Comparative Evaluation of Action Recognition Methods via Riemannian Manifolds, Fisher Vectors and GMMs: Ideal and Challenging Conditions

We present a comparative evaluation of various techniques for action recognition while keeping as many variables as possible controlled. We employ two categories of Riemannian manifolds: symmetric positive definite matrices and linear subspaces. For both categories we use their corresponding nearest neighbour classifiers, kernels, and recent kernelised sparse representations. We compare against traditional action recognition techniques based on Gaussian mixture models and Fisher vectors (FVs). We evaluate these action recognition techniques under ideal conditions, as well as their sensitivity in more challenging conditions (variations in scale and translation). Despite recent advancements for handling manifolds, manifold based techniques obtain the lowest performance and their kernel representations are more unstable in the presence of challenging conditions. The FV approach obtains the highest accuracy under ideal conditions. Moreover, FV best deals with moderate scale and translation changes

Second-order Democratic Aggregation

Aggregated second-order features extracted from deep convolutional networks have been shown to be effective for texture generation, fine-grained recognition, material classification, and scene understanding. In this paper, we study a class of orderless aggregation functions designed to minimize interference or equalize contributions in the context of second-order features and we show that they can be computed just as efficiently as their first-order counterparts and they have favorable properties over aggregation by summation. Another line of work has shown that matrix power normalization after aggregation can significantly improve the generalization of second-order representations. We show that matrix power normalization implicitly equalizes contributions during aggregation thus establishing a connection between matrix normalization techniques and prior work on minimizing interference. Based on the analysis we present {\gamma}-democratic aggregators that interpolate between sum ({\gamma}=1) and democratic pooling ({\gamma}=0) outperforming both on several classification tasks. Moreover, unlike power normalization, the {\gamma}-democratic aggregations can be computed in a low dimensional space by sketching that allows the use of very high-dimensional second-order features. This results in a state-of-the-art performance on several datasets

DeepKSPD: Learning Kernel-matrix-based SPD Representation for Fine-grained Image Recognition

Being symmetric positive-definite (SPD), covariance matrix has traditionally been used to represent a set of local descriptors in visual recognition. Recent study shows that kernel matrix can give considerably better representation by modelling the nonlinearity in the local descriptor set. Nevertheless, neither the descriptors nor the kernel matrix is deeply learned. Worse, they are considered separately, hindering the pursuit of an optimal SPD representation. This work proposes a deep network that jointly learns local descriptors, kernel-matrix-based SPD representation, and the classifier via an end-to-end training process. We derive the derivatives for the mapping from a local descriptor set to the SPD representation to carry out backpropagation. Also, we exploit the Daleckii-Krein formula in operator theory to give a concise and unified result on differentiating SPD matrix functions, including the matrix logarithm to handle the Riemannian geometry of kernel matrix. Experiments not only show the superiority of kernel-matrix-based SPD representation with deep local descriptors, but also verify the advantage of the proposed deep network in pursuing better SPD representations for fine-grained image recognition tasks

Second-order Temporal Pooling for Action Recognition

Deep learning models for video-based action recognition usually generate features for short clips (consisting of a few frames); such clip-level features are aggregated to video-level representations by computing statistics on these features. Typically zero-th (max) or the first-order (average) statistics are used. In this paper, we explore the benefits of using second-order statistics. Specifically, we propose a novel end-to-end learnable feature aggregation scheme, dubbed temporal correlation pooling that generates an action descriptor for a video sequence by capturing the similarities between the temporal evolution of clip-level CNN features computed across the video. Such a descriptor, while being computationally cheap, also naturally encodes the co-activations of multiple CNN features, thereby providing a richer characterization of actions than their first-order counterparts. We also propose higher-order extensions of this scheme by computing correlations after embedding the CNN features in a reproducing kernel Hilbert space. We provide experiments on benchmark datasets such as HMDB-51 and UCF-101, fine-grained datasets such as MPII Cooking activities and JHMDB, as well as the recent Kinetics-600. Our results demonstrate the advantages of higher-order pooling schemes that when combined with hand-crafted features (as is standard practice) achieves state-of-the-art accuracy.Comment: Accepted in the International Journal of Computer Vision (IJCV