence map. We show that this architecture outperforms a number of others, including one that uses optical flow solely at the input layers, one that regresses joint coordinates directly, and one that predicts heatmaps without spatial fusion. The new architecture outperforms the state of the art by a large margin on three video pose estimation datasets, including the very challenging Poses in the Wild dataset, and outperforms other deep methods that don't use a graphical model on the single-image FLIC benchmark (and also Chen & Yuille and Tompson et al. in the high precision region).Comment: ICCV'1

Learning Human Motion Models for Long-term Predictions

We propose a new architecture for the learning of predictive spatio-temporal motion models from data alone. Our approach, dubbed the Dropout Autoencoder LSTM, is capable of synthesizing natural looking motion sequences over long time horizons without catastrophic drift or motion degradation. The model consists of two components, a 3-layer recurrent neural network to model temporal aspects and a novel auto-encoder that is trained to implicitly recover the spatial structure of the human skeleton via randomly removing information about joints during training time. This Dropout Autoencoder (D-AE) is then used to filter each predicted pose of the LSTM, reducing accumulation of error and hence drift over time. Furthermore, we propose new evaluation protocols to assess the quality of synthetic motion sequences even for which no ground truth data exists. The proposed protocols can be used to assess generated sequences of arbitrary length. Finally, we evaluate our proposed method on two of the largest motion-capture datasets available to date and show that our model outperforms the state-of-the-art on a variety of actions, including cyclic and acyclic motion, and that it can produce natural looking sequences over longer time horizons than previous methods

Learning joint feature adaptation for zero-shot recognition

Zero-shot recognition (ZSR) aims to recognize target-domain data instances of unseen classes based on the models learned from associated pairs of seen-class source and target domain data. One of the key challenges in ZSR is the relative scarcity of source-domain features (e.g. one feature vector per class), which do not fully account for wide variability in target-domain instances. In this paper we propose a novel framework of learning data-dependent feature transforms for scoring similarity between an arbitrary pair of source and target data instances to account for the wide variability in target domain. Our proposed approach is based on optimizing over a parameterized family of local feature displacements that maximize the source-target adaptive similarity functions. Accordingly we propose formulating zero-shot learning (ZSL) using latent structural SVMs to learn our similarity functions from training data. As demonstration we design a specific algorithm under the proposed framework involving bilinear similarity functions and regularized least squares as penalties for feature displacement. We test our approach on several benchmark datasets for ZSR and show significant improvement over the state-of-the-art. For instance, on aP&Y dataset we can achieve 80.89% in terms of recognition accuracy, outperforming the state-of-the-art by 11.15%

Empiricism without Magic: Transformational Abstraction in Deep Convolutional Neural Networks

In artificial intelligence, recent research has demonstrated the remarkable potential of Deep Convolutional Neural Networks (DCNNs), which seem to exceed state-of-the-art performance in new domains weekly, especially on the sorts of very difficult perceptual discrimination tasks that skeptics thought would remain beyond the reach of artificial intelligence. However, it has proven difficult to explain why DCNNs perform so well. In philosophy of mind, empiricists have long suggested that complex cognition is based on information derived from sensory experience, often appealing to a faculty of abstraction. Rationalists have frequently complained, however, that empiricists never adequately explained how this faculty of abstraction actually works. In this paper, I tie these two questions together, to the mutual benefit of both disciplines. I argue that the architectural features that distinguish DCNNs from earlier neural networks allow them to implement a form of hierarchical processing that I call “transformational abstraction”. Transformational abstraction iteratively converts sensory-based representations of category exemplars into new formats that are increasingly tolerant to “nuisance variation” in input. Reflecting upon the way that DCNNs leverage a combination of linear and non-linear processing to efficiently accomplish this feat allows us to understand how the brain is capable of bi-directional travel between exemplars and abstractions, addressing longstanding problems in empiricist philosophy of mind. I end by considering the prospects for future research on DCNNs, arguing that rather than simply implementing 80s connectionism with more brute-force computation, transformational abstraction counts as a qualitatively distinct form of processing ripe with philosophical and psychological significance, because it is significantly better suited to depict the generic mechanism responsible for this important kind of psychological processing in the brain