- MULTIVARIATE MATHEMATICAL MORPHOLOGY FOR DCE-MRI IMAGE ANALYSIS IN ANGIOGENESIS STUDIES
Guillaume Noyel, Jesus Angulo, Dominique Jeulin, Daniel Balvay, Charles-André Cuenod
We propose a new computer aided detection framework for tumours acquired on DCE-MRI (Dynamic Contrast Enhanced Magnetic Resonance Imaging) series on small animals. To perform this approach, we consider DCE-MRI series as multivariate images. A full multivariate segmentation method based on dimensionality reduction, noise filtering, supervised classification and stochastic watershed is explained and tested on several data sets. The two main key-points introduced in this paper are noise reduction preserving contours and spatio temporal segmentation by stochastic watershed. Noise reduction is performed in a special way to select factorial axes of Factor Correspondence Analysis in order to preserves contours. Then a spatio-temporal approach based on stochastic watershed is used to segment tumours. The results obtained are in accordance with the diagnosis of the medical doctors.
- PARAMETER ESTIMATION IN NON-HOMOGENEOUS BOOLEAN MODELS: AN APPLICATION TO PLANT DEFENSE RESPONSE
Maria Angeles Gallego, Maria Victoria Ibanez, Amelia Simó
Many medical and biological problems require to extract information from microscopical images. Boolean models have been extensively used to analyze binary images of random clumps in many scientific fields. In this paper, a particular type of Boolean model with an underlying non-stationary point process is considered. The intensity of the underlying point process is formulated as a fixed function of the distance to a region of interest. A method to estimate the parameters of this Boolean model is introduced, and its performance is checked in two different settings. Firstly, a comparative study with other existent methods is done using simulated data. Secondly, the method is applied to analyze the longleaf data set, which is a very popular data set in the context of point processes included in the R package spatstat. Obtained results show that the new method provides as accurate estimates as those obtained with more complex methods developed for the general case. Finally, to illustrate the application of this model and this method, a particular type of phytopathological images are analyzed. These images show callose depositions in leaves of Arabidopsis plants. The analysis of callose depositions, is very popular in the phytopathological literature to quantify activity of plant immunity.
- MULTISCALE IMAGE ANALYSIS BASED ON ROBUST AND ADAPTIVE MORPHOLOGICAL SCALE-SPACES
El Hadji Samba Diop, Jesus Angulo
Mathematical morphology is a powerful tool for image analysis; however, classical morphological operators suffer from lacks of robustness against noise, and also intrinsic image features are not accounted at all in the process. We propose in this work a new and different way to overcome such limits, by introducing both robustness and locally adaptability in morphological operators, which are now defined in a manner such that intrinsic image features are accounted. Dealing with partial differential equations (PDEs) for generalized Cauchy problems, we show that proposed PDEs are equivalent to impose robustness and adaptability of corresponding sup-inf operators, to structuring functions. Accurate numerical schemes are also provided to solve proposed PDEs, and experiments conducted for both synthetic and real images, show the efficiency and robustness of our approach.
- ESTIMATION OF MINKOWSKI TENSORS FROM DIGITAL GREY-SCALE IMAGES
Anne Marie Svane
It was shown in Svane (2014b) that local algorithms based on grey-scale images sometimes lead to asymptotically unbiased estimators for surface area and integrated mean curvature. This paper extends the results to estimators for Minkowski tensors. In particular, asymptotically unbiased local algorithms for estimation of all volume and surface tensors and certain mean curvature tensors are given. This requires an extension of the asymptotic formulas of Svane (2014b) to estimators with position dependent weights.
- SPATIAL-VARIANT MORPHOLOGICAL FILTERS WITH NONLOCAL-PATCH-DISTANCE-BASED AMOEBA KERNEL FOR IMAGE DENOISING
Shuo Yang, Jian-Xun Li
Filters of the Spatial-Variant amoeba morphology can preserve edges better, but with too much noise being left. For better denoising, this paper presents a new method to generate structuring elements for Spatially-Variant amoeba morphology. The amoeba kernel in the proposed strategy is divided into two parts: one is the patch distance based amoeba center, and another is the geodesic distance based amoeba boundary, by which the nonlocal patch distance and local geodesic distance are both taken into consideration. Compared to traditional amoeba kernel, the new one has more stable center and its shape can be less influenced by noise in pilot image. What’s more important is that the nonlocal processing approach can induce a couple of adjoint dilation and erosion, and combinations of them can construct adaptive opening, closing, alternating sequential filters, etc. By designing the new amoeba kernel, a family of morphological filters therefore is derived. Finally, this paper presents a series of results on both synthetic and real images along with comparisons with current state-of-the-art techniques, including novel applications to medical image processing and noisy SAR image restoration.