Probing ergodicity in granular matter

When a granular system is tapped, its volume changes. Here, using a well-defined macroscopic protocol, we prepare an ensemble of granular systems and track the statistics of volume changes as a function of the number of taps. This is in contrast to previous studies, which have focused on single trajectories and assumed ergodicity. We devise a new method to assess the convergence properties of a sequence of ensemble volume histograms and introduce a reasonable approximate version of an invariant histogram. We then compare these invariant histograms with histograms generated by sampling a long trajectory for one system and observe nonergodicity, which we quantify. Finally, we use the overlapping histogram method to assess potential compatibility with Edwards’ canonical assumption. Our histograms are incompatible with this assumption

Gromov-Monge quasi-metrics and distance distributions

Applications in data science, shape analysis and object classification frequently require maps between metric spaces which preserve geometry as faithfully as possible. In this paper, we combine the Monge formulation of optimal transport with the Gromov-Hausdorff distance construction to define a measure of the minimum amount of geometric distortion required to map one metric measure space onto another. We show that the resulting quantity, called Gromov-Monge distance, defines an extended quasi-metric on the space of isomorphism classes of metric measure spaces and that it can be promoted to a true metric on certain subclasses of mm-spaces. We also give precise comparisons between Gromov-Monge distance and several other metrics which have appeared previously, such as the Gromov-Wasserstein metric and the continuous Procrustes metric of Lipman, Al-Aifari and Daubechies. Finally, we derive polynomial-time computable lower bounds for Gromov-Monge distance. These lower bounds are expressed in terms of distance distributions, which are classical invariants of metric measure spaces summarizing the volume growth of metric balls. In the second half of the paper, which may be of independent interest, we study the discriminative power of these lower bounds for simple subclasses of metric measure spaces. We first consider the case of planar curves, where we give a counterexample to the Curve Histogram Conjecture of Brinkman and Olver. Our results on plane curves are then generalized to higher dimensional manifolds, where we prove some sphere characterization theorems for the distance distribution invariant. Finally, we consider several inverse problems on recovering a metric graph from a collection of localized versions of distance distributions. Results are derived by establishing connections with concepts from the fields of computational geometry and topological data analysis.Comment: Version 2: Added many new results and improved expositio

Objects classification in still images using the region covariance descriptor

The goal of the Object Classification is to classify the objects in images. Classification aims for the recognition of generic classes, which is also known as Generic Object Recognition. This is quite different from Specific Object Recognition, such as recognizing specific person, own car, and etc. Human beings are generally better in recognizing generic classes than specific objects. Classification is a much harder problem to solve by artificial systems. Classification algorithm must be robust to changes in illumination, object scale, view point, and etc. The algorithm also has to manage large intra class variations and small inter class variations. In recent literature, some of the classification methods use Bag of Visual Words model. In this work the main emphasis is on region descriptor and representation of training images. Given a set of training images, interest points are detected through interest point detectors. Region around an interest point is described by a descriptor. Region covariance descriptor is adopted from porikli et al. [21], where they used this descriptor for object detection and classification. This region covariance descriptor is combined with Bag of Visual words model. We have used a different set of features for Classification task. Covariance of d-features, e.g. spatial location, Gaussian kernel with three different s values, first order Gaussian derivatives with two different s values, and second order Gaussian derivatives with four different s values, characterizes a region of interest. An image is also represented by Bag of Visual words obtained with both SIFT and Covariance descriptors. We worked on five datasets; Caltech-4, Caltech-3, Animal, Caltech-10, and Flower (17 classes), with first four taken from Caltech-256 and Caltech-101 datasets. Many researchers used Caltech-4 dataset for object classification task. The region covariance descriptor is outperforming SIFT descriptor on both Caltech-4 and Caltech-3 datasets, whereas Combined representation (SIFT + Covariance) is outperforming both SIFT and Covarianc

Validating the detection of everyday concepts in visual lifelogs

The Microsoft SenseCam is a small lightweight wearable camera used to passively capture photos and other sensor readings from a user's day-to-day activities. It can capture up to 3,000 images per day, equating to almost 1 million images per year. It is used to aid memory by creating a personal multimedia lifelog, or visual recording of the wearer's life. However the sheer volume of image data captured within a visual lifelog creates a number of challenges, particularly for locating relevant content. Within this work, we explore the applicability of semantic concept detection, a method often used within video retrieval, on the novel domain of visual lifelogs. A concept detector models the correspondence between low-level visual features and high-level semantic concepts (such as indoors, outdoors, people, buildings, etc.) using supervised machine learning. By doing so it determines the probability of a concept's presence. We apply detection of 27 everyday semantic concepts on a lifelog collection composed of 257,518 SenseCam images from 5 users. The results were then evaluated on a subset of 95,907 images, to determine the precision for detection of each semantic concept and to draw some interesting inferences on the lifestyles of those 5 users. We additionally present future applications of concept detection within the domain of lifelogging. © 2008 Springer Berlin Heidelberg

Polar Transformation on Image Features for Orientation-Invariant Representations

The choice of image feature representation plays a crucial role in the analysis of visual information. Although vast numbers of alternative robust feature representation models have been proposed to improve the performance of different visual tasks, most existing feature representations (e.g. handcrafted features or Convolutional Neural Networks (CNN)) have a relatively limited capacity to capture the highly orientation-invariant (rotation/reversal) features. The net consequence is suboptimal visual performance. To address these problems, this study adopts a novel transformational approach, which investigates the potential of using polar feature representations. Our low level consists of a histogram of oriented gradient, which is then binned using annular spatial bin-type cells applied to the polar gradient. This gives gradient binning invariance for feature extraction. In this way, the descriptors have significantly enhanced orientation-invariant capabilities. The proposed feature representation, termed it orientation-invariant histograms of oriented gradients (Oi-HOG), is capable of accurately processing facial expression recognition (FER). In the context of the CNN architecture, we propose two polar convolution operations, referred to as Full Polar Convolution (FPolarConv) and Local Polar Convolution (LPolarConv), and use these to develop polar architectures for the CNN orientation-invariant representation. Experimental results show that the proposed orientation-invariant image representation, based on polar models for both handcrafted features and deep learning features, is both competitive with state-of-the-art methods and maintains a compact representation on a set of challenging benchmark image datasets

Application of integral invariants to apictorial jigsaw puzzle assembly

We present a method for the automatic assembly of apictorial jigsaw puzzles. This method relies on integral area invariants for shape matching and an optimization process to aggregate shape matches into a final puzzle assembly. Assumptions about individual piece shape or arrangement are not necessary. We illustrate our method by solving example puzzles of various shapes and sizes.Comment: 17 pages. J Math Imaging Vis (2022

Computing von Kries Illuminant Changes by Piecewise Inversion of Cumulative Color Histograms

We present a linear algorithm for the computation of the illuminant change occurring between two color pictures of a scene. We model the light variations with the von Kries diagonal transform and we estimate it by minimizing a dissimilarity measure between the piecewise inversions of the cumulative color histograms of the considered images. We also propose a method for illuminant invariant image recognition based on our von Kries transform estimate