Orthogonal Range Reporting and Rectangle Stabbing for Fat Rectangles

In this paper we study two geometric data structure problems in the special case when input objects or queries are fat rectangles. We show that in this case a significant improvement compared to the general case can be achieved. We describe data structures that answer two- and three-dimensional orthogonal range reporting queries in the case when the query range is a \emph{fat} rectangle. Our two-dimensional data structure uses $O(n)$ words and supports queries in $O(\log\log U +k)$ time, where $n$ is the number of points in the data structure, $U$ is the size of the universe and $k$ is the number of points in the query range. Our three-dimensional data structure needs $O(n\log^{\varepsilon}U)$ words of space and answers queries in $O(\log \log U + k)$ time. We also consider the rectangle stabbing problem on a set of three-dimensional fat rectangles. Our data structure uses $O(n)$ space and answers stabbing queries in $O(\log U\log\log U +k)$ time.Comment: extended version of a WADS'19 pape

Scalable Image Retrieval by Sparse Product Quantization

Fast Approximate Nearest Neighbor (ANN) search technique for high-dimensional feature indexing and retrieval is the crux of large-scale image retrieval. A recent promising technique is Product Quantization, which attempts to index high-dimensional image features by decomposing the feature space into a Cartesian product of low dimensional subspaces and quantizing each of them separately. Despite the promising results reported, their quantization approach follows the typical hard assignment of traditional quantization methods, which may result in large quantization errors and thus inferior search performance. Unlike the existing approaches, in this paper, we propose a novel approach called Sparse Product Quantization (SPQ) to encoding the high-dimensional feature vectors into sparse representation. We optimize the sparse representations of the feature vectors by minimizing their quantization errors, making the resulting representation is essentially close to the original data in practice. Experiments show that the proposed SPQ technique is not only able to compress data, but also an effective encoding technique. We obtain state-of-the-art results for ANN search on four public image datasets and the promising results of content-based image retrieval further validate the efficacy of our proposed method.Comment: 12 page

Internal Pattern Matching Queries in a Text and Applications

We consider several types of internal queries: questions about subwords of a text. As the main tool we develop an optimal data structure for the problem called here internal pattern matching. This data structure provides constant-time answers to queries about occurrences of one subword $x$ in another subword $y$ of a given text, assuming that $|y|=\mathcal{O}(|x|)$, which allows for a constant-space representation of all occurrences. This problem can be viewed as a natural extension of the well-studied pattern matching problem. The data structure has linear size and admits a linear-time construction algorithm. Using the solution to the internal pattern matching problem, we obtain very efficient data structures answering queries about: primitivity of subwords, periods of subwords, general substring compression, and cyclic equivalence of two subwords. All these results improve upon the best previously known counterparts. The linear construction time of our data structure also allows to improve the algorithm for finding $\delta$-subrepetitions in a text (a more general version of maximal repetitions, also called runs). For any fixed $\delta$ we obtain the first linear-time algorithm, which matches the linear time complexity of the algorithm computing runs. Our data structure has already been used as a part of the efficient solutions for subword suffix rank & selection, as well as substring compression using Burrows-Wheeler transform composed with run-length encoding.Comment: 31 pages, 9 figures; accepted to SODA 201

Searching for Hyperbolicity

This is an expository paper, based on by a talk given at the AWM Research Symposium 2017. It is intended as a gentle introduction to geometric group theory with a focus on the notion of hyperbolicity, a theme that has inspired the field from its inception to current-day research

Designing the printed book as an interactive environment

Reading a book demands a certain level of interaction from the reader. The cover must be opened and pages turned to navigate the information inside. Conventions have been developed over the life of the book to assist the reader in this navigation and provide orientation. The evolution of electronic reading material has given readers greater opportunities for interacting with their reading material, but many readers still prefer reading from a printed book. This paper investigates how the interactive organizational paradigm of hypertext can be implemented in a printed book to give the reader the opportunity for greater interaction and benefit from some of the advantages that electronic reading environments provide. The investigation in this paper follows an iterative design process in consultation with a panel of four experts. Through four rounds of consultation and refinement two potential solutions were developed for the incorporation of hypertext methods in a printed book

