An improved fast edit approach for two-string approximated mean computation applied to OCR

This paper presents a new fast algorithm for computing an approximation to the mean of two strings of characters representing a 2D shape and its application to a new Wilson-based editing procedure. The approximate mean is built up by including some symbols from the two original strings. In addition, a Greedy approach to this algorithm is studied, which allows us to reduce the time required to compute an approximate mean. The new dataset editing scheme relaxes the criterion for deleting instances proposed by the Wilson editing procedure. In practice, not all instances misclassified by their near neighbors are pruned. Instead, an artificial instance is added to the dataset in the hope of successfully classifying the instance in the future. The new artificial instance is the approximated mean of the misclassified sample and its same-class nearest neighbor. Experiments carried out over three widely known databases of contours show that the proposed algorithm performs very well when computing the mean of two strings, and outperforms methods proposed by other authors. In particular, the low computational time required by the heuristic approach makes it very suitable when dealing with long length strings. Results also show that the proposed preprocessing scheme can reduce the classification error in about 83% of trials. There is empirical evidence that using the Greedy approximation to compute the approximated mean does not affect the performance of the editing procedure.This work is partially supported by the Spanish CICYT under project DPI2006-15542-C04-01, the Spanish MICINN through project TIN2009-14205-CO4-01 and by the Spanish research program Consolider Ingenio 2010: MIPRCV (CSD2007-00018)

Boosting Perturbation-Based Iterative Algorithms to Compute the Median String

[Abstract] The most competitive heuristics for calculating the median string are those that use perturbation-based iterative algorithms. Given the complexity of this problem, which under many formulations is NP-hard, the computational cost involved in the exact solution is not affordable. In this work, the heuristic algorithms that solve this problem are addressed, emphasizing its initialization and the policy to order possible editing operations. Both factors have a significant weight in the solution of this problem. Initial string selection influences the algorithm’s speed of convergence, as does the criterion chosen to select the modification to be made in each iteration of the algorithm. To obtain the initial string, we use the median of a subset of the original dataset; to obtain this subset, we employ the Half Space Proximal (HSP) test to the median of the dataset. This test provides sufficient diversity within the members of the subset while at the same time fulfilling the centrality criterion. Similarly, we provide an analysis of the stop condition of the algorithm, improving its performance without substantially damaging the quality of the solution. To analyze the results of our experiments, we computed the execution time of each proposed modification of the algorithms, the number of computed editing distances, and the quality of the solution obtained. With these experiments, we empirically validated our proposal.This work was supported in part by the Comisión Nacional de Investigación Científica y Tecnológica - Programa de Formación de Capital Humano Avanzado (CONICYT-PCHA)/Doctorado Nacional/2014-63140074 through the Ph.D. Scholarship, in part by the European Union's Horizon 2020 under the Marie Sklodowska-Curie under Grant 690941, in part by the Millennium Institute for Foundational Research on Data (IMFD), and in part by the FONDECYT-CONICYT under Grant 1170497. The work of ÓSCAR PEDREIRA was supported in part by the Xunta de Galicia/FEDER-UE refs under Grant CSI ED431G/01 and Grant GRC: ED431C 2017/58, in part by the Office of the Vice President for Research and Postgraduate Studies of the Universidad Católica de Temuco, VIPUCT Project 2020EM-PS-08, and in part by the FEQUIP 2019-INRN-03 of the Universidad Católica de TemucoXunta de Galicia; ED431G/01Xunta de Galicia; ED431C 2017/58Chile. Comisión Nacional de Investigación Científica y Tecnológica; 2014-63140074Chile. Comisión Nacional de Investigación Científica y Tecnológica; 1170497Universidad Católica de Temuco (Chile); 2020EM-PS-08Universidad Católica de Temuco (Chile); 2019-INRN-0

