Supervised pattern classification based on optimum-path forest

We present a supervised classification method which represents each class by one or more optimum-path trees rooted at some key samples, called prototypes. The training samples are nodes of a complete graph, whose arcs are weighted by the distances between the feature vectors of their nodes. Prototypes are identified in all classes and the minimization of a connectivity function by dynamic programming assigns to each training sample a minimumcost path from its most strongly connected prototype. This competition among prototypes partitions the graph into an optimum-path forest rooted at them. The class of the samples in an optimum-path tree is assumed to be the same of its root. A test sample is classified similarly, by identifying which tree would contain it, if the sample were part of the training set. By choice of the graph model and connectivity function, one can devise other optimum-path forest classifiers. We present one of them, which is fast, simple, multi-class, parameter independent, does not make any assumption about the shapes of the classes, and can handle some degree of overlapping between classes. We also propose a general algorithm to learn from errors on an evaluation set without increasing the training set, and show the advantages of our method with respect to SVM, ANN-MLP, and k-NN classifiers in several experiments with datasets of various types

Computerized Classification of Surface Spikes in Three-Dimensional Electron Microscopic Reconstructions of Viruses

The purpose of this research is to develop computer techniques for improved three-dimensional (3D) reconstruction of viruses from electron microscopic images of them and for the subsequent improved classification of the surface spikes in the resulting reconstruction. The broader impact of such work is the following. Influenza is an infectious disease caused by rapidly-changing viruses that appear seasonally in the human population. New strains of influenza viruses appear every year, with the potential to cause a serious global pandemic. Two kinds of spikes – hemagglutinin (HA) and neuraminidase (NA) – decorate the surface of the virus particles and these proteins are primarily responsible for the antigenic changes observed in influenza viruses. Identification of the locations of the surface spikes of both kinds in a new strain of influenza virus can be of critical importance for the development of a vaccine that protects against such a virus. Two major categories of reconstruction techniques are transform methods such as weighted backprojection (WBP) and series expansion methods such as the algebraic reconstruction techniques (ART) and the simultaneous iterative reconstruction technique (SIRT). Series expansion methods aim at estimating the object to be reconstructed by a linear combination of some fixed basis functions and they typically estimate the coefficients in such an expansion by an iterative algorithm. The choice of the set of basis functions greatly influences the efficacy of the output of a series expansion method. It has been demonstrated that using spherically symmetric basis functions (blobs), instead of the more traditional voxels, results in reconstructions of superior quality. Our own research shows that, with the recommended data-processing steps performed on the projection images prior to reconstruction, ART (with its free parameters appropriately tuned) provides 3D reconstructions of viruses from tomographic tilt series that allow reliable quantification of the surface proteins and that the same is not achieved using WBP or SIRT, which are the methods that have been routinely applied by practicing electron microscopists. Image segmentation is the process of recognizing different objects in an image. Segmenting an object from a background is not a trivial task, especially when the image is corrupted by noise and/or shading. One concept that has been successfully used to achieve segmentation in such corrupted images is fuzzy connectedness. This technique assigns to each element in an image a grade of membership in an object. Classifications methods use set of relevant features to identify the objects of each class. To distinguish between HA and NA spikes in this research, discussions with biologists suggest that there may be a single feature that can be used reliably for the classification process. The result of the fuzzy connectedness technique we conducted to segment spikes from the background confirms the correctness of the biologists’ assumption. The single feature we used is the ratio of the width of the spike’s head to the width of its stem in 3D space; the ratio appears to be greater for NA than it is for HA. The proposed classifier is tested on different types of 3D reconstructions derived from simulated data. A statistical hypothesis testing based methodology allowed us to evaluate the relative suitability of reconstruction methods for the given classification task

