To Fall Or Not To Fall: A Visual Approach to Physical Stability Prediction

Understanding physical phenomena is a key competence that enables humans and animals to act and interact under uncertain perception in previously unseen environments containing novel object and their configurations. Developmental psychology has shown that such skills are acquired by infants from observations at a very early stage. In this paper, we contrast a more traditional approach of taking a model-based route with explicit 3D representations and physical simulation by an end-to-end approach that directly predicts stability and related quantities from appearance. We ask the question if and to what extent and quality such a skill can directly be acquired in a data-driven way bypassing the need for an explicit simulation. We present a learning-based approach based on simulated data that predicts stability of towers comprised of wooden blocks under different conditions and quantities related to the potential fall of the towers. The evaluation is carried out on synthetic data and compared to human judgments on the same stimuli

Group Invariance, Stability to Deformations, and Complexity of Deep Convolutional Representations

The success of deep convolutional architectures is often attributed in part to their ability to learn multiscale and invariant representations of natural signals. However, a precise study of these properties and how they affect learning guarantees is still missing. In this paper, we consider deep convolutional representations of signals; we study their invariance to translations and to more general groups of transformations, their stability to the action of diffeomorphisms, and their ability to preserve signal information. This analysis is carried by introducing a multilayer kernel based on convolutional kernel networks and by studying the geometry induced by the kernel mapping. We then characterize the corresponding reproducing kernel Hilbert space (RKHS), showing that it contains a large class of convolutional neural networks with homogeneous activation functions. This analysis allows us to separate data representation from learning, and to provide a canonical measure of model complexity, the RKHS norm, which controls both stability and generalization of any learned model. In addition to models in the constructed RKHS, our stability analysis also applies to convolutional networks with generic activations such as rectified linear units, and we discuss its relationship with recent generalization bounds based on spectral norms

Inversion of the star transform

We define the star transform as a generalization of the broken ray transform introduced by us in previous work. The advantages of using the star transform include the possibility to reconstruct the absorption and the scattering coefficients of the medium separately and simultaneously (from the same data) and the possibility to utilize scattered radiation which, in the case of the conventional X-ray tomography, is discarded. In this paper, we derive the star transform from physical principles, discuss its mathematical properties and analyze numerical stability of inversion. In particular, it is shown that stable inversion of the star transform can be obtained only for configurations involving odd number of rays. Several computationally-efficient inversion algorithms are derived and tested numerically.Comment: Accepted to Inverse Problems in this for

Colour Contrast Occurrence matrix: a vector and perceptual texture feature

International audienceTexture discrimination was the second more important task studied after colour perception and characterization.Nevertheless, few works explore the colour extension of these works and none for vectorial processing ofthis important visual information. In this work we propose a novel and vector processing for colour texturecharacterization, the color contrast occurrence matrix C2O. This new texture feature is based on the colourdierence assessment. To be link to the human perception, the colour dierence is expressed using a perceptualdistance expressed in CIELab and two angles characterizing the chromaticity and darker or lighter direction.Through this new attribute, we analyze the stability to changes in illumination, viewpoint and spectrum of thelight source in front of dierent texture image databases . Thanks to our construction, we avoid the main limit ofexisting texture features requiring an initial colour quantization or a binarization inside the texture construction.Keeping the small local contrast, we obtain a more accurate texture feature description explaining the obtainedresults. Then we carry out the construction of a features vector by occurrence quantization, keeping the initialideas of Julesz, Haralick and Ojala, for the classication purposes. The results show best correct classicationpercentages in databases that with important spatio-chromatic complexity as ALOT

Invariant template matching in systems with spatiotemporal coding: a vote for instability

We consider the design of a pattern recognition that matches templates to images, both of which are spatially sampled and encoded as temporal sequences. The image is subject to a combination of various perturbations. These include ones that can be modeled as parameterized uncertainties such as image blur, luminance, translation, and rotation as well as unmodeled ones. Biological and neural systems require that these perturbations be processed through a minimal number of channels by simple adaptation mechanisms. We found that the most suitable mathematical framework to meet this requirement is that of weakly attracting sets. This framework provides us with a normative and unifying solution to the pattern recognition problem. We analyze the consequences of its explicit implementation in neural systems. Several properties inherent to the systems designed in accordance with our normative mathematical argument coincide with known empirical facts. This is illustrated in mental rotation, visual search and blur/intensity adaptation. We demonstrate how our results can be applied to a range of practical problems in template matching and pattern recognition.Comment: 52 pages, 12 figure