Angle Tree: Nearest Neighbor Search in High Dimensions with Low Intrinsic Dimensionality

We propose an extension of tree-based space-partitioning indexing structures for data with low intrinsic dimensionality embedded in a high dimensional space. We call this extension an Angle Tree. Our extension can be applied to both classical kd-trees as well as the more recent rp-trees. The key idea of our approach is to store the angle (the "dihedral angle") between the data region (which is a low dimensional manifold) and the random hyperplane that splits the region (the "splitter"). We show that the dihedral angle can be used to obtain a tight lower bound on the distance between the query point and any point on the opposite side of the splitter. This in turn can be used to efficiently prune the search space. We introduce a novel randomized strategy to efficiently calculate the dihedral angle with a high degree of accuracy. Experiments and analysis on real and synthetic data sets shows that the Angle Tree is the most efficient known indexing structure for nearest neighbor queries in terms of preprocessing and space usage while achieving high accuracy and fast search time.Comment: To be submitted to IEEE Transactions on Pattern Analysis and Machine Intelligenc

PCA-RECT: An Energy-efficient Object Detection Approach for Event Cameras

We present the first purely event-based, energy-efficient approach for object detection and categorization using an event camera. Compared to traditional frame-based cameras, choosing event cameras results in high temporal resolution (order of microseconds), low power consumption (few hundred mW) and wide dynamic range (120 dB) as attractive properties. However, event-based object recognition systems are far behind their frame-based counterparts in terms of accuracy. To this end, this paper presents an event-based feature extraction method devised by accumulating local activity across the image frame and then applying principal component analysis (PCA) to the normalized neighborhood region. Subsequently, we propose a backtracking-free k-d tree mechanism for efficient feature matching by taking advantage of the low-dimensionality of the feature representation. Additionally, the proposed k-d tree mechanism allows for feature selection to obtain a lower-dimensional dictionary representation when hardware resources are limited to implement dimensionality reduction. Consequently, the proposed system can be realized on a field-programmable gate array (FPGA) device leading to high performance over resource ratio. The proposed system is tested on real-world event-based datasets for object categorization, showing superior classification performance and relevance to state-of-the-art algorithms. Additionally, we verified the object detection method and real-time FPGA performance in lab settings under non-controlled illumination conditions with limited training data and ground truth annotations.Comment: Accepted in ACCV 2018 Workshops, to appea

Graph indexing and retrieval based on graph prototypes

[ANGLÈS] Taking a query from a high number of data stored into a database, as fast as possible, is a recurrent problem in the field of computer sciences practically since its origins. At the existence of this problem, it’s necessary to add, moreover, the fact that actually databases contains data types of more diverse and unexpected character possible. Now we are not talking about originating databases which only contained sets of numbers or characters strings. (...) All that I want to make into the present work and I think that was achieved as far as possible, has been to develop and to present a methodology to carry out this process. The Metric Trees of prototypes are based on a well-known strategy, which is based on grouping the data stored in database at the smartest possible way. But also we has added the concept of a graph prototype. A structure that contains information of a set of instances represented by graphs, used until now for classification and recognition. In this thesis we have used graphs as representatives of elements that have to be queried in databases. Note that graphs have the capacity to represent complex objects, for this reason the number of graph databases is increasing. Due to in the literature appears different ways to build a prototype, the work presented here shows a comparative study between the main methods. Combining these two concepts, the Metric Tree and the graph prototype, we propose the construction of metric trees where the graph prototypes are routing nodes to help to decide the way to explore when we make a search in the tree. We have used Metric Trees to make classification and to find all instances that are lower than a maximum distance. (...)[CATALÀ] El trobar-nos davant una gran quantitat de dades i tenir que fer cerques d’aquestes el més ràpid possible és un problema recurrent en el camp de les ciències de la computació pràcticament des dels seus orígens. A l'existència d'aquest problema, se li ha d’afegir, a més a més, el fet de que actualment les bases de dades emmagatzemen tipus de dades de la naturalesa més diversa i molts cops inesperada possible. Ja no parlem de les bases de dades originaries que únicament contenien números o cadenes caràcters. (...) El que he volgut en aquest treball i penso que en la mesura del que era possible s'ha aconseguit, és desenvolupar i presentar una metodologia per portar a terme aquest procés. Els Metric Trees de prototips, que es basen en la ja coneguda estratègia d'agrupar les dades que anem guardant a una base de dades de la forma més intel·ligent possible per no haver d’explorar totes les instàncies que tenim quan volem fer una cerca, però a més a més s'ha afegit el concepte de prototip. Una estructura, que agrupa la informació d'un conjunt d'instàncies, utilitzada fins ara per a fer classificació i reconeixement. Conjugant aquests dos conceptes, el de Metric Tree i el de prototip, plantejem la construcció d'arbres de cerca on els prototips siguin els nodes intermedis, que ens ajudin a decidir quin camí explorar quan volem fer una cerca sobre l'arbre. I utilitzant, aquests tant per a fer classificació com per a buscar totes les instàncies que estiguin una distància més petita d’una distància máxima. Tot això tenint present, que les dades amb que treballem són grafs, és a dir que la metodologia presentada, té la versatilitat de poder-se aplicar, a qualsevol tipus d'informació que es pugui representar d'aquesta manera. (...