Image segmentation via convolution of a level-set function with a Rigaut Kernel

Subakan, Özlem N.; Vemuri, Baba C.

doi:10.1109/cvpr.2008.4587460

Cited by 9 publications

(6 citation statements)

References 22 publications

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“…Their product is defined by array (element-by-element) multiplication. The quaternion convolution operation in the spatial domain corresponds to the product operation in the frequency domain [10][11][12][13][14]. This is the same as the case of the conventional convolution.…”

Section: Filtering With Quaternion Fourier Transformsmentioning

confidence: 99%

Applying Quaternion Fourier Transforms for Enhancing Color Images

Khalil¹

2012

IJIGSP

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The Fourier transforms play a critical role in a broad range of image processing applications, including enhancement, analysis, restoration, and compression. Until recently, it was common to use the conventional methods to deal with colored images. These methods are based on RGB decomposition of the colored image by separating it into three separate scalar images and computing the Fourier transforms of these images separately. The computing of the Hypercomplex 2D Fourier transform of a color image as a whole unit has only recently been realized. This paper is concerned with frequency domain noise reduction of color images using quaternion Fourier transforms. The approach is based on obtaining quaternion Fourier transform of the color image and applying the Gaussian filter to it in the frequency domain. The filtered image is then obtained by calculating the inverse quaternion Fourier transforms.

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Section: Filtering With Quaternion Fourier Transformsmentioning

confidence: 99%

Applying Quaternion Fourier Transforms for Enhancing Color Images

Khalil¹

2012

IJIGSP

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“…Continuous mixture models have been presented in various contexts Vemuri 2007a, 2007b;Jian et al 2007;Subakan et al 2007;Subakan and Vemuri 2008). In this paper, we propose continuous mixtures to model the local orientation information extracted via the proposed QGFs.…”

Section: Introductionmentioning

confidence: 98%

A Quaternion Framework for Color Image Smoothing and Segmentation

2010

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In this paper, we present feature/detail preserving models for color image smoothing and segmentation using the Hamiltonian quaternion framework. First, we introduce a novel quaternionic Gabor filter (QGF) which can combine the color channels and the orientations in the image plane. We show that these filters are optimally localized both in the spatial and frequency domains and provide a good approximation to quaternionic quadrature filters. Using the QGFs, we extract the local orientation information in the color images. Second, in order to model this derived orientation information, we propose continuous mixtures of appropriate exponential basis functions and derive analytic expressions for these models. These analytic expressions take the form of spatially varying kernels which, when convolved with a color image or the signed distance function of an evolving contour (placed in the color image), yield a detail preserving smoothing and segmentation, respectively. Several examples on widely used image databases are shown to depict the performance of our algorithms.

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“…The level-set models are more computationally expensive and often require knowing the number of regions and appearance statistics of each region a priori, but they are free in topology and do not need explicit parameterization. So the level-set approach is commonly used in segmenting multiple objects [8] and achieves good result in tubular structure segmentation [21]. Coupled surface constraints and dual-front implementation of level set active contours [13] also provide the flexibility of capturing variable degrees of localness in optimization.…”

Section: Introductionmentioning

confidence: 99%

Active volume models for 3D medical image segmentation

Shen

Qian

et al. 2009

2009 IEEE Conference on Computer Vision and Pattern Recognition

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In this paper, we propose a novel predictive model for object boundary, which can integrate information from any sources. The model is a dynamic "object" model whose manifestation includes a deformable surface representing shape, a volumetric interior carrying appearance statistics, and an embedded classifier that separates object from background based on current feature information. Unlike Snakes, Level Set, Graph Cut, MRF and CRF approaches, the model is "self-contained" in that it does not model the background, but rather focuses on an accurate representation of the foreground object's attributes. As we will show, however, the model is capable of reasoning about the background statistics thus can detect when is change sufficient to invoke a boundary decision. The shape of the 3D model is considered as an elastic solid, with a simplex-mesh (i.e. finite element triangulation) surface made of thousands of vertices. Deformations of the model are derived from a linear system that encodes external forces from the boundary of a Region of Interest (ROI), which is a binary mask representing the object region predicted by the current model. Efficient optimization and fast convergence of the model are achieved using the Finite Element Method (FEM). Other advantages of the model include the ease of dealing with topology changes and its ability to incorporate human interactions. Segmentation and validation results are presented for experiments on noisy 3D medical images.

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Image segmentation via convolution of a level-set function with a Rigaut Kernel

Cited by 9 publications

References 22 publications

Applying Quaternion Fourier Transforms for Enhancing Color Images

Applying Quaternion Fourier Transforms for Enhancing Color Images

A Quaternion Framework for Color Image Smoothing and Segmentation

Active volume models for 3D medical image segmentation

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