Image Segmentation by Image Foresting Transform with Non-smooth Connectivity Functions

Abstract-Image segmentation, such as to extract an object from a background, is very useful for medical and biological image analysis. In this work, we propose new methods for interactive segmentation of multidimensional images, based on the Image Foresting Transform (IFT), by exploiting for the first time non-smooth connectivity functions (NSCF) with a strong theoretical background. The new algorithms provide global optimum solutions according to an energy function of graph cut, subject to high-level boundary constraints (polarity and shape), or consist in a sequence of paths' optimization in residual graphs. Our experimental results indicate substantial improvements in accuracy in relation to other state-of-the-art methods, by allowing the customization of the segmentation to a given target object

Image Segmentation by Image Foresting Transform with Non-smooth Connectivity Functions

Abstract-In the framework of the Image Foresting Transform (IFT), there is a class of connectivity functions that were vaguely explored, which corresponds to the non-smooth connectivity functions (NSCF). These functions are more adaptive to cope with the problems of field inhomogeneity, which are common in MR images of 3 Tesla. In this work, we investigate the NSCF from the standpoint of theoretical and experimental aspects. We formally classify several non-smooth functions according to a proposed diagram representation. Then, we investigate some theoretical properties for some specific regions of the diagram. Our analysis reveals that many NSCFs are, in fact, the result of a sequence of optimizations, each of them involving a maximal set of elements, in a well-structured way. Our experimental results indicate that substantial improvements can be obtained by NSCFs in the 3D segmentation of MR images of 3 Tesla, when compared to smooth connectivity functions

Uma abordagem de agrupamento baseada na técnica de divisão e conquista e floresta de caminhos ótimos

