Scale-invariant segmentation of dynamic contrast-enhanced perfusion MR-images with inherent scale selection

Selection of the best set of scales is problematic when developing signaldriven approaches for pixel-based image segmentation. Often, different possibly conflicting criteria need to be fulfilled in order to obtain the best tradeoff between uncertainty (variance) and location accuracy. The optimal set of scales depends on several factors: the noise level present in the image material, the prior distribution of the different types of segments, the class-conditional distributions associated with each type of segment as well as the actual size of the (connected) segments. We analyse, theoretically and through experiments, the possibility of using the overall and class-conditional error rates as criteria for selecting the optimal sampling of the linear and morphological scale spaces. It is shown that the overall error rate is optimised by taking the prior class distribution in the image material into account. However, a uniform (ignorant) prior distribution ensures constant class-conditional error rates. Consequently, we advocate for a uniform prior class distribution when an uncommitted, scaleinvariant segmentation approach is desired. Experiments with a neural net classifier developed for segmentation of dynamic MR images, acquired with a paramagnetic tracer, support the theoretical results. Furthermore, the experiments show that the addition of spatial features to the classifier, extracted from the linear or morphological scale spaces, improves the segmentation result compared to a signal-driven approach based solely on the dynamic MR signal. The segmentation results obtained from the two types of features are compared using two novel quality measures that characterise spatial properties of labelled images

Colour morphological sieves for scale-space image processing

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Uma abordagem multi-escala para segmentação de imagens

Orientador : Neucimar Jeronimo LeiteDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Neste trabalho abordamos o problema de segmentação de imagens através da sua representação multi-escala. Para tanto, consideramos a teoria do espaço-escala morfológico, recentemente introduzida na literatura, denominada MMDE (Multiscale Morphological DilationErosion). Este método, associado à LDA, reduz monotonicamente o número de extremos de uma imagem e, consequentemente, o número de regiões segmentadas, a partir de uma suavização da imagem original. No entanto, quando associado à segmentação de imagens, o espaço-escala MMDE apresenta dois grandes problemas: o deslocamento espacial da LDA ao longo das escalas e a dificuldade de se caracterizar o conjunto de extremos presente nos diferentes níveis de representação. O primeiro problema é abordado em nosso trabalho a partir de uma modificação homotópica da imagem. Para o espaço-escala MMDE é garantido que a posição e a altura dos mínimos (para escalas negativas) e dos máximos (para escalas positivas) são mantidas ao longo das escalas. Assim, esta propriedade permite que o conjunto de mínimos (máximos) obtidos em uma determinada escala seja utilizado como marcador num processo de reconstrução geodésica e segmentação. Garantida a preservação das estruturas da imagem, consideramos uma análise do modo como os seus extremos se fundem ao longo das escalas, e definimos um novo espaço-escala morfológico no qual a suavização é dada por uma operação idempotente. Para este espaço-escala, apresentamos critérios de controle monotônico da fusão dos extremos, obtendo um melhor conjunto de marcadores para a segmentação. Estes métodos consistem em definir, a partir de informações estritamente locais, pontos da imagem original que não devem ser transformados durante a suavização, evitando, assim, que extremos significativos se fundamAbstract: ln this work we consider the problem of image segmentation by means of a multiscale representation. This multiscale representation is based on a recently proposed morphological scale-space theory, the Multiscale Morphological Dilation-Erosion - MMDE, which associated to the watershed transform, reduces monotonicly the number of extrema of an image and, consequently, the number of its segmented regions. This method has two basic problems concerning image segmentation: the spatial shifting of the watershed lines throughout the scales and the di:fficulty to characterize the set of the image extrema across these different scales. The first problem is considered here by means of a homotopic modification of the original image. The MMDE approach states that the position and the amplitude of the extrema in the original and transformed images do not change across scales. This property allows us to use a set of these extrema, present at a certain scale, as marker in a homotopic modification and segmentation of the original image. Also, we consider an analysis of the way the image extrema merge across scales and introduce a new morphological scale-space in which the monotonic reduction of the image extrema is given by an idempotent operation. For this scale-space, We consider some monotonic-preserving merging criteria, taking into account only local information, which can be used to prevent significant image extrema from merging and to define better sets of markers for segmentationMestradoMestre em Ciência da Computaçã

