Manitest: Are classifiers really invariant?

Invariance to geometric transformations is a highly desirable property of automatic classifiers in many image recognition tasks. Nevertheless, it is unclear to which extent state-of-the-art classifiers are invariant to basic transformations such as rotations and translations. This is mainly due to the lack of general methods that properly measure such an invariance. In this paper, we propose a rigorous and systematic approach for quantifying the invariance to geometric transformations of any classifier. Our key idea is to cast the problem of assessing a classifier's invariance as the computation of geodesics along the manifold of transformed images. We propose the Manitest method, built on the efficient Fast Marching algorithm to compute the invariance of classifiers. Our new method quantifies in particular the importance of data augmentation for learning invariance from data, and the increased invariance of convolutional neural networks with depth. We foresee that the proposed generic tool for measuring invariance to a large class of geometric transformations and arbitrary classifiers will have many applications for evaluating and comparing classifiers based on their invariance, and help improving the invariance of existing classifiers.Comment: BMVC 201

Fingerprint Recognition Using Translation Invariant Scattering Network

Fingerprint recognition has drawn a lot of attention during last decades. Different features and algorithms have been used for fingerprint recognition in the past. In this paper, a powerful image representation called scattering transform/network, is used for recognition. Scattering network is a convolutional network where its architecture and filters are predefined wavelet transforms. The first layer of scattering representation is similar to sift descriptors and the higher layers capture higher frequency content of the signal. After extraction of scattering features, their dimensionality is reduced by applying principal component analysis (PCA). At the end, multi-class SVM is used to perform template matching for the recognition task. The proposed scheme is tested on a well-known fingerprint database and has shown promising results with the best accuracy rate of 98\%.Comment: IEEE Signal Processing in Medicine and Biology Symposium, 201

Navier-Stokes Equation by Stochastic Variational Method

We show for the first time that the stochastic variational method can naturally derive the Navier-Stokes equation starting from the action of ideal fluid. In the frame work of the stochastic variational method, the dynamical variables are extended to stochastic quantities. Then the effect of dissipation is realized as the direct consequence of the fluctuation-dissipation theorem. The present result reveals the potential availability of this approach to describe more general dissipative processes.Comment: 5 pages, no figure, discussions and references are added, errors in Sec. IV were correcte

On gauged linear sigma models with torsion

We study a broad class of two dimensional gauged linear sigma models (GLSMs) with off-shell N=(2,2) supersymmetry that flow to nonlinear sigma models (NLSMs) on noncompact geometries with torsion. These models arise from coupling chiral, twisted chiral, and semichiral multiplets to known as well as to a new N=(2,2) vector multiplet, the constrained semichiral vector multiplet (CSVM). We discuss three kinds of models, corresponding to torsionful deformations of standard GLSMs realizing Kahler, hyperkahler, and Calabi-Yau manifolds. The (2,2) supersymmetry guarantees that these spaces are generalized Kahler. Our analysis of the geometric structure is performed at the classical level, but we also discuss quantum aspects such as R-symmetry anomalies. We provide an explicit example of a generalized Kahler structure on the conifold.Comment: 39 pages, 1 figure. v2: References adde

Dynamic texture recognition using time-causal and time-recursive spatio-temporal receptive fields

This work presents a first evaluation of using spatio-temporal receptive fields from a recently proposed time-causal spatio-temporal scale-space framework as primitives for video analysis. We propose a new family of video descriptors based on regional statistics of spatio-temporal receptive field responses and evaluate this approach on the problem of dynamic texture recognition. Our approach generalises a previously used method, based on joint histograms of receptive field responses, from the spatial to the spatio-temporal domain and from object recognition to dynamic texture recognition. The time-recursive formulation enables computationally efficient time-causal recognition. The experimental evaluation demonstrates competitive performance compared to state-of-the-art. Especially, it is shown that binary versions of our dynamic texture descriptors achieve improved performance compared to a large range of similar methods using different primitives either handcrafted or learned from data. Further, our qualitative and quantitative investigation into parameter choices and the use of different sets of receptive fields highlights the robustness and flexibility of our approach. Together, these results support the descriptive power of this family of time-causal spatio-temporal receptive fields, validate our approach for dynamic texture recognition and point towards the possibility of designing a range of video analysis methods based on these new time-causal spatio-temporal primitives.Comment: 29 pages, 16 figure

Advances in Hyperspectral Image Classification: Earth monitoring with statistical learning methods

Hyperspectral images show similar statistical properties to natural grayscale or color photographic images. However, the classification of hyperspectral images is more challenging because of the very high dimensionality of the pixels and the small number of labeled examples typically available for learning. These peculiarities lead to particular signal processing problems, mainly characterized by indetermination and complex manifolds. The framework of statistical learning has gained popularity in the last decade. New methods have been presented to account for the spatial homogeneity of images, to include user's interaction via active learning, to take advantage of the manifold structure with semisupervised learning, to extract and encode invariances, or to adapt classifiers and image representations to unseen yet similar scenes. This tutuorial reviews the main advances for hyperspectral remote sensing image classification through illustrative examples.Comment: IEEE Signal Processing Magazine, 201