Bruno M. Carvalho

Multiseeded segmentation using fuzzy connectedness

Fuzzy connectedness has been effectively used to segment out an object in a badly corrupted image. We generalize the approach by providing a definition which is shown to always determine a simultaneous segmentation of multiple objects. For any set of seed points, the segmentation is uniquely determined by the definition. An algorithm for finding this segmentation is presented and its output is illustrated. The algorithm is fast as compared to other segmentation algorithms in current use. We also report on an evaluation of the accuracy and robustness of the algorithm based on experiments in which several users were repeatedly asked to identify the seed points for the algorithm in a number of images.

Algorithms for Fuzzy Segmentation

Fuzzy segmentation is an effective way of segmenting out objects in pictures containing both random noise and shading. This is illustrated both on mathematically created pictures and on some obtained from medical imaging. A theory of fuzzy segmentation is presented. To perform fuzzy segmentation, a ‘connectedness map’ needs to be produced. It is demonstrated that greedy algorithms for creating such a connectedness map are faster than the previously used dynamic programming technique. Once the connectedness map is created, segmentation is completed by a simple thresholding of the connectedness map. This approach is efficacious in instances where simple thresholding of the original picture fails.

Simultaneous fuzzy segmentation of multiple objects

Fuzzy segmentation is a technique that assigns to each element in an image (which may have been corrupted by noise and/or shading) a grade of membership in an object (which is believed to be contained in the image). In an earlier work, the first two authors extended this concept by presenting and illustrating an algorithm which simultaneously assigns to each element in an image a grade of membership in each one of a number of objects (which are believed to be contained in the image). In this paper, we prove the existence of such a fuzzy segmentation that is uniquely specified by a desirable mathematical property, show further examples of its use in medical imaging, and illustrate that on several biomedical examples a new implementation of the algorithm that produces the segmentation is approximately seven times faster than the previously used implementation. We also compare our method with two recently published related methods.

Binary Tomography for Triplane Cardiography

The problem of reconstructing a binary image (usually an image in the plane and not necessarily on a Cartesian grid) from a few projections translates into the problem of solving a system of equations which is very underdetermined and leads in general to a large class of solutions. It is desirable to limit the class of possible solutions, by using appropriate prior information, to only those which are reasonably typical of the class of images which contains the unknown image that we wish to reconstruct. One may indeed pose the following hypothesis: if the image is a typical member of a class of images having a certain distribution, then by using this information we can limit the class of possible solutions to only those which are close to the given unknown image. This hypothesis is experimentally validated for the Specific case of a class of binary images representing cardiac cross-sections, where the probability of the occurrence of a particular image of the class is determined by a Gibbs distribution and reconstruction is to be done from the three noisy projections.

Multiseeded Fuzzy Segmentation on the Face Centered Cubic Grid

Fuzzy connectedness has been effectively used to segment out objects in volumes containing noise and/or shading. Multiseeded fuzzy segmentation is a generalized approach that produces a unique simultaneous segmentation of multiple objects. Fcc (face centered cubic) grids are grids formed by rhombic dodecahedral voxels that can be used to represent volumes with fewer elements than a normal cubic grid. Tomographic reconstructions (PET and CT) are used to evaluate the accuracy and speed of the algorithm.

Low-dose, large-angled cone-beam helical CT data reconstruction using algebraic reconstruction techniques

Abstract We report on results on the use of two variants of the algebraic reconstruction techniques (ART) for reconstructing from helical cone-beam computerized tomography (CT) data: a standard one that considers a single ray in an iterative step and a block version which treats simultaneously several cone-beam projections when calculating an iterative step. Both algorithms were implemented using the modified Kaiser-Bessel window functions, also known as blobs, placed on the body-centered cubic (bcc) grid. The algorithms were used to reconstruct phantoms from data collected for the PI-geometry for four different maximum cone-beam angles (2.39, 7.13, 9.46 and 18.43°). Both scattering and quantum noise (for three different noise levels) were introduced to create noisy projections that simulate low-dose examinations. The results presented here (for both noiseless and noisy data sets) point to the facts that, as opposed to a filtered back-projection algorithm, the quality of the reconstructions produced by the ART methods does not suffer from the increase in the cone-beam angle and it is more robust in the presence of noise.

Algebraic reconstruction techniques using smooth basis functions for helical cone-beam tomography

Algorithms for image reconstruction from projections form the foundations of modern methods of tomographic imaging in radiology, such as helical cone-beam X-ray computerized tomography (CT). An image modeling tool, but one which has been often intermingled with image reconstruction algorithms, is the representation of images and volumes using blobs, which are radially symmetric bell-shaped functions. A volume is represented as a superposition of scaled and shifted versions of the same blob. Once we have chosen this blob and the grid points at which its shifted versions are centered, a volume is determined by the finite set of scaling coefficients; the task of the reconstruction algorithm is then to estimate this set of coefficients from the projection data. This can be done by any of a number of optimization techniques, which are typically iterative. Block-iterative algebraic reconstruction techniques (ART) are known to have desirable limiting convergence properties (some related to a generalization of least squares estimation). For many modes of practical applications, such algorithms have been demonstrated to give efficacious results even if the process is stopped after cycling through the data only once. In this paper we illustrate that ART using blobs delivers high-quality reconstructions also from helical cone-beam CT data. We are interested in answering the following: “For what variants of block-iterative ART can we simultaneously obtain desirable limiting convergence behavior and good practical performance by the early iterates?” We suggest a number of approaches to efficient parallel implementation of such algorithms,including the use of footprints to calculate the projections of a blob.

Simultaneous Fuzzy Segmentation of Multiple Objects

Abstract Fuzzy segmentation is a technique that assigns to each element in an image (corrupted by noise and/or shading) a grade of membership in an object (which is believed to be contained in the image). In an earlier work the first two authors extended this concept by presenting and illustrating an algorithm which simultaneously assigns to each element in an image a grade of membership in each one of a number of objects (which are believed to be contained in the image). In this paper we establish the correctness of this algorithm (in the sense of producing an output that is uniquely specified by a desirable mathematical property) and present a further example of its use in medical imaging. We also compare our method with two recently published related methods.

Fuzzy segmentation of color video shots

Fuzzy segmentation is a region growing technique that assigns a grade of membership to an object to each element in an image In this paper we present a method for segmenting video shots by using a fast implementation of the fuzzy segmentation technique The video shot is treated as a three-dimensional volume with different z slices being occupied by different frames of the video shot The volume is interactively segmented based on selected seed elements, that will determine the affinity functions based on their intensity and color properties Experiments with a synthetic video under different noise conditions are performed, as well as examples of two real video shot segmentations are presented, showing the applicability of our method.

Texture fuzzy segmentation using adaptive affinity functions

Digital image segmentation is the process of assigning distinct labels to different objects in a digital image, and the fuzzy segmentation algorithm has been used successfully in the segmentation of images from several modalities. However, the traditional fuzzy segmentation algorithm fails to segment objects that are characterized by textures whose patterns cannot be successfully described by simple statistics computed over a very restricted area. In this paper we present an extension of the fuzzy segmentation algorithm that achieves the segmentation of textures by employing adaptive affinity functions. The adaptive affinity functions change the size of the area (neighborhood) where they compute the texture descriptors, according to the characteristics of the texture being processed. We performed experiments on images from the Brodatz database as well as on a Synthetic Aperture Radar (SAR) image, showing the successful application of our method.