Tensor Processing for Texture and Colour Segmentation

2014 22nd International Conference on Pattern Recognition, 2014

This paper deals with the computation of the histogram of tensor images, that is, images where at each pixel is given a n × n positive definite symmetric matrix, SPD(n). An approach based on orthogonal series density estimation is introduced, which is particularly useful for the case of measures based on Riemannian metrics. By considering SPD(n) as the space of the covariance matrices of multivariate gaussian distributions, we obtain the corresponding density estimation for the measure of both the Fisher metric and the Wasserstein metric. Experimental results on the application of such histogram estimation to DTI image segmentation, texture segmentation and texture recognition are included.

This paper investigates structure tensor field regularization applied to directional textured image analysis. From previous works on tensor filtering, we demonstrate that, knowing that the structure tensor is a specific tool coding the local geometry of the image, the tensor field filtering process must be driven by a geometric dissimilarity measure to define the adaptability of the smoothing process. We propose a new dissimilarity measure combining two terms devoted respectively to the orientation and to the shape component of the tensor. This intelligible encoding exhibiting the geometric structure of the image enables us to overcome major drawbacks of conventional Euclidean and Riemannian approaches for which the dissimilarity measure emphasizes only the local manifold geometry. Finally, for seismic imaging application, our method compared to existing ones shows that relevant information can be extracted by enhancing the seismic structures identification.

This paper investigates structure tensor field regularization applied to directional textured image analysis. From previous works on tensor filtering, we demonstrate that, knowing that the structure tensor is a specific tool coding the local geometry of the image, the tensor field filtering process must be driven by a geometric dissimilarity measure to define the adaptability of the smoothing process. We propose a new dissimilarity measure combining two terms devoted respectively to the orientation and to the shape component of the tensor. This intelligible encoding exhibiting the geometric structure of the image enables us to overcome major drawbacks of conventional Euclidean and Riemannian approaches for which the dissimilarity measure emphasizes only the local manifold geometry. Finally, for seismic imaging application, our method compared to existing ones shows that relevant information can be extracted by enhancing the seismic structures identification.

Advances in Pattern Recognition, 2009

Diffusion MRI, which is sensitive to the Brownian motion of molecules, has become today an excellent medical tool for probing the tissue micro-structure of cerebral white matter in vivo and non-invasively. It makes it possible to reconstruct fiber pathways and segment major fiber bundles that reflect the structures in the brain which are not visible to other non-invasive imaging modalities. Since this is possible without operating on the subject, but by integrating partial information from Diffusion Weighted Images into a reconstructed 'complete' image of diffusion, Diffusion MRI opens a whole new domain of image processing. Here we shall explore the role that tensors play in the mathematical model. We shall primarily deal with Cartesian tensors and begin with 2nd order tensors, since these are at the core of Diffusion Tensor Imaging. We shall then explore higher and even ordered symmetric tensors, that can take into account more complex micro-geometries of biological tissues such as axonal crossings in the white matter.

Mathematics and visualization, 2006

The structure tensor, also known as second moment matrix or Förstner interest operator, is a very popular tool in image processing. Its purpose is the estimation of orientation and the local analysis of structure in general. It is based on the integration of data from a local neighborhood. Normally, this neighborhood is defined by a Gaussian window function and the structure tensor is computed by the weighted sum within this window. Some recently proposed methods, however, adapt the computation of the structure tensor to the image data. There are several ways how to do that. This article wants to give an overview of the different approaches, whereas the focus lies on the methods based on robust statistics and nonlinear diffusion. Furthermore, the dataadaptive structure tensors are evaluated in some applications. Here the main focus lies on optic flow estimation, but also texture analysis and corner detection are considered.

1989

A new, computationally inexpensive, approach to texture recognition and segmentation is proposed based on a discriminating quantity called the texture energy tensor (TET). The TET is defined as the sum over a window of the products of pixel pairs at fixed vector displacement. For mathematical textures the TET gives easy to interpret results. Texture classification and segmentation using Laws masks or "tuned masks" and "texture energy" is shown to be a special case of a TET approach.

Scientific Visualization: …

We present a topology-based segmentation as means for visualizing 2D symmetric tensor fields. The segmentation uses directional as well as eigenvalue characteristics of the underlying field to delineate cells of similar (or dissimilar) behavior in the tensor field. A ...

Information processing in medical imaging : proceedings of the ... conference, 2005

We address the problem of the segmentation of cerebral white matter structures from diffusion tensor images. Our approach is grounded on the theoretically well-founded differential geometrical properties of the space of multivariate normal distributions. We introduce a variational formulation, in the level set framework, to estimate the optimal segmentation according to the following hypothesis: Diffusion tensors exhibit a Gaussian distribution in the different partitions. Moreover, we must respect the geometric constraints imposed by the interfaces existing among the cerebral structures and detected by the gradient of the diffusion tensor image. We validate our algorithm on synthetic data and report interesting results on real datasets. We focus on two structures of the white matter with different properties and respectively known as the corpus callosum and the corticospinal tract.

Pattern Recognition, 2010

This paper develops new geometrical filtering and edge detection algorithms for processing non-Euclidean image data. We view image data as residing on a Riemannian manifold, and we work with a representation based on the exponential map for this manifold together with the Riemannian weighted mean of image data. We show how the weighted mean can be efficiently computed using Newton's method, which converges faster than the gradient descent method described elsewhere in the literature. Based on geodesic distances and the exponential map, we extend the classical median filter and the Perona-Malik anisotropic diffusion technique to smooth non-Euclidean image data. We then propose an anisotropic Gaussian kernel for image filtering, and we also show how both the median filter and the anisotropic Gaussian filter can be combined to develop a new edge preserving filter, which is effective at removing both Gaussian noise and impulse noise. By using the intrinsic metric of the feature manifold, we also generalise Di Zenzo's structure tensor to non-Euclidean images for edge detection. We demonstrate the applications of our Riemannian filtering and edge detection algorithms both on directional and tensor-valued images.

Mathematics and Visualization, 2012

Tensor voting is a well-known robust technique for extracting perceptual information from clouds of points. This chapter proposes a general methodology to adapt tensor voting to different types of images in the specific context of image structure estimation. This methodology is based on the structural relationships between tensor voting and the so-called structure tensor, which is the most popu-1 2 R. Moreno et al.