Multi modal multi-semantic image retrieval

PhDThe rapid growth in the volume of visual information, e.g. image, and video can overwhelm users’ ability to find and access the specific visual information of interest to them. In recent years, ontology knowledge-based (KB) image information retrieval techniques have been adopted into in order to attempt to extract knowledge from these images, enhancing the retrieval performance. A KB framework is presented to promote semi-automatic annotation and semantic image retrieval using multimodal cues (visual features and text captions). In addition, a hierarchical structure for the KB allows metadata to be shared that supports multi-semantics (polysemy) for concepts. The framework builds up an effective knowledge base pertaining to a domain specific image collection, e.g. sports, and is able to disambiguate and assign high level semantics to ‘unannotated’ images. Local feature analysis of visual content, namely using Scale Invariant Feature Transform (SIFT) descriptors, have been deployed in the ‘Bag of Visual Words’ model (BVW) as an effective method to represent visual content information and to enhance its classification and retrieval. Local features are more useful than global features, e.g. colour, shape or texture, as they are invariant to image scale, orientation and camera angle. An innovative approach is proposed for the representation, annotation and retrieval of visual content using a hybrid technique based upon the use of an unstructured visual word and upon a (structured) hierarchical ontology KB model. The structural model facilitates the disambiguation of unstructured visual words and a more effective classification of visual content, compared to a vector space model, through exploiting local conceptual structures and their relationships. The key contributions of this framework in using local features for image representation include: first, a method to generate visual words using the semantic local adaptive clustering (SLAC) algorithm which takes term weight and spatial locations of keypoints into account. Consequently, the semantic information is preserved. Second a technique is used to detect the domain specific ‘non-informative visual words’ which are ineffective at representing the content of visual data and degrade its categorisation ability. Third, a method to combine an ontology model with xi a visual word model to resolve synonym (visual heterogeneity) and polysemy problems, is proposed. The experimental results show that this approach can discover semantically meaningful visual content descriptions and recognise specific events, e.g., sports events, depicted in images efficiently. Since discovering the semantics of an image is an extremely challenging problem, one promising approach to enhance visual content interpretation is to use any associated textual information that accompanies an image, as a cue to predict the meaning of an image, by transforming this textual information into a structured annotation for an image e.g. using XML, RDF, OWL or MPEG-7. Although, text and image are distinct types of information representation and modality, there are some strong, invariant, implicit, connections between images and any accompanying text information. Semantic analysis of image captions can be used by image retrieval systems to retrieve selected images more precisely. To do this, a Natural Language Processing (NLP) is exploited firstly in order to extract concepts from image captions. Next, an ontology-based knowledge model is deployed in order to resolve natural language ambiguities. To deal with the accompanying text information, two methods to extract knowledge from textual information have been proposed. First, metadata can be extracted automatically from text captions and restructured with respect to a semantic model. Second, the use of LSI in relation to a domain-specific ontology-based knowledge model enables the combined framework to tolerate ambiguities and variations (incompleteness) of metadata. The use of the ontology-based knowledge model allows the system to find indirectly relevant concepts in image captions and thus leverage these to represent the semantics of images at a higher level. Experimental results show that the proposed framework significantly enhances image retrieval and leads to narrowing of the semantic gap between lower level machinederived and higher level human-understandable conceptualisation

Using Apache Lucene to Search Vector of Locally Aggregated Descriptors

Surrogate Text Representation (STR) is a profitable solution to efficient similarity search on metric space using conventional text search engines, such as Apache Lucene. This technique is based on comparing the permutations of some reference objects in place of the original metric distance. However, the Achilles heel of STR approach is the need to reorder the result set of the search according to the metric distance. This forces to use a support database to store the original objects, which requires efficient random I/O on a fast secondary memory (such as flash-based storages). In this paper, we propose to extend the Surrogate Text Representation to specifically address a class of visual metric objects known as Vector of Locally Aggregated Descriptors (VLAD). This approach is based on representing the individual sub-vectors forming the VLAD vector with the STR, providing a finer representation of the vector and enabling us to get rid of the reordering phase. The experiments on a publicly available dataset show that the extended STR outperforms the baseline STR achieving satisfactory performance near to the one obtained with the original VLAD vectors.Comment: In Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2016) - Volume 4: VISAPP, p. 383-39