Pedro Jussieu de Rezende

Point set pattern matching in d-dimensions

In this paper we apply computational geometry techniques to obtain an efficient algorithm for the following point set pattern matching problem. Given a setS ofn points and a setP ofk points in thed-dimensional Euclidean space, determine whetherP matches anyk-subset ofS, where a match can be any similarity, i.e., the setP is allowed to undergo translation, rotation, reflection, and global scaling. Motivated by the need to traverse the sets in an orderly fashion to shun exponential complexity, we circumvent the lack of a total order for points in high-dimensional spaces by using an extension of one-dimensional sorting to higher dimensions (which we call “circular sorting”). This mechanism enables us to achieve the orderly traversal we sought. An optimal algorithm (in time and space) is described for performing circular sorting in arbitrary dimensions. The time complexity of the resulting algorithm for point set pattern matching is O(n logn+kn) for dimension one and O(knd) for dimensiond≥2.

An active learning paradigm based on a priori data reduction and organization

Abstract In the past few years, active learning has been reasonably successful and it has drawn a lot of attention. However, recent active learning methods have focused on strategies in which a large unlabeled dataset has to be reprocessed at each learning iteration. As the datasets grow, these strategies become inefficient or even a tremendous computational challenge. In order to address these issues, we propose an effective and efficient active learning paradigm which attains a significant reduction in the size of the learning set by applying an a priori process of identification and organization of a small relevant subset. Furthermore, the concomitant classification and selection processes enable the classification of a very small number of samples, while selecting the informative ones. Experimental results showed that the proposed paradigm allows to achieve high accuracy quickly with minimum user interaction, further improving its efficiency.

A data reduction and organization approach for efficient image annotation

The labor-intensive and time-consuming process of annotating data is a serious bottleneck in many pattern recognition applications when handling massive datasets. Active learning strategies have been sought to reduce the cost on human annotation, by means of automatically selecting the most informative unlabeled samples for annotation. The critical issue lies on the selection of such samples. As an effective solution, we propose an active learning approach that preprocesses the dataset, efficiently reduces and organizes a learning set of samples and selects the most representative ones for human annotation. Experiments performed on real datasets show that the proposed approach requires only a few iterations to achieve high accuracy, keeping user involvement to a minimum.

Interactive Segmentation by Image Foresting Transform on Superpixel Graphs

There are many scenarios in which user interaction is essential for effective image segmentation. In this paper, we present a new interactive segmentation method based on the Image Foresting Transform (IFT). The method over segments the input image, creates a graph based on these segments (super pixels), receives markers (labels) drawn by the user on some super pixels and organizes a competition to label every pixel in the image. Our method has several interesting properties: it is effective, efficient, capable of segmenting multiple objects in almost linear time on the number of super pixels, readily extendable through previously published techniques, and benefits from domain-specific feature extraction. We also present a comparison with another technique based on the IFT, which can be seen as its pixel-based counterpart. Another contribution of this paper is the description of automatic (robot) users. Given a ground truth image, these robots simulate interactive segmentation by trained and untrained users, reducing the costs and biases involved in comparing segmentation techniques.

A hybrid GRASP heuristic to construct effective drawings of proportional symbol maps

Proportional symbol map is a cartographic tool that employs symbols to represent data associated with specific locations. Each symbol is drawn at the location of an event and its size is proportional to the numerical data collected at that point on the map. The symbols considered here are opaque disks. When two or more disks overlap, part of their boundaries may not be visible and it might be difficult to gauge their size. Therefore, the order in which the disks are drawn affects the visual quality of a map. In this work, we focus on stacking drawings, i.e., a drawing that corresponds to the disks being stacked up, in sequence, starting from the one at the bottom of the stack. We address the Max-Total problem, which consists in maximizing the total visible boundary of all disks. We propose a sophisticated heuristic based on GRASP that includes most of the advanced techniques described in the literature for this procedure. We tested both sequential and parallel implementations on benchmark instances and the comparison against optimal solutions confirms the high quality of our heuristic. To the best of our knowledge, this is the first time a metaheuristic is applied to this problem.