Orientador: Alexandre Xavier FalcãoDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: O agrupamento de dados é um dos principais desafios em problemas de Ciência de Dados. Apesar do seu progresso científico em quase um século de existência, algoritmos de agrupamento ainda falham na identificação de grupos (clusters) naturalmente relacionados com a semântica do problema. Ademais, os avanços das tecnologias de aquisição, comunicação, e armazenamento de dados acrescentam desafios cruciais com o aumento considerável de dados, os quais não são tratados pela maioria das técnicas. Essas questões são endereçadas neste trabalho através da proposta de uma abordagem de divisão e conquista para uma técnica de agrupamento única em encontrar um grupo por domo da função de densidade de probabilidade dos dados --- o algoritmo de agrupamento por floresta de caminhos ótimos (OPF - Optimum-Path Forest). Nesta técnica, amostras são interpretadas como nós de um grafo cujos arcos conectam os $k$-vizinhos mais próximos no espaço de características. Os nós são ponderados pela sua densidade de probabilidade e um mapa de conexidade é maximizado de modo que cada máximo da função densidade de probabilidade se torna a raiz de uma árvore de caminhos ótimos (grupo). O melhor valor de $k$ é estimado por otimização em um intervalo de valores dependente da aplicação. O problema com este método é que um número alto de amostras torna o algoritmo inviável, devido ao espaço de memória necessário para armazenar o grafo e o tempo computacional para encontrar o melhor valor de $k$. Visto que as soluções existentes levam a resultados ineficazes, este trabalho revisita o problema através da proposta de uma abordagem de divisão e conquista com dois níveis. No primeiro nível, o conjunto de dados é dividido em subconjuntos (blocos) menores e as amostras pertencentes a cada bloco são agrupadas pelo algoritmo OPF. Em seguida, as amostras representativas de cada grupo (mais especificamente as raízes da floresta de caminhos ótimos) são levadas ao segundo nível, onde elas são agrupadas novamente. Finalmente, os rótulos de grupo obtidos no segundo nível são transferidos para todas as amostras do conjunto de dados através de seus representantes do primeiro nível. Nesta abordagem, todas as amostras, ou pelo menos muitas delas, podem ser usadas no processo de aprendizado não supervisionado, sem afetar a eficácia do agrupamento e, portanto, o procedimento é menos susceptível a perda de informação relevante ao agrupamento. Os resultados mostram agrupamentos satisfatórios em dois cenários, segmentação de imagem e agrupamento de dados arbitrários, tendo como base a comparação com abordagens populares. No primeiro cenário, a abordagem proposta atinge os melhores resultados em todas as bases de imagem testadas. No segundo cenário, os resultados são similares aos obtidos por uma versão otimizada do método original de agrupamento por floresta de caminhos ótimosAbstract: Data clustering is one of the main challenges when solving Data Science problems. Despite its progress over almost one century of research, clustering algorithms still fail in identifying groups naturally related to the semantics of the problem. Moreover, the advances in data acquisition, communication, and storage technologies add crucial challenges with a considerable data increase, which are not handled by most techniques. We address these issues by proposing a divide-and-conquer approach to a clustering technique, which is unique in finding one group per dome of the probability density function of the data --- the Optimum-Path Forest (OPF) clustering algorithm. In the OPF-clustering technique, samples are taken as nodes of a graph whose arcs connect the $k$-nearest neighbors in the feature space. The nodes are weighted by their probability density values and a connectivity map is maximized such that each maximum of the probability density function becomes the root of an optimum-path tree (cluster). The best value of $k$ is estimated by optimization within an application-specific interval of values. The problem with this method is that a high number of samples makes the algorithm prohibitive, due to the required memory space to store the graph and the computational time to obtain the clusters for the best value of $k$. Since the existing solutions lead to ineffective results, we decided to revisit the problem by proposing a two-level divide-and-conquer approach. At the first level, the dataset is divided into smaller subsets (blocks) and the samples belonging to each block are grouped by the OPF algorithm. Then, the representative samples (more specifically the roots of the optimum-path forest) are taken to a second level where they are clustered again. Finally, the group labels obtained in the second level are transferred to all samples of the dataset through their representatives of the first level. With this approach, we can use all samples, or at least many samples, in the unsupervised learning process without affecting the grouping performance and, therefore, the procedure is less likely to lose relevant grouping information. We show that our proposal can obtain satisfactory results in two scenarios, image segmentation and the general data clustering problem, in comparison with some popular baselines. In the first scenario, our technique achieves better results than the others in all tested image databases. In the second scenario, it obtains outcomes similar to an optimized version of the traditional OPF-clustering algorithmMestradoCiência da ComputaçãoMestre em Ciência da ComputaçãoCAPE

