Plateau Problem in the Watershed Transform

The watershed transform is one of best known and widely used methods for image segmentation in mathematical morphology. Since the definition, deriving from geology and nature observation is quite intuitive and straightforward to implement; many fast and powerful algorithms for watershed transform have already been presented. However, there still occur problems when one wishes to achieve a precise solution on blurred or noised image. The same range of problems is faced when a plateau occurs in the image. In this paper several methods for plateau reduction are discussed and some novel ideas proposed. All algorithms are performed on a set of both natural and synthetic images

Tie-zone : the bridge between watershed transforms and fuzzy connectedness

Orientador: Roberto de Alencar LotufoTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de ComputaçãoResumo: Esta tese introduz o novo conceito de transformada de zona de empate que unifica as múltiplas soluções de uma transformada de watershed, conservando apenas as partes comuns em todas estas, tal que as partes que diferem constituem a zona de empate. A zona de empate aplicada ao watershed via transformada imagem-floresta (TZ-IFT-WT) se revela um elo inédito entre transformadas de watershed baseadas em paradigmas muito diferentes: gota d'água, inundação, caminhos ótimos e floresta de peso mínimo. Para todos esses paradigmas e os algoritmos derivados, é um desafio se ter uma solução única, fina, e que seja consistente com uma definição. Por isso, propõe-se um afinamento da zona de empate, único e consistente. Além disso, demonstra-se que a TZ-IFT-WT também é o dual de métodos de segmentação baseados em conexidade nebulosa. Assim, a ponte criada entre as abordagens morfológica e nebulosa permite aproveitar avanços de ambas. Em conseqüência disso, o conceito de núcleo de robustez para as sementes é explorado no caso do watershed.Abstract: This thesis introduces the new concept of tie-zone transform that unifies the multiple solutions of a watershed transform, by conserving only the common parts among them such that the differing parts constitute the tie zone. The tie zone applied to the watershed via image-foresting transform (TZ-IFTWT) proves to be a link between watershed transforms based on very different paradigms: drop of water, flooding, optimal paths and forest of minimum weight. For all these paradigms and the derived algorithms, it is a challenge to get a unique and thin solution which is consistent with a definition. That is why we propose a unique and consistent thinning of the tie zone. In addition, we demonstrate that the TZ-IFT-WT is also the dual of segmentation methods based on fuzzy connectedness. Thus, the bridge between the morphological and the fuzzy approaches allows to take benefit from the advance of both. As a consequence, the concept of cores of robustness for the seeds is exploited in the case of watersheds.DoutoradoEngenharia de ComputaçãoDoutor em Engenharia Elétric

Contributions to Medical Image Segmentation and Signal Analysis Utilizing Model Selection Methods

This thesis presents contributions to model selection techniques, especially based on information theoretic criteria, with the goal of solving problems appearing in signal analysis and in medical image representation, segmentation, and compression.The field of medical image segmentation is wide and is quickly developing to make use of higher available computational power. This thesis concentrates on several applications that allow the utilization of parametric models for image and signal representation. One important application is cell nuclei segmentation from histological images. We model nuclei contours by ellipses and thus the complicated problem of separating overlapping nuclei can be rephrased as a model selection problem, where the number of nuclei, their shapes, and their locations define one segmentation. In this thesis, we present methods for model selection in this parametric setting, where the intuitive algorithms are combined with more principled ones, namely those based on the minimum description length (MDL) principle. The results of the introduced unsupervised segmentation algorithm are compared with human subject segmentations, and are also evaluated with the help of a pathology expert.Another considered medical image application is lossless compression. The objective has been to add the task of image segmentation to that of image compression such that the image regions can be transmitted separately, depending on the region of interest for diagnosis. The experiments performed on retinal color images show that our modeling, in which the MDL criterion selects the structure of the linear predictive models, outperforms publicly available image compressors such as the lossless version of JPEG 2000.For time series modeling, the thesis presents an algorithm which allows detection of changes in time series signals. The algorithm is based on one of the most recent implementations of the MDL principle, the sequentially normalized maximum likelihood (SNML) models.This thesis produces contributions in the form of new methods and algorithms, where the simplicity of information theoretic principles are combined with a rather complex and problem dependent modeling formulation, resulting in both heuristically motivated and principled algorithmic solutions