Robust active learning for the diagnosis of parasites

We have developed an automated system for the diagnosis of intestinal parasites from optical microscopy images. The objects (species of parasites and impurities) segmented from these images form a large dataset. We are interested in the active learning problem of selecting a reasonably small number of objects to be labeled under an experts supervision for use in training a pattern classifier. However, impurities are very numerous, constitute several clusters in the feature space, and can be quite similar to some species of parasites, leading to a significant challenge for active learning methods. We propose a technique that pre-organizes the data and then properly balances the selection of samples from all classes and uncertain samples for training. Early data organization avoids reprocessing of the large dataset at each learning iteration, enabling the halting of sample selection after a desired number of samples per iteration, yielding interactive response time. We validate our method by comparing it with state-of-the-art approaches, using a previously labeled dataset of almost 6000 objects. Moreover, we report results from experiments on a very realistic scenario, consisting of a dataset with over 140,000 unlabeled objects, under unbalanced classes, the absence of some classes, and the presence of a very large set of impurities. HighlightsA robust active learning method, called RDS, based on a priori data organization.RDS properly balances sample diversity and uncertainty for useful sample selection.It provides high classification accuracy for the automated diagnosis of parasites.Comparisons with different clustering, classification and other literature methods.RDS was evaluated by an experienced expert in parasitology using a realistic scenario.

Engineering Art Galleries

The Art Gallery Problem (AGP) is one of the most well-known problems in Computational Geometry (CG), with a rich history in the study of algorithms, complexity, and variants. Recently there has been a surge in experimental work on the problem. In this survey, we describe this work, show the chronology of developments, and compare current algorithms, including two unpublished versions, in an exhaustive experiment. Furthermore, we show what core algorithmic ingredients have led to recent successes.

Optimizing the layout of proportional symbol maps

Proportional symbol maps are a cartographic tool to assist in the visualization and analysis of quantitative data associated with specific locations (earthquake magnitudes, oil well production, temperature at weather stations, etc.). Symbol sizes are proportional to the magnitude of the quantities that they represent. We present a novel integer programming model to draw opaque disks on a map with the objective of maximizing the total visible border of all disks (an established measure of quality). We focus on drawings obtained by layering symbols on top of each other, known as stacking drawings. We introduce decomposition techniques, and several new families of facet-defining inequalities, which are implemented in a cut-and-branch algorithm. We assess the effectiveness of our approach through a series of computational experiments using real demographic and geophysical data. To the best of our knowledge, we are the first to provide provably optimal solutions to some of those problem instances.

Algorithm 966: A Practical Iterative Algorithm for the Art Gallery Problem Using Integer Linear Programming

In the last few decades, the search for exact algorithms for known NP-hard geometric problems has intensified. Many of these solutions use Integer Linear Programming (ILP) modeling and rely on state-of-the- art solvers to be able to find optimal solutions for large instances in a matter of minutes. In this work, we discuss an ILP-based algorithm that solves to optimality the Art Gallery Problem (AGP), one of the most studied problems in computational geometry. The basic idea of our method is to iteratively generate upper and lower bounds for the problem through the resolution of discretized versions of the AGP, which are reduced to instances of the Set Cover Problem. Our algorithm was implemented and tested on almost 3,000 instances and attained optimal solutions for the vast majority of them, greatly increasing the set of instances for which exact solutions are known. To the best of our knowledge, in spite of the extensive study of the AGP in the last four decades, no other algorithm has shown the ability to solve the AGP as effectively and efficiently as the one described here. Evidence of its robustness is presented through tests done on a number of classes of polygons of various sizes with and without holes. A software package implementing the algorithm is made available.

Superpixel-Based Interactive Classification of Very High Resolution Images

Very high resolution (VHR) images are large datasets for pixel annotation -- a process that has depended on the supervised training of an effective pixel classifier. Active learning techniques have mitigated this problem, but pixel descriptors are limited to local image information and the large number of pixels makes the response time to the users actions impractical, during active learning. To circumvent the problem, we present an active learning strategy that relies on superpixel descriptors and a priori dataset reduction. Firstly, we compare VHR image annotation using superpixel- and pixel-based classifiers, as designed by the same state-of-the-art active learning technique -- Multi-Class Level Uncertainty (MCLU). Even with the dataset reduction provided by the superpixel representation, MCLU remains unfeasible for user interaction. Therefore, we propose a technique to considerably reduce the superpixel dataset for active learning. Moreover, we subdivide the reduced dataset into a list of subsets with random sample rearrangement to gain both speed and sample diversity during the active learning process.