Análise visual aplicada à análise de imagens

Orientadores: Alexandre Xavier Falcão, Alexandru Cristian Telea, Pedro Jussieu de Rezende, Johannes Bernardus Theodorus Maria RoerdinkTese (doutorado) - Universidade Estadual de Campinas, Instituto de Computação e Universidade de GroningenResumo: Análise de imagens é o campo de pesquisa preocupado com a extração de informações a partir de imagens. Esse campo é bastante importante para aplicações científicas e comerciais. O objetivo principal do trabalho apresentado nesta tese é permitir interatividade com o usuário durante várias tarefas relacionadas à análise de imagens: segmentação, seleção de atributos, e classificação. Neste contexto, permitir interatividade com o usuário significa prover mecanismos que tornem possível que humanos auxiliem computadores em tarefas que são de difícil automação. Com respeito à segmentação de imagens, propomos uma nova técnica interativa que combina superpixels com a transformada imagem-floresta. A vantagem principal dessa técnica é permitir rápida segmentação interativa de imagens grandes, além de permitir extração de características potencialmente mais ricas. Os experimentos sugerem que nossa técnica é tão eficaz quanto a alternativa baseada em pixels. No contexto de seleção de atributos e classificação, propomos um novo sistema de visualização interativa que combina exploração do espaço de atributos (baseada em redução de dimensionalidade) com avaliação automática de atributos. Esse sistema tem como objetivo revelar informações que levem ao desenvolvimento de conjuntos de atributos eficazes para classificação de imagens. O mesmo sistema também pode ser aplicado para seleção de atributos para segmentação de imagens e para classificação de padrões, apesar dessas tarefas não serem nosso foco. Apresentamos casos de uso que mostram como esse sistema pode prover certos tipos de informação qualitativa sobre sistemas de classificação de imagens que seriam difíceis de obter por outros métodos. Também mostramos como o sistema interativo proposto pode ser adaptado para a exploração de resultados computacionais intermediários de redes neurais artificiais. Essas redes atualmente alcançam resultados no estado da arte em muitas aplicações de classificação de imagens. Através de casos de uso envolvendo conjuntos de dados de referência, mostramos que nosso sistema pode prover informações sobre como uma rede opera que levam a melhorias em sistemas de classificação. Já que os parâmetros de uma rede neural artificial são tipicamente adaptados iterativamente, a visualização de seus resultados intermediários pode ser vista como uma tarefa dependente de tempo. Com base nessa perspectiva, propomos uma nova técnica de redução de dimensionalidade dependente de tempo que permite a redução de mudanças desnecessárias nos resultados causadas por pequenas mudanças nos dados. Experimentos preliminares mostram que essa técnica é eficaz em manter a coerência temporal desejadaAbstract: We define image analysis as the field of study concerned with extracting information from images. This field is immensely important for commercial and interdisciplinary applications. The overarching goal behind the work presented in this thesis is enabling user interaction during several tasks related to image analysis: image segmentation, feature selection, and image classification. In this context, enabling user interaction refers to providing mechanisms that allow humans to assist machines in tasks that are difficult to automate. Such tasks are very common in image analysis. Concerning image segmentation, we propose a new interactive technique that combines superpixels with the image foresting transform. The main advantage of our proposed technique is enabling faster interactive segmentation of large images, although it also enables potentially richer feature extraction. Our experiments show that our technique is at least as effective as its pixel-based counterpart. In the context of feature selection and image classification, we propose a new interactive visualization system that combines feature space exploration (based on dimensionality reduction) with automatic feature scoring. This visualization system aims to provide insights that lead to the development of effective feature sets for image classification. The same system can also be applied to select features for image segmentation and (general) pattern classification, although these tasks are not our focus. We present use cases that show how this system may provide a kind of qualitative feedback about image classification systems that would be very difficult to obtain by other (non-visual) means. We also show how our proposed interactive visualization system can be adapted to explore intermediary computational results of artificial neural networks. Such networks currently achieve state-of-the-art results in many image classification applications. Through use cases involving traditional benchmark datasets, we show that our system may enable insights about how a network operates that lead to improvements along the classification pipeline. Because the parameters of an artificial neural network are typically adapted iteratively, visualizing its intermediary computational results can be seen as a time-dependent task. Motivated by this, we propose a new time-dependent dimensionality reduction technique that enables the reduction of apparently unnecessary changes in results due to small changes in the data (temporal coherence). Preliminary experiments show that this technique is effective in enforcing temporal coherenceDoutoradoCiência da ComputaçãoDoutor em Ciência da Computação2012/24121-9;FAPESPCAPE

Méthodes multi-organes rapides avec a priori de forme pour la localisation et la segmentation en imagerie médicale 3D