Object Detection By K-connected Seed Competition

The notion of "strength of connectedness" between pixels has been successfully used in image segmentation. We present an extension to these works, which can considerably increase the efficiency of object definition tasks. A set of pixels is said a k-connected component with respect to a seed pixel when the strength of connectedness of any pixel in that set with respect to the seed is higher than or equal to a threshold. While the previous approaches either assume no competition with a single threshold for all seeds or eliminate the threshold for seed competition, we found that seed competition with different thresholds can reduce the number of seeds and the need for user interaction during segmentation. We also propose automatic and user-friendly interactive methods for determining the thresholds. The improvements are demonstrated through several segmentation experiments involving medical images. © 2005 IEEE.200597104Beucher, S., Meyer, F., The morphological approach to segmentation: The watershed transformation (1993) Mathematical Morphology in Image Processing, pp. 433-481. , chapter 12, Marcel DekkerFalcão, A.X., Bergo, F.P.G., Interactive volume segmentation with differential image foresting transforms (2004) IEEE Trans. on Medical Imaging, 23 (9), pp. 1100-1108A. X. Falcão, F. P. G. Bergo, and P. A. V. Miranda. Image segmentation by tree pruning. In Proc. of the XV11 Brazillian Symposium on Computer Graphics and Image Processing, pages 65-71. IEEE, Oct 2004Falcão, A.X., Costa, L.F., da Cunha, B.S., Multiscale skeletons by image foresting transform and its applications to neuromorphometry (2002) Pattern Recognition, 35 (7), pp. 1571-1582Falcão, A.X., Stolfi, J., Lotufo, R.A., The image foresting transform: Theory, algorithms, and applications (2004) IEEE Trans. on Pattern Analysis and Machine Intelligence, 26 (1), pp. 19-29Falcão, A.X., Udupa, J.K., Miyazawa, F.K., An ultrafast user-steered image segmentation paradigm: Live-wireon-the-fly (2000) IEEE Trans. on Medical Imaging, 19 (1), pp. 55-62Falcão, A.X., Udupa, J.K., Samarasekera, S., Sharma, S., Hirsch, B.E., Lotufo, R.A., User-steered image segmentation paradigms: Live-wire and live-lane (1998) Graphical Models and Image Processing, 60 (4), pp. 233-260. , JulFelkel, P., Bruckschwaiger, M., Wegenkittl, R., Implementation and complexity of the watershed-from-markers algorithm computed as a minimal cost forest (2001) Computer Graphics Forum (EUROGRAPHICS), 20 (3). , C 26-35Grau, V., Mewes, A.U.J., Alcaniz, M., Kikinis, R., Warfield, S.K., Improved watershed transform for medical image segmentation using prior information (2004) IEEE Trans. on Medical Imaging, 23 (4), pp. 447-458. , AprHerman, G.T., Carvalho, B.M., Multiseeded segmentation using fuzzy connectedness (2001) IEEE Trans. on Pattern Analysis and Machine Intelligence, 23 (5), pp. 460-474Lei, T., Udupa, J.K., Saha, P.K., Odhner, D., Artery-vein separation via MRA - An image processing approach (2001) IEEE Trans. on Medical Imaging, 20 (8)Lotufo, R.A., Falcão, A.X., The ordered queue and the optimality of the watershed approaches (2000) Mathematical Morphology and its Applications to Image and Signal Processing, 18, pp. 341-350. , Kluwer, JunMeijster, A., Wilkinson, M.H.F., A comparison of algorithms tor connected set openings and closings (2002) IEEE Trans. on Pattern Analysis and Machine Intelligence, 24 (4), p. 484494. , AprMoonis, G., Liu, J., Udupa, J.K., Hackney, D.B., Estimation of tumor volume with fuzzy-connectedness segmentation of MR images (2002) American Journal of Neuroradiology, 23, pp. 356-363. , MarNguyen, H.T., Worring, M., van den Boomgaard, R., Watersnakes: Energy-driven watershed segmentation (2003) IEEE Trans. on Pattern Analysis and Machine Intelligence, 25 (3), pp. 330-342. , MarSaha, P.K., Udupa, J.K., Fuzzy connected object delineation: Axiomatic path strength definition and the case of multiple seeds (2001) Computer Vision and Image Understanding, 83, pp. 275-295Saha, P.K., Udupa, J.K., Relative fuzzy connectedness among multiple objects: Theory, algorithms, and applications in image segmentation (2001) Computer Vision and Image Understanding, 82, pp. 42-56Saha, P.K., Udupa, J.K., Odhner, D., Scale-based fuzzy connected image segmentation: Theory, algorithms, and validation (2000) Computer Vision and Image Understanding, 77 (2), pp. 145-174Torres, R.S., Falcão, A.X., Costa, L.F., A graph-based approach for multiscale shape analysis (2004) Pattern Recognition, 37 (6), pp. 1163-1174Udupa, J.K., Samarasekera, S., Fuzzy connectedness and object definition: Theory, algorithms, and applications in image segmentation (1996) Graphical Models and Image Processing, 58, pp. 246-261Vincent, L., Soille, P., Watersheds in digital spaces: An efficient algorithm based on immersion simulations (1991) IEEE Trans. on Pattern Analysis and Machine Intelligence, 13 (6). , Ju

Duality Between The Watershed By Image Foresting Transform And The Fuzzy Connectedness Segmentation Approaches

