Adaptation of Tensor Voting to Image Structure Estimation

2012 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, 2012

We address the problem of unsupervised segmentation and grouping in 2D and 3D space, where samples are corrupted by noise, and in the presence of outliers. The problem has attracted attention in previous research work, but non-parametric outlier filtering and inlier denoising are still challenging. Tensor voting is a non-parametric algorithm that can infer local data geometric structure. Standard tensor voting considers outlier noise explicitly, but may suffer from serious problems if the inlier data is also noisy. In this paper, we propose probabilistic Tensor Voting, a Bayesian extension of standard tensor voting, taking into consideration both probabilistic and geometric meaning. Probabilistic tensor voting explicitly considers both outlier and inlier noise, and can handle them simultaneously. In the new framework, the representation consists of a 2nd order symmetric tensor, a polarity vector, and a new type 2 polarity vector orthogonal to the first one. We give a theoretical interpretation of our framework. Experimental results show that our approach outperforms other methods, including standard tensor voting.

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.

2006

In many image analysis applications there is a need to extract curves in noisy images. To achieve a more robust extraction, one can exploit correlations of oriented features over a spatial context in the image. Tensor voting is an existing technique to extract features in this way. In this paper, we present a new computational scheme for tensor voting on a dense field of rank-2 tensors. Using steerable filter theory, it is possible to rewrite the tensor voting operation as a linear combination of complex-valued convolutions. This approach has computational advantages since convolutions can be implemented efficiently. We provide speed measurements to indicate the gain in speed, and illustrate the use of steerable tensor voting on medical applications.

IEEE Transactions on Medical Imaging, 2000

In this paper, a novel approach is proposed for perceptual grouping and localization of ill-defined curvilinear structures. Our approach builds upon the tensor voting and the iterative voting frameworks. Its efficacy lies on iterative refinements of curvilinear structures by gradually shifting from an exploratory to an exploitative mode. Such a mode shifting is achieved by reducing the aperture of the tensor voting fields, which is shown to improve curve grouping and inference by enhancing the concentration of the votes over promising, salient structures. The proposed technique is validated on delineating adherens junctions that are imaged through fluorescence microscopy. However, the method is also applicable for screening other organisms based on characteristics of their cell wall structures. Adherens junctions maintain tissue structural integrity and cell-cell interactions. Visually, they exhibit fibrous patterns that may be diffused, heterogeneous in fluorescence intensity, or punctate and frequently perceptual. Besides the application to real data, the proposed method is compared to prior methods on synthetic and annotated real data, showing high precision rates.

Computer Vision-ECCV …, 2004

Tensor voting is an efficient algorithm for perceptual grouping and feature extraction, particularly for contour extraction. In this paper two studies on tensor voting are presented. First the use of iterations is investigated, and second, a new method for integrating curvature information is evaluated. In opposition to other grouping methods, tensor voting claims the advantage to be non-iterative. Although noniterative tensor voting methods provide good results in many cases, the algorithm can be iterated to deal with more complex data configurations. The experiments conducted demonstrate that iterations substantially improve the process of feature extraction and help to overcome limitations of the original algorithm. As a further contribution we propose a curvature improvement for tensor voting. On the contrary to the curvature-augmented tensor voting proposed by Tang and Medioni, our method takes advantage of the curvature calculation already performed by the classical tensor voting and evaluates the full curvature, sign and amplitude. Some new curvature-modified voting fields are also proposed. Results show a lower degree of artifacts, smoother curves, a high tolerance to scale parameter changes and also more noise-robustness.

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.

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.

Lecture Notes in Computer Science, 2005

In this paper, we propose an original approach for texture and colour segmentation based on the tensor processing of the nonlinear structure tensor. While the tensor structure is a well established tool for image segmentation, its advantages were only partly used because of the vector processing of that information. In this work, we use more appropriate definitions of tensor distance grounded in concepts from information theory and compare their performance on a large number of images. We clearly show that the traditional Frobenius norm-based tensor distance is not the most appropriate one. Symmetrized KL divergence and Riemannian distance intrinsic to the manifold of the symmetric positive definite matrices are tested and compared. Adding to that, the extended structure tensor and the compact structure tensor are two new concepts that we present to incorporate gray or colour information without losing the tensor properties. The performance and the superiority of the Riemannian based approach over some recent studies are demonstrated on a large number of gray-level and colour data sets as well as real images.

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.

IEEE Transactions on Pattern Analysis and Machine Intelligence, 2014

We comment on a paper that describes a closed-form formulation to Tensor Voting, a technique to perceptually group clouds of points, usually applied to infer features in images. The authors proved an analytic solution to the technique, a highly relevant contribution considering that the original formulation required numerical integration, a time-consuming task. Their work constitutes the first closed-form expression for the Tensor Voting framework. In this work we first observe that the proposed formulation leads to unexpected results which do not satisfy the constraints for a Tensor Voting output, hence they cannot be interpreted. Given that the closed-form expression is said to be an analytic equivalent solution, unexpected outputs should not be encountered unless there are flaws in the proof. We analyzed the underlying math to find which were the causes of these unexpected results. In this commentary we show that their proposal does not in fact provide a proper analytic solution to Tensor Voting and we indicate the flaws in the proof.