With the ubiquity of imaging in medical applications (diagnostic, treatment follow-up, surgery planning. . . ), image processing algorithms have become of primary importance. Algorithms help clinicians extract critical information more quickly and more reliably from increasingly large and complex acquisitions. In this context, anatomy localization and segmentation is a crucial component in modern clinical workflows. Due to particularly high requirements in terms of robustness, accuracy and speed, designing such tools remains a challengingtask.In this work, we propose a complete pipeline for the segmentation of multiple organs in medical images. The method is generic, it can be applied to varying numbers of organs, on different imaging modalities. Our approach consists of three components: (i) an automatic localization algorithm, (ii) an automatic segmentation algorithm, (iii) a framework for interactive corrections. We present these components as a coherent processing chain, although each block could easily be used independently of the others. To fulfill clinical requirements, we focus on robust and efficient solutions. Our anatomy localization method is based on a cascade of Random Regression Forests (Cuingnet et al., 2012). One key originality of our work is the use of shape priors for each organ (thanks to probabilistic atlases). Combined with the evaluation of the trained regression forests, they result in shape-consistent confidence maps for each organ instead of simple bounding boxes. Our segmentation method extends the implicit template deformation framework of Mory et al. (2012) to multiple organs. The proposed formulation builds on the versatility of the original approach and introduces new non-overlapping constraintsand contrast-invariant forces. This makes our approach a fully automatic, robust and efficient method for the coherent segmentation of multiple structures. In the case of imperfect segmentation results, it is crucial to enable clinicians to correct them easily. We show that our automatic segmentation framework can be extended with simple user-driven constraints to allow for intuitive interactive corrections. We believe that this final component is key towards the applicability of our pipeline in actual clinical routine.Each of our algorithmic components has been evaluated on large clinical databases. We illustrate their use on CT, MRI and US data and present a user study gathering the feedback of medical imaging experts. The results demonstrate the interest in our method and its potential for clinical use.Avec l’utilisation de plus en plus répandue de l’imagerie dans la pratique médicale (diagnostic, suivi, planification d’intervention, etc.), le développement d’algorithmes d’analyse d’images est devenu primordial. Ces algorithmes permettent aux cliniciens d’analyser et d’interpréter plus facilement et plus rapidement des données de plus en plus complexes. Dans ce contexte, la localisation et la segmentation de structures anatomiques sont devenues des composants critiques dans les processus cliniques modernes. La conception de tels outils pour répondre aux exigences de robustesse, précision et rapidité demeure cependant un réel défi technique.Ce travail propose une méthode complète pour la segmentation de plusieurs organes dans des images médicales. Cette méthode, générique et pouvant être appliquée à un nombre varié de structures et dans différentes modalités d’imagerie, est constituée de trois composants : (i) un algorithme de localisation automatique, (ii) un algorithme de segmentation, (iii) un outil de correction interactive. Ces différentes parties peuvent s’enchaîner aisément pour former un outil complet et cohérent, mais peuvent aussi bien être utilisées indépendemment. L’accent a été mis sur des méthodes robustes et efficaces afin de répondre aux exigences cliniques. Notre méthode de localisation s’appuie sur une cascade de régression par forêts aléatoires (Cuingnet et al., 2012). Elle introduit l’utilisation d’informations a priori de forme, spécifiques à chaque organe (grâce à des atlas probabilistes) pour des résultats plus cohérents avec la réalité anatomique. Notre méthode de segmentation étend la méthode de segmentation par modèle implicite (Mory et al., 2012) à plusieurs modèles. La formulation proposée permet d’obtenir des déformations cohérentes, notamment en introduisant des contraintes de non recouvrement entre les modèles déformés. En s’appuyant sur des forces images polyvalentes, l’approche proposée se montre robuste et performante pour la segmentation de multiples structures. Toute méthode automatique n’est cependant jamais parfaite. Afin que le clinicien garde la main sur le résultat final, nous proposons d’enrichir la formulation précédente avec des contraintes fournies par l’utilisateur. Une optimisation localisée permet d’obtenir un outil facile à utiliser et au comportement intuitif. Ce dernier composant est crucial pour que notre outil soit réellement utilisable en pratique. Chacun de ces trois composants a été évalué sur plusieurs grandes bases de données cliniques (en tomodensitométrie, imagerie par résonance magnétique et ultrasons). Une étude avec des utilisateurs nous a aussi permis de recueillir des retours positifs de plusieurs experts en imagerie médicale. Les différents résultats présentés dans ce manuscrit montrent l’intérêt de notre méthode et son potentiel pour une utilisation clinique

