SCHEMI DI SUDDIVISIONE PER LA MODELLAZIONE GRAFICA

La presente tesi affronta lo studio di una particolare classe di metodi iterativi, detti schemi di suddivisione, utilizzati principalmente in computer graphics per la modellazione e la manipolazione di curve e superfici a partire da un insieme discreto di dati. L'origine di tali metodi è attribuita allo studio di problemi geometrici di smussamento degli spigoli di una superficie poliedrica, talvolta chiamati ``wood carver algorithms'' (algoritmi dell'intagliatore) in quanto le ripetute operazioni di smussamento ricordano le fasi di intaglio e levigazione caratteristiche della lavorazione artigianale del legno. Attualmente essi rappresentano uno degli strumenti matematici indispensabili nell'ambito della Computer Aided Geometric Design (CAGD), ossia di quella branca delle scienze applicate che si occupa della ricerca di metodi matematici e di tecnologie software per l'elaborazione assistita dal calcolatore di oggetti geometrici, quali appunto curve, superfici e volumi, che costituiscono gli elementi di base per la rappresentazione di un qualsiasi oggetto tridimensionale. Gli schemi di suddivisione sono determinati da poche semplici regole lineari che, usate ripetutamente, permettono di generare forme ed oggetti ``regolari'' a partire da una loro rappresentazione ``grossolana''. Formalmente sono definiti da una successione di operatori lineari, $\{\mathcal{S}_{\mathbf{a}^{(k)}} :\ell^\infty{(\mathbb{Z}^s)}\to\ell^\infty{(\mathbb{Z}^s)}\}_{k\geq0}$, dette regole di raffinamento, della forma (\mathcal{S}_{\mathbf{a}^{(k)}} \mathbf{f})_\alpha =\sum_{\beta\in\mathbb{Z}^s } {a}_{\alpha-2\beta}^{(k)} f_\beta, \quad \bb f=\{f_\beta\}_{\beta\in\mathbb{Z}^s }\in \ell^\infty{(\mathbb{Z}^s)},\,\, k\in\mathbb{N} dove $\{\mathbf{a}^{(k)}\}_{k\geq0}$ \`e una successione di elementi di $\ell^\infty{(\mathbb{Z}^s)}$: $\mathbf{a}^{(k)}=\{{a}_{\gamma}^{(k)}\}_{\gamma\in\mathbb{Z}^s}$. Sono metodi computazionalmente efficienti, piuttosto facili da implementare e soprattutto permettono di definire curve e superfici con un certo grado di regolarità. Malgrado la semplicità degli algoritmi in sé, però, l'analisi della convergenza della sequenza $\{\mathbf{f}^{(k)}\}_{k>0}$, con $\mathbf{f}^{(k)}=\mathcal{S}_{\mathbf{a}^{(k-1)}} \cdots\mathcal{S}_{\mathbf{a}^{(0)}}\mathbf{f}^{(0)}$ ed $\mathbf{f}^{(0)}\in\ell^\infty{(\mathbb{Z}^s)}$, può rivelarsi anche molto complessa. Ci sono ovviamente delle eccezioni: una scelta opportuna delle regole utilizzate nella fase di raffinamento consente una analisi esaustiva della convergenza e della regolarità della superficie limite. Nella tesi è stato approfondito lo studio della convergenza e della regolarità delle funzioni limite, ponendo particolare attenzione al caso stazionario. È stato analizzato nel dettaglio il caso univariato e bivariato, dove, grazie ad un formalismo basato sulle serie formali di Laurent, è possibile fornire delle condizioni necessarie e sufficienti di convergenza di facile verificabilità. I risultati ottenuti sono stati riletti in chiave matriciale per tenere vivo il legame con l'aspetto pratico ed implementativo degli schemi. Si è inoltre fornita una breve panoramica dei più importanti schemi univariati e bivariati presenti in letteratura, trattando, in particolare, lo studio dell'algoritmo di Chaikin e dello schema di Loop, per i quali è stata anche curata un'implementazione in ambiente Matlab. Lo schema di Loop, infine, è stato applicato a reti iniziali di diversa natura (reti aperte, chiuse, regolari e non regolari), permettendoci di apprezzare le potenzialità degli algoritmi di suddivisione e il loro utilizzo nell'ambito della modellazione grafica

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

Investigating binary partition power in metric query

It is generally understood that, as dimensionality increases, the minimum cost of metric query tends from (log ) to () in both space and time, where is the size of the data set. With low dimensionality, the former is easy to achieve; with very high dimensionality, the latter is inevitable. We previously described BitPart as a novel mechanism suitable for performing exact metric search in “high(er)” dimensions. The essential tradeoff of BitPart is that its space cost is linear with respect to the size of the data, but the actual space required for each object may be small as log2 bits, which allows even very large data sets to be queried using only main memory. Potentially the time cost still scales with (log ). Together these attributes give exact search which outperforms indexing structures if dimensionality is within a certain range. In this article, we reiterate the design of BitPart in this context. The novel contribution is an in-depth examination of what the notion of “high(er)” means in practical terms. To do this we introduce the notion of exclusion power, and show its application to some generated data sets across different dimensions.Publisher PD