Learning the Consensus of Multiple Correspondences between Data Structures

En aquesta tesi presentem un marc de treball per aprendre el consens donades múltiples correspondències. S'assumeix que les diferents parts involucrades han generat aquestes correspondències per separat, i el nostre sistema actua com un mecanisme que calibra diferents característiques i considera diferents paràmetres per aprendre les millors assignacions i així, conformar una correspondència amb la major precisió possible a costa d'un cost computacional raonable. Aquest marc de treball de consens és presentat en una forma gradual, començant pels desenvolupaments més bàsics que utilitzaven exclusivament conceptes ben definits o únicament un parell de correspondències, fins al model final que és capaç de considerar múltiples correspondències, amb la capacitat d'aprendre automàticament alguns paràmetres de ponderació. Cada pas d'aquest marc de treball és avaluat fent servir bases de dades de naturalesa variada per demostrar efectivament que és possible tractar diferents escenaris de matching. Addicionalment, dos avanços suplementaris relacionats amb correspondències es presenten en aquest treball. En primer lloc, una nova mètrica de distància per correspondències s'ha desenvolupat, la qual va derivar en una nova estratègia per a la cerca de mitjanes ponderades. En segon lloc, un marc de treball específicament dissenyat per a generar correspondències al camp del registre d'imatges s'ha modelat, on es considera que una de les imatges és una imatge completa, i l'altra és una mostra petita d'aquesta. La conclusió presenta noves percepcions de com el nostre marc de treball de consens pot ser millorada, i com els dos desenvolupaments paral·lels poden convergir amb el marc de treball de consens.En esta tesis presentamos un marco de trabajo para aprender el consenso dadas múltiples correspondencias. Se asume que las distintas partes involucradas han generado dichas correspondencias por separado, y nuestro sistema actúa como un mecanismo que calibra distintas características y considera diferentes parámetros para aprender las mejores asignaciones y así, conformar una correspondencia con la mayor precisión posible a expensas de un costo computacional razonable. El marco de trabajo de consenso es presentado en una forma gradual, comenzando por los acercamientos más básicos que utilizaban exclusivamente conceptos bien definidos o únicamente un par de correspondencias, hasta el modelo final que es capaz de considerar múltiples correspondencias, con la capacidad de aprender automáticamente algunos parámetros de ponderación. Cada paso de este marco de trabajo es evaluado usando bases de datos de naturaleza variada para demostrar efectivamente que es posible tratar diferentes escenarios de matching. Adicionalmente, dos avances suplementarios relacionados con correspondencias son presentados en este trabajo. En primer lugar, una nueva métrica de distancia para correspondencias ha sido desarrollada, la cual derivó en una nueva estrategia para la búsqueda de medias ponderadas. En segundo lugar, un marco de trabajo específicamente diseñado para generar correspondencias en el campo del registro de imágenes ha sido establecida, donde se considera que una de las imágenes es una imagen completa, y la otra es una muestra pequeña de ésta. La conclusión presenta nuevas percepciones de cómo nuestro marco de trabajo de consenso puede ser mejorada, y cómo los dos desarrollos paralelos pueden converger con éste.In this work, we present a framework to learn the consensus given multiple correspondences. It is assumed that the several parties involved have generated separately these correspondences, and our system acts as a mechanism that gauges several characteristics and considers different parameters to learn the best mappings and thus, conform a correspondence with the highest possible accuracy at the expense of a reasonable computational cost. The consensus framework is presented in a gradual form, starting from the most basic approaches that used exclusively well-known concepts or only two correspondences, until the final model which is able to consider multiple correspondences, with the capability of automatically learning some weighting parameters. Each step of the framework is evaluated using databases of varied nature to effectively demonstrate that it is capable to address different matching scenarios. In addition, two supplementary advances related on correspondences are presented in this work. Firstly, a new distance metric for correspondences has been developed, which lead to a new strategy for the weighted mean correspondence search. Secondly, a framework specifically designed for correspondence generation in the image registration field has been established, where it is considered that one of the images is a full image, and the other one is a small sample of it. The conclusion presents insights of how our consensus framework can be enhanced, and how these two parallel developments can converge with it