User-centered design and evaluation of interactive segmentation methods for medical images

Segmentation of medical images is a challenging task that aims to identify a particular structure present on the image. Among the existing methods involving the user at different levels, from a fully-manual to a fully-automated task, interactive segmentation methods provide assistance to the user during the task to reduce the variability in the results and allow occasional corrections of segmentation failures. Therefore, they offer a compromise between the segmentation efficiency and the accuracy of the results. It is the user who judges whether the results are satisfactory and how to correct them during the segmentation, making the process subject to human factors. Despite the strong influence of the user on the outcomes of a segmentation task, the impact of such factors has received little attention, with the literature focusing the assessment of segmentation processes on computational performance. Yet, involving the user performance in the analysis is more representative of a realistic scenario. Our goal is to explore the user behaviour in order to improve the efficiency of interactive image segmentation processes. This is achieved through three contributions. First, we developed a method which is based on a new user interaction mechanism to provide hints as to where to concentrate the computations. This significantly improves the computation efficiency without sacrificing the quality of the segmentation. The benefits of using such hints are twofold: (i) because our contribution is based on user interaction, it generalizes to a wide range of segmentation methods, and (ii) it gives comprehensive indications about where to focus the segmentation search. The latter advantage is used to achieve the second contribution. We developed an automated method based on a multi-scale strategy to: (i) reduce the user’s workload and, (ii) improve the computational time up to tenfold, allowing real-time segmentation feedback. Third, we have investigated the effects of such improvements in computations on the user’s performance. We report an experiment that manipulates the delay induced by the computation time while performing an interactive segmentation task. Results reveal that the influence of this delay can be significantly reduced with an appropriate interaction mechanism design. In conclusion, this project provides an effective image segmentation solution that has been developed in compliance with user performance requirements. We validated our approach through multiple user studies that provided a step forward into understanding the user behaviour during interactive image segmentation