Aggregating Local Descriptors for Epigraphs Recognition

In this paper, we consider the task of recognizing epigraphs in images such as photos taken using mobile devices. Given a set of 17,155 photos related to 14,560 epigraphs, we used a k-NearestNeighbor approach in order to perform the recognition. The contribution of this work is in evaluating state-of-the-art visual object recognition techniques in this specific context. The experimental results conducted show that Vector of Locally Aggregated Descriptors obtained aggregating SIFT descriptors is the best choice for this task.The Fourth International Conference on Digital Presentation and Preservation of Cultural and Scientific Heritage—DiPP2014 is supported by the Ministry of Education and Science and is under the patronage of UNESCO

Supermetric search

Metric search is concerned with the efficient evaluation of queries in metric spaces. In general, a large space of objects is arranged in such a way that, when a further object is presented as a query, those objects most similar to the query can be efficiently found. Most mechanisms rely upon the triangle inequality property of the metric governing the space. The triangle inequality property is equivalent to a finite embedding property, which states that any three points of the space can be isometrically embedded in two-dimensional Euclidean space. In this paper, we examine a class of semimetric space that is finitely four-embeddable in three-dimensional Euclidean space. In mathematics this property has been extensively studied and is generally known as the four-point property. All spaces with the four-point property are metric spaces, but they also have some stronger geometric guarantees. We coin the term supermetric space as, in terms of metric search, they are significantly more tractable. Supermetric spaces include all those governed by Euclidean, Cosine, Jensen–Shannon and Triangular distances, and are thus commonly used within many domains. In previous work we have given a generic mathematical basis for the supermetric property and shown how it can improve indexing performance for a given exact search structure. Here we present a full investigation into its use within a variety of different hyperplane partition indexing structures, and go on to show some more of its flexibility by examining a search structure whose partition and exclusion conditions are tailored, at each node, to suit the individual reference points and data set present there. Among the results given, we show a new best performance for exact search using a well-known benchmark

Modelling string structure in vector spaces

Searching for similar strings is an important and frequent database task both in terms of human interactions and in absolute world-wide CPU utilisation. A wealth of metric functions for string comparison exist. However, with respect to the wide range of classification and other techniques known within vector spaces, such metrics allow only a very restricted range of techniques. To counter this restriction, various strategies have been used for mapping string spaces into vector spaces, approximating the string distances within the mapped space and therefore allowing vector space techniques to be used. In previous work we have developed a novel technique for mapping metric spaces into vector spaces, which can therefore be applied for this purpose. In this paper we evaluate this technique in the context of string spaces, and compare it to other published techniques for mapping strings to vectors. We use a publicly available English lexicon as our experimental data set, and test two different string metrics over it for each vector mapping. We find that our novel technique considerably outperforms previously used technique in preserving the actual distance.Publisher PD

SPLX-Perm: A Novel Permutation-Based Representation for Approximate Metric Search

Many approaches for approximate metric search rely on a permutation-based representation of the original data objects. The main advantage of transforming metric objects into permutations is that the latter can be efficiently indexed and searched using data structures such as inverted-files and prefix trees. Typically, the permutation is obtained by ordering the identifiers of a set of pivots according to their distances to the object to be represented. In this paper, we present a novel approach to transform metric objects into permutations. It uses the object-pivot distances in combination with a metric transformation, called n-Simplex projection. The resulting permutation-based representation , named SPLX-Perm, is suitable only for the large class of metric space satisfying the n-point property. We tested the proposed approach on two benchmarks for similarity search. Our preliminary results are encouraging and open new perspectives for further investigations on the use of the n-Simplex projection for supporting permutation-based indexing

Interactive video retrieval in the age of effective joint embedding deep models: lessons from the 11th VBS

This paper presents findings of the eleventh Video Browser Showdown competition, where sixteen teams competed in known-item and ad-hoc search tasks. Many of the teams utilized state-of-the-art video retrieval approaches that demonstrated high effectiveness in challenging search scenarios. In this paper, a broad survey of all utilized approaches is presented in connection with an analysis of the performance of participating teams. Specifically, both high-level performance indicators are presented with overall statistics as well as in-depth analysis of the performance of selected tools implementing result set logging. The analysis reveals evidence that the CLIP model represents a versatile tool for cross-modal video retrieval when combined with interactive search capabilities. Furthermore, the analysis investigates the effect of different users and text query properties on the performance in search tasks. Last but not least, lessons learned from search task preparation are presented, and a new direction for ad-hoc search based tasks at Video Browser Showdown is introduced

Interactive video retrieval evaluation at a distance: comparing sixteen interactive video search systems in a remote setting at the 10th Video Browser Showdown

The Video Browser Showdown addresses difficult video search challenges through an annual interactive evaluation campaign attracting research teams focusing on interactive video retrieval. The campaign aims to provide insights into the performance of participating interactive video retrieval systems, tested by selected search tasks on large video collections. For the first time in its ten year history, the Video Browser Showdown 2021 was organized in a fully remote setting and hosted a record number of sixteen scoring systems. In this paper, we describe the competition setting, tasks and results and give an overview of state-of-the-art methods used by the competing systems. By looking at query result logs provided by ten systems, we analyze differences in retrieval model performances and browsing times before a correct submission. Through advances in data gathering methodology and tools, we provide a comprehensive analysis of ad-hoc video search tasks, discuss results, task design and methodological challenges. We highlight that almost all top performing systems utilize some sort of joint embedding for text-image retrieval and enable specification of temporal context in queries for known-item search. Whereas a combination of these techniques drive the currently top performing systems, we identify several future challenges for interactive video search engines and the Video Browser Showdown competition itself