Gait-based carried object detection using persistent homology

There are surveillance scenarios where it is important to emit an alarm when a person carrying an object is detected. In order to detect when a person is carrying an object, we build models of naturally-walking and object-carrying persons using topological features. First, a stack of human silhouettes, extracted by background subtraction and thresholding, are glued through their gravity centers, forming a 3D digital image I. Second, different filters (i.e. orderings of the cells) are applied on ∂ K(I) (cubical complex obtained from I) which capture relations among the parts of the human body when walking. Finally, a topological signature is extracted from the persistence diagrams according to each filter. We build some clusters of persons walking naturally, without carrying object and some clusters of persons carrying bags. We obtain vector prototypes for each cluster. Simple distances to the means are calculated for detecting the presence of carrying object. The measure cosine is used to give a similarity value between topological signatures. The accuracies obtained are 95.7% and 95.9% for naturally-walking and object-carrying respectively

Designing a topological algorithm for 3D activity recognition

Voxel carving is a non-invasive and low-cost technique that is used for the reconstruction of a 3D volume from images captured from a set of cameras placed around the object of interest. In this paper we propose a method to topologically analyze a video sequence of 3D reconstructions representing a tennis player performing different forehand and backhand strokes with the aim of providing an approach that could be useful in other sport activities

Persistent homology-based gait recognition robust to upper body variations

Gait recognition is nowadays an important biometric technique for video surveillance tasks, due to the advantage of using it at distance. However, when the upper body movements are unrelated to the natural dynamic of the gait, caused for example by carrying a bag or wearing a coat, the reported results show low accuracy. With the goal of solving this problem, we apply persistent homology to extract topological features from the lowest fourth part of the body silhouettes. To obtain the features, we modify our previous algorithm for gait recognition, to improve its efficacy and robustness to variations in the amount of simplices of the gait complex. We evaluate our approach using the CASIA-B dataset, obtaining a considerable accuracy improvement of 93:8%, achieving at the same time invariance to upper body movements unrelated with the dynamic of the gait.Ministerio de Economía y Competitividad MTM2015-67072-

Topological signature for periodic motion recognition

In this paper, we present an algorithm that computes the topological signature for a given periodic motion sequence. Such signature consists of a vector obtained by persistent homology which captures the topological and geometric changes of the object that models the motion. Two topological signatures are compared simply by the angle between the corresponding vectors. With respect to gait recognition, we have tested our method using only the lowest fourth part of the body's silhouette. In this way, the impact of variations in the upper part of the body, which are very frequent in real scenarios, decreases considerably. We have also tested our method using other periodic motions such as running or jumping. Finally, we formally prove that our method is robust to small perturbations in the input data and does not depend on the number of periods contained in the periodic motion sequence.Comment: arXiv admin note: substantial text overlap with arXiv:1707.0698

Persistent-homology-based gait recognition

Gait recognition is an important biometric technique for video surveillance tasks, due to the advantage of using it at distance. In this paper, we present a persistent homology-based method to extract topological features (the so-called topological gait signature) from the the body silhouettes of a gait sequence. It has been used before in sev- eral conference papers of the same authors for human identi cation, gender classi cation, carried object detection and monitoring human activities at distance. The novelty of this paper is the study of the sta- bility of the topological gait signature under small perturbations and the number of gait cycles contained in a gait sequence. In other words, we show that the topological gait signature is robust to the presence of noise in the body silhouettes and to the number of gait cycles con- tained in a given gait sequence. We also show that computing our topological gait signature of only the lowest fourth part of the body silhouette, we avoid the upper body movements that are unrelated to the natural dynamic of the gait, caused for example by carrying a bag or wearing a coat.Ministerio de Economía y Competitividad MTM2015-67072-

Persistent Homology Tools for Image Analysis

Topological Data Analysis (TDA) is a new field of mathematics emerged rapidly since the first decade of the century from various works of algebraic topology and geometry. The goal of TDA and its main tool of persistent homology (PH) is to provide topological insight into complex and high dimensional datasets. We take this premise onboard to get more topological insight from digital image analysis and quantify tiny low-level distortion that are undetectable except possibly by highly trained persons. Such image distortion could be caused intentionally (e.g. by morphing and steganography) or naturally in abnormal human tissue/organ scan images as a result of onset of cancer or other diseases. The main objective of this thesis is to design new image analysis tools based on persistent homological invariants representing simplicial complexes on sets of pixel landmarks over a sequence of distance resolutions. We first start by proposing innovative automatic techniques to select image pixel landmarks to build a variety of simplicial topologies from a single image. Effectiveness of each image landmark selection demonstrated by testing on different image tampering problems such as morphed face detection, steganalysis and breast tumour detection. Vietoris-Rips simplicial complexes constructed based on the image landmarks at an increasing distance threshold and topological (homological) features computed at each threshold and summarized in a form known as persistent barcodes. We vectorise the space of persistent barcodes using a technique known as persistent binning where we demonstrated the strength of it for various image analysis purposes. Different machine learning approaches are adopted to develop automatic detection of tiny texture distortion in many image analysis applications. Homological invariants used in this thesis are the 0 and 1 dimensional Betti numbers. We developed an innovative approach to design persistent homology (PH) based algorithms for automatic detection of the above described types of image distortion. In particular, we developed the first PH-detector of morphing attacks on passport face biometric images. We shall demonstrate significant accuracy of 2 such morph detection algorithms with 4 types of automatically extracted image landmarks: Local Binary patterns (LBP), 8-neighbour super-pixels (8NSP), Radial-LBP (R-LBP) and centre-symmetric LBP (CS-LBP). Using any of these techniques yields several persistent barcodes that summarise persistent topological features that help gaining insights into complex hidden structures not amenable by other image analysis methods. We shall also demonstrate significant success of a similarly developed PH-based universal steganalysis tool capable for the detection of secret messages hidden inside digital images. We also argue through a pilot study that building PH records from digital images can differentiate breast malignant tumours from benign tumours using digital mammographic images. The research presented in this thesis creates new opportunities to build real applications based on TDA and demonstrate many research challenges in a variety of image processing/analysis tasks. For example, we describe a TDA-based exemplar image inpainting technique (TEBI), superior to existing exemplar algorithm, for the reconstruction of missing image regions