Geometric data understanding : deriving case specific features

There exists a tradition using precise geometric modeling, where uncertainties in data can be considered noise. Another tradition relies on statistical nature of vast quantity of data, where geometric regularity is intrinsic to data and statistical models usually grasp this level only indirectly. This work focuses on point cloud data of natural resources and the silhouette recognition from video input as two real world examples of problems having geometric content which is intangible at the raw data presentation. This content could be discovered and modeled to some degree by such machine learning (ML) approaches like deep learning, but either a direct coverage of geometry in samples or addition of special geometry invariant layer is necessary. Geometric content is central when there is a need for direct observations of spatial variables, or one needs to gain a mapping to a geometrically consistent data representation, where e.g. outliers or noise can be easily discerned. In this thesis we consider transformation of original input data to a geometric feature space in two example problems. The first example is curvature of surfaces, which has met renewed interest since the introduction of ubiquitous point cloud data and the maturation of the discrete differential geometry. Curvature spectra can characterize a spatial sample rather well, and provide useful features for ML purposes. The second example involves projective methods used to video stereo-signal analysis in swimming analytics. The aim is to find meaningful local geometric representations for feature generation, which also facilitate additional analysis based on geometric understanding of the model. The features are associated directly to some geometric quantity, and this makes it easier to express the geometric constraints in a natural way, as shown in the thesis. Also, the visualization and further feature generation is much easier. Third, the approach provides sound baseline methods to more traditional ML approaches, e.g. neural network methods. Fourth, most of the ML methods can utilize the geometric features presented in this work as additional features.Geometriassa käytetään perinteisesti tarkkoja malleja, jolloin datassa esiintyvät epätarkkuudet edustavat melua. Toisessa perinteessä nojataan suuren datamäärän tilastolliseen luonteeseen, jolloin geometrinen säännönmukaisuus on datan sisäsyntyinen ominaisuus, joka hahmotetaan tilastollisilla malleilla ainoastaan epäsuorasti. Tämä työ keskittyy kahteen esimerkkiin: luonnonvaroja kuvaaviin pistepilviin ja videohahmontunnistukseen. Nämä ovat todellisia ongelmia, joissa geometrinen sisältö on tavoittamattomissa raakadatan tasolla. Tämä sisältö voitaisiin jossain määrin löytää ja mallintaa koneoppimisen keinoin, esim. syväoppimisen avulla, mutta joko geometria pitää kattaa suoraan näytteistämällä tai tarvitaan neuronien lisäkerros geometrisia invariansseja varten. Geometrinen sisältö on keskeinen, kun tarvitaan suoraa avaruudellisten suureiden havainnointia, tai kun tarvitaan kuvaus geometrisesti yhtenäiseen dataesitykseen, jossa poikkeavat näytteet tai melu voidaan helposti erottaa. Tässä työssä tarkastellaan datan muuntamista geometriseen piirreavaruuteen kahden esimerkkiohjelman suhteen. Ensimmäinen esimerkki on pintakaarevuus, joka on uudelleen virinneen kiinnostuksen kohde kaikkialle saatavissa olevan datan ja diskreetin geometrian kypsymisen takia. Kaarevuusspektrit voivat luonnehtia avaruudellista kohdetta melko hyvin ja tarjota koneoppimisessa hyödyllisiä piirteitä. Toinen esimerkki koskee projektiivisia menetelmiä käytettäessä stereovideosignaalia uinnin analytiikkaan. Tavoite on löytää merkityksellisiä paikallisen geometrian esityksiä, jotka samalla mahdollistavat muun geometrian ymmärrykseen perustuvan analyysin. Piirteet liittyvät suoraan johonkin geometriseen suureeseen, ja tämä helpottaa luonnollisella tavalla geometristen rajoitteiden käsittelyä, kuten väitöstyössä osoitetaan. Myös visualisointi ja lisäpiirteiden luonti muuttuu helpommaksi. Kolmanneksi, lähestymistapa suo selkeän vertailumenetelmän perinteisemmille koneoppimisen lähestymistavoille, esim. hermoverkkomenetelmille. Neljänneksi, useimmat koneoppimismenetelmät voivat hyödyntää tässä työssä esitettyjä geometrisia piirteitä lisäämällä ne muiden piirteiden joukkoon