A Scaled Morphological Toggle Operator For Image Transformations

Scale dependent signal representations have proved to be useful in several image processing applications. In this paper, we define a toggle operator for binarization/segmentation purposes based on scaled versions of an image transformed by morphological operations. The toggle decision rule, determining the new value of a pixel, considers local spatial information, in contrast to other multiscale approaches that takes into account mainly global information (e.g., the scale signal under study). We show that the proposed operator can identify significant image extrema information in such a way that when it is used in a binarization process yields very good segmentation and filtering results. Our algorithm is validated against known threshold-based segmentation methods using images of different classes and subjected to different lighting conditions. © 2006 IEEE.323330Haralick, R., Stenberg, S., Zhuang, X., Image analysis using mathematical morphology (1987) IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-9 (4), pp. 532-550Jackway, P., Gradient watershed in morphological scale-space (1996) IEEE Transactions on Image Processing, 15, pp. 913-921Jackway, P., Deriche, M., Scale-space proprieties of the multiscale morphological dilation-erosion (1996) IEEE Transactions on Pattern Analysis and Machine Intelligence, 18, pp. 38-51Jang, B., Chin, R., Morphological scale-space for 2d shape smoothing (1998) Computer Vision and Image Understanding, 70 (2), pp. 121-141Kapur, J., Sahoo, P., Wong, A., A new method for graylevel picture thresholding using the entropy of the histogram (1985) Computer Vision, Graphics, and Image Processing, 29, pp. 273-285Kramer, H.P., Bruckner, J.B., Iterations of a non-linear transformation for enhancement of digital images (1975) Pattern Recognition, 7, pp. 53-58Leite, N.J., Teixeira, M.D., Morphological scale-space theory for segmentation problems (1999) IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing, pp. 364-368Leite, N.J., Teixeira, M.D., An idempotent scale-space approach for morphological segmentation (2000) Mathematical Morphology and its Applications to Image and Signal Processing, pp. 291-300. , Kluwer Academic PublishersLifshitz, L., Pizer, S., A multiresolution hierarchical approach to image segmentation based on intensity extrema (1990) IEEE Transactions on Pattern Analysis and Machine Intelligence, 12 (4), pp. 529-540Marsden, J., Hoffman, M., (1993) Elementary Classical Analysis, , FreemanMatheron, G., (1975) Random Sets and Integral Geometry, , John Wiley and SonsOtsu, N., A threshold selection method from grey-level histograms (1979) IEEE Transactions on Systems, Man and Cybernetics, 9 (1), pp. 377-393Park, K., Lee, C., Scale-space using mathematical morphology (1996) IEEE Transactions on Pattern Analysis and Machine Intelligence, 18 (11), pp. 1121-1126Parker, J., (1996) Algorithms for Image Processing and Computer Vision, , WileyRidler, T., Calvard, S., Picture thresholding using a iterative selection method (1978) IEEE Transactions on Systems, Man and Cybernetics, SMC-8 (8), pp. 233-260Rosenfeld, A., Kak, A., (1982) Digital Picture Processing, , Academic PressSchavemaker, J.G.M., Reinders, M.J.T., Gerbrands, J., Backer, E., Image sharpening by morphological filtering (1999) Pattern Recognition, 33, pp. 997-1012Serra, J., (1982) Image Analysis and Mathematical Morphology, , Academic PressSerra, J., Image Analysis and Mathematical Morphology (1988) Theoretical Advances, 2. , Academic PressSerra, J., Vicent, L., An overview of morphological filtering (1992) Circuits, Systems and Signal Processing, 11 (1), pp. 47-108Soille, P., (2003) Morphological Image Analysis: Principles and Applications, , Springer-VerlagWellner, P., Adaptive thresholding for the digital desk Technical Report EPC1993-110, Xerox, 1993Witkin, A.P., Scale-space filtering: A new approach to multiscale description (1984) Image Understanding, pp. 79-95. , Able