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Deep convolutional neural networks (DCNNs) are currently the method of choice both for generative, as well as for discriminative learning in computer vision and machine learning. The success of DCNNs can be attributed to the careful selection of their building blocks (e.g., residual blocks, rectifiers, sophisticated normalization schemes, to mention but a few). In this paper, we propose Π-Nets, a new class of function approximators based on polynomial expansions. Π-Nets are polynomial neural networks, i.e., the output is a high-order polynomial of the input. The unknown parameters, which are naturally represented by high-order tensors, are estimated through a collective tensor factorization with factors sharing. We introduce three tensor decompositions that significantly reduce the number of parameters and show how they can be efficiently implemented by hierarchical neural networks. We empirically demonstrate that Π-Nets are very expressive and they even produce good results without the use of non-linear activation functions in a large battery of tasks and signals, i.e., images, graphs, and audio. When used in conjunction with activation functions, Π-Nets produce state-of-the-art results in three challenging tasks, i.e., image generation, face verification and 3D mesh representation learning. The source code is available at https://github.com/grigorisg9gr/polynomial_nets.

Face detection/alignment methods have reached a satisfactory state in static images captured under arbitrary conditions. Such methods typically perform (joint) fitting for each frame and are used in commercial applications; however in the majority of the real-world scenarios the dynamic scenes are of interest. We argue that generic fitting per frame is suboptimal (it discards the informative correlation of sequential frames) and propose to learn person-specific statistics from the video to improve the generic results. To that end, we introduce a meticulously studied pipeline, which we name PD 2 T, that performs person-specific detection and landmark localisation. We carry out extensive experimentation with a diverse set of i) generic fitting results, ii) different objects (human faces, animal faces) that illustrate the powerful properties of our proposed pipeline and experimentally verify that PD 2 T outperforms all the compared methods.

Model-free tracking is a well-studied task in computer vision. Typically, a rectangular bounding box containing a single object is provided in the first (few) frame(s) and then the method tracks the object in the rest frames. However, for deformable objects (e.g. faces, bodies) the single bounding box scenario is sub-optimal; a part-based approach would be more effective. The current state-of-the-art part-based approach is incrementally trained discriminative Deformable Part Models (DPM). Nevertheless, training discriminative DPMs with one or a few examples poses a huge challenge. We argue that a generative model is a better fit for the task. We utilise the powerful pictorial structures, which we augment with incremental updates to account for object adaptations. Our proposed incremental pictorial structures, which we call IPST, are experimentally validated in different scenarios. In a thorough experimentation we demonstrate that IPST outperforms the existing model-free methods in facial landmark tracking, body tracking, animal tracking (newly introduced to verify the strength in ad hoc cases).

Recently, technologies such as face detection, facial landmark localisation and face recognition and verification have matured enough to provide effective and efficient solutions for imagery captured under arbitrary conditions (referred to as "in-the-wild"). This is partially attributed to the fact that comprehensive "in-the-wild" benchmarks have been developed for face detection, landmark localisation and recognition/verification. A very important technology that has not been thoroughly evaluated yet is deformable face tracking "in-the-wild". Until now, the performance has mainly been assessed qualitatively by visually assessing the result of a deformable face tracking technology on short videos. In this paper, we perform the first, to the best of our knowledge, thorough evaluation of state-of-the-art deformable face tracking pipelines using the recently introduced 300 VW benchmark. We evaluate many different architectures focusing mainly on the task of on-line deformable face tracking. In particular, we compare the following general strategies: (a) generic face detection plus generic facial landmark localisation, (b) generic model free tracking plus generic facial landmark localisation, as well as (c) hybrid approaches using state-of-the-art face detection, model free tracking and facial landmark localisation technologies. Our evaluation reveals future avenues for further research on the topic., (© The Author(s) 2017.)