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. © 2013 IEEE.131138Falcao, A.X., Udupa, J.K., Samarasekera, S., Sharma, S., Hirsch, B.E., Lotufo, R.A., User-steered image segmentation paradigms: Livewire and live-lane (1998) Graphical Models and Image Processing, 60 (4), pp. 233-260Falcao, A., Udupa, J., Miyazawa, F., An ultra-fast user-steered image segmentation paradigm: Live wire on the fly (2000) Medical Imaging, IEEE Transactions on, 19 (1), pp. 55-62. , janFalcao, A., Bergo, F., Interactive volume segmentation with differential image foresting transforms (2004) Medical Imaging, IEEE Transactions on, 23 (9), pp. 1100-1108. , septBoykov, Y., Jolly, M.-P., Interactive graph cuts for optimal boundary ampRegion segmentation of objects in n-d images (2001) Computer Vision, Eighth IEEE International Conference on, 1, pp. 105-112Protiere, A., Sapiro, G., Interactive image segmentation via adaptive weighted distances (2007) Image Processing, IEEE Transactions on, 16 (4), pp. 1046-1057De Miranda, P.A.V., Falcao, A.X., Udupa, J.K., Synergistic arc-weight estimation for interactive image segmentation using graphs (2010) Comput. Vis. Image Underst., 114 (1), pp. 85-99Ciesielski, K., Udupa, J., Falcao, A., Miranda, P., Fuzzy connectedness image segmentation in graph cut formulation: A linear-time algorithm and a comparative analysis (2012) Journal of Mathematical Imaging and Vision, 44, pp. 375-398Cootes, T.F., Taylor, C.J., Cooper, D.H., Graham, J., Active shape models-their training and application (1995) Comput. Vis. Image Underst., 61 (1), pp. 38-59Ganser, K.A., Dickhaus, H., Metzner, R., Wirtz, C.R., A deformable digital brain atlas system according to talairach and tournoux (2004) Medical Image Analysis, 8 (1), pp. 3-22Duta, N., Sonka, M., Segmentation and interpretation of mr brain images. An improved active shape model (1998) Medical Imaging, IEEE Transactions on, 17 (6), pp. 1049-1062Grau, V., Mewes, A., Alcaniz, M., Kikinis, R., Warfield, S., Improved watershed transform for medical image segmentation using prior information (2004) Medical Imaging, IEEE Transactions on, 23 (4), pp. 447-458. , aprilLiu, J., Udupa, J., Oriented active shape models (2009) Medical Imaging, IEEE Transactions on, 28 (4), pp. 571-584Falcao, A., Stolfi, J., De Lotufo Alencar, R., The image foresting transform: Theory, algorithms, and applications (2004) Pattern Analysis and Machine Intelligence, IEEE Transactions on, 26 (1), pp. 19-29Papa, J.P., Falcao, A.X., Suzuki, C.T.N., Supervised pattern classification based on optimum-path forest (2009) International Journal of Imaging Systems and Technology, 19 (2), pp. 120-131Rocha, L.M., Cappabianco, F.A.M., Falcao, A.X., Data clustering as an optimum-path forest problem with applications in image analysis (2009) International Journal of Imaging Systems and Technology, 19 (2), pp. 50-68Saito, P.T., De Rezende, P.J., Falcao, A.X., Suzuki, C.T., Gomes, J.F., Improving active learning with sharp data reduction (2012) Proc. of the 20th Intl. Conf. in Central Europe on Computer Graphics, Visualization and Computer Vision (WSCG), pp. 27-34Tighe, J., Lazebnik, S., Superparsing-scalable nonparametric image parsing with superpixels (2013) International Journal of Computer Vision, 101 (2), pp. 329-349Xu, C., Corso, J.J., Evaluation of super-voxel methods for early video processing (2012) Computer Vision and Pattern Recognition (CVPR), pp. 1202-1209Malmberg, F., Strand, R., Faster fuzzy connectedness via precomputation (2013) Mathematical Morphology and Its Applications to Image and Signal Processing (ISMM), , in pressKohli, P., Nickisch, H., Rother, C., Rhemann, C., User-centric learning and evaluation of interactive segmentation systems (2012) Int. J. Computer Vision, 100 (3), pp. 261-274Lotufo, R., Falcao, A., Zampirolli, F., IFT-Watershed from grayscale marker (2002) Computer Graphics and Image Processing, 2002. Proceedings. XV Brazilian Symposium on, pp. 146-152Najman, L., Couprie, M., Building the component tree in quasilinear time (2006) Image Processing, IEEE Transactions on, 15 (11), pp. 3531-3539Rother, C., Kolmogorov, V., Blake, A., Grabcut: Interactive foreground extraction using iterated graph cuts (2004) ACM SIGGRAPH 2004 Papers, pp. 309-314. , New York, NY, USA: ACMBlake, A., Rother, C., Brown, M., Pérez, P., Torr, P.H.S., Interactive image segmentation using an adaptive gmmrf model (2004) European Conference on Computer Vision (ECCV), pp. 428-441Gulshan, V., Rother, C., Criminisi, A., Blake, A., Zisserman, A., Geodesic star convexity for interactive image segmentation (2010) Computer Vision and Pattern Recognition (CVPR), IEEE Conference on, pp. 3129-3136Alpert, S., Galun, M., Brandt, A., Basri, R., Image segmentation by probabilistic bottom-up aggregation and cue integration (2012) IEEE Transactions on Pattern Analysis and Machine Intelligence, 34 (2), pp. 315-32