This paper makes a rereading of two successful image segmentation approaches, the fuzzy connectedness (FC) and the watershed (WS) approaches, by analyzing both by means of the Image Foresting Transform (IFT). This graphbased transform provides a sound framework for analyzing and implementing these methods. This paradigm allows to show the duality existing between the WS by IFT and the FC segmentation approaches. Both can be modeled by an optimal forest computation in a dual form (maximization of the similarities or minimization of the dissimilarities), the main difference being the input parameters: the weights associated to each arc of the graph representing the image. In the WS approach, such weights are based on the (possibly filtered) image gradient values whereas they are based on much more complex affinity values in the FC theory. An efficient algorithm for both FC and IFT-WS computation is proposed. Segmentation robustness issue is also discussed. © 2006 IEEE.5360Audigier, R., Lotufo, R., Tie-zone watershed, bottlenecks and segmentation robustness analysis (2005) XVIII Brazilian Symp. on Comp. Graph, and Image Proc. (SIBGRAPI'05), pp. 55-62. , Natal, Brazil, Oct, IEEE PressAudigier, R., Lotufo, R., Couprie, M., The tie-zone watershed: Definition, algorithm and applications (2005) Proceedings of IEEE Int. Conf. on Image Processing (ICIP'05), 2, pp. 654-657. , Genova, Italy, SeptBerge, C., (1958) Théorie des graphes et ses applications, , Dunod, Paris, FranceBeucher, S., Lantuéjoul, C., Use of watersheds in contour detection (1979) International Workshop on Image Processing, Real-Time Edge and Motion Detection/Estimation, , Rennes, FranceBeucher, S., Meyer, F., The Morphological Approach to Segmentation: The Watershed Transform (1993) Mathematical Morphology in Image Processing, pp. 433-481. , E. R. Dougherty, editor, chapter 12, Marcel Dekker, Inc, New York NY, USACouprie, M., Bertrand, G., Topological grayscale watershed transformation (1997) SPIE Vision Geometry V Proceedings, 3168, pp. 136-146Dijkstra, E., A note on two problems in connexion with graphs (1959) Numerische MathematikDougherty, E., Lotufo, R., (2003) Hands-on Morphological Image Processing, , SPIE, The International Society for Optical Engineering, Bellingham Washington, USA, AugFalcão, A., Stolfi, J., Lotufo, R., The image foresting transform: Theory, algorithms, and applications (2004) IEEE Trans. Pattern Anal. Mach. Intell, 26 (1), pp. 19-29. , JanHerman, G.T., Carvalho, B.M., Multiseeded segmentation using fuzzy connectedness (2001) IEEE Trans. Pattern Anal. Mach. Intell, 23 (5), pp. 460-474Lotufo, R., Falcão, A., The Ordered Queue and the Optimality of the Watershed Approaches (2000) 5th International Symposium on Mathematical Morphology, pp. 341-350. , Palo Alto CA, USA, June, Kluwer AcademicLotufo, R., Falcão, A., Zampirolli, F., IFT-watershed from gray-scale marker (2002) XV Brazilian Symp. on Computer Graph, and Image Proc, pp. 146-152. , Fortaleza CE, Brazil, Oct, IEEE Computer SocietyMeyer, F., Topographic distance and watershed lines (1994) Signal Processing, 38, pp. 113-125Meyer, F., Beucher, S., Morphological segmentation (1990) Journal of Visual Comm. and Image Repr, 1 (1), pp. 21-46Najman, L., Schmitt, M., Watershed of a continuous function (1994) Signal Processing, 38 (1), pp. 99-112J. Roerdink and A. Meijster. The watershed transform: Definitions, algorithms and parallelization strategies. Fundamenta Informaticae, 41(1-2):187-228, Jan. 2000. Special issue on mathematical morphologySaha, P., Udupa, J., Relative fuzzy connectedness among multiple objects: Theory, algorithms, and applications in image segmentation (2001) Computer Vision and Image Understanding, 82 (1), pp. 42-56. , AprilSaha, P., Udupa, J., Odhner, D., Scale-based fuzzy connected image segmentation: Theory, algorithms, and validation (2000) Computer Vision and Image Understanding, 77 (2), pp. 145-174. , FebruaryUdupa, J., Saha, P., Lotufo, R., Relative fuzzy connectedness and object definition: Theory, algorithms, and applications in image segmentation (2002) IEEE Trans. Pattern Anal. Mach. Intell, 24 (11), pp. 1485-1500. , NovemberUdupa, J.K., Samarasekera, S., Fuzzy connectedness and object definition: Theory, algorithms, and applications in image segmentation (1996) Graph. Models Image Process, 58 (3), pp. 246-261. , MayVincent, L., Soille, P., Watersheds in digital spaces: An efficient algorithm based on immersion simulations (1991) IEEE Trans. PatternAnal Mach. Intell, 13 (6), pp. 583-598Zhuge, Y., Udupa, J., Saha, P., Vectorial scale-based fuzzy-connected image segmentation (2006) Computer Vision and Image Understanding, 101 (3), pp. 177-193. , Marc