Thomas P. Weldon

EFFICIENT GABOR FILTER DESIGN FOR TEXTURE SEGMENTATION

Gabor filters have been successfully applied to a broad range of image processing tasks. The present paper considers the design of a single filter to segment a two-texture image. A new efficient algorithm for Gabor-filter design is presented, along with methods for estimating filter output statistics. The algorithm draws upon previous results that showed that the output of a Gabor-filtered texture is modeled well by a Rician distribution. A measure of the total output power is used to select the center frequency of the filter and is used to estimate the Rician statistics of the Gabor-filtered image. The method is further generalized to include the statistics of postfiltered outputs that are generated by a Gaussian filtering operation following the Gabor filter. The new method typically requires an order of magnitude less computation to design a filter than a previously proposed method. Experimental results demonstrate the efficacy of the method.

Gabor filter design for multiple texture segmentation

A method is presented for the design of a single Gabor filter for the segmentation of multitextured images. Earlier methods were limited to filters designed for one or two textures or to filters selected from a predetermined filter bank. Our proposed method yields new insight into the design of Gabor filters for segmenting multitextured images and lays an essential foundation for the design of multiple Gabor filters. In the method, Rician statistics of filtered textures at two different Gabor-filter envelope scales are used to efficiently generate probability density estimates for each filtered texture over an extensive set of candidate filter parameters. Variable degrees of postfiltering and the accompanying effect on postfilter output statistics are also included in the design procedure. The result is a unified framework that analytically relates the texture power spectra, Gabor-filter parameters, postfiltering effects, and image-segmentation error. Finally, the resulting filter design is based on all constituent textures and is not constrained to a limited set of candidate filters.

Design of multiple Gabor filters for texture segmentation

This paper presents a method for the design of multiple Gabor filters for segmenting multi-textured images. Although design methods for a single Gabor filter have been presented previously, the development of general multi-filter multi-texture design methods largely remains an open problem. Previous multi-filter design approaches required one filter per texture or were constrained to pairs of textures. Other approaches employed ad hoc banks of Gabor filters for texture segmentation, where the parameters of the constituent filters were restricted to fixed values and were not necessarily tuned for a specific texture-segmentation problem. The proposed method removes these restrictions on the number of filters and the number of textures. This offers the potential to improve the segmentation performance or to reduce the number of filters. Further, the development of the design method and mathematical models provide new insight into the design of multiple Gabor filters for texture segmentation. Results are presented that confirm the efficacy of our filter-design method and support underlying mathematical models.

An algorithm for designing multiple Gabor filters for segmenting multi-textured images

We present an algorithm for the design of multiple Gabor filters for the segmentation of multi-textured images. We draw upon earlier results that provide a segmentation error measure based on the predicted vector output statistics of multiple filter channels. This segmentation error measure is used to design the filter channels for a particular segmentation task. In our approach, the filter parameters are free to vary from channel to channel and are not restricted to some predetermined decomposition of the frequency plane. Thus, our method can generate more effective filter designs and result in more effective features for image segmentation than prior methods. Finally, we present texture segmentation results that confirm the efficacy of the proposed procedure. These results show effective segmentation of 8 textures using as few as 2 filters, whereas earlier approaches required 13 to 40 filters to segment 5 textures.

DESIGNING MULTIPLE GABOR FILTERS FOR MULTITEXTURE IMAGE SEGMENTATION

We consider the problem of segmenting multitextured images using multiple Gabor lters. In particular, we present a mathematical framework for a multichannel texture-segmentation system consisting of a parallel bank of lter channels, a vector classier stage, and a postprocessing stage. The framework establishes mathematical relationships between the predicted texture-segmentation error, the frequency spectra of constituent textures, and the parameters of the lter channels. The framework also permits the systematic formulation of lter-design procedures and provides predicted vector output statistics that are useful for classier design. This paper focuses on the mathematical framework and provides experimental results that conrm the utility of the framework in the design of a complete image-segmentation system. The results demonstrate eective segmentation using a straightforward classier and fewer than half the number of lters needed in previously proposed approaches. Subject terms: Gabor prelter, Gabor lter, Gabor function, texture segmentation, statistical image analysis, texture analysis, computer vision, image segmentation.

Integrated approach to texture segmentation using multiple Gabor filters

This paper presents an integrated approach using multiple Gabor filters for the segmentation of multi-textured images. The approach includes both the design of the constituent Gabor filters and the design of the classifier and postprocessing. The classifier uses a mixture density to reduce localization error at texture boundaries, and the postprocessing uses morphological operators to remove spurious misclassifications at texture boundaries. Results are presented that confirm the efficacy of the postprocessing methods and the overall integrated approach.

Combined image-processing algorithms for improved optical coherence tomography of prostate nerves

Cavernous nerves course along the surface of the prostate gland and are responsible for erectile function. These nerves are at risk of injury during surgical removal of a cancerous prostate gland. In this work, a combination of segmentation, denoising, and edge detection algorithms are applied to time-domain optical coherence tomography (OCT) images of rat prostate to improve identification of cavernous nerves. First, OCT images of the prostate are segmented to differentiate the cavernous nerves from the prostate gland. Then, a locally adaptive denoising algorithm using a dual-tree complex wavelet transform is applied to reduce speckle noise. Finally, edge detection is used to provide deeper imaging of the prostate gland. Combined application of these three algorithms results in improved signal-to-noise ratio, imaging depth, and automatic identification of the cavernous nerves, which may be of direct benefit for use in laparoscopic and robotic nerve-sparing prostate cancer surgery.

Extracting halftones from printed documents using texture analysis

Separating halftones from text is an important step in document analysis. We present an algorithm that accurately extracts halftones from other information in printed documents. We treat halftone extraction as a texture-segmentation problem. We show that commonly used halftones, consisting of a pattern of dots, can be viewed as a texture. This texture exhibits a distinct spectral component that can be detected using a properly tuned Gabor filter. The Gabor filter essentially transforms halftones into high-contrast regions that can be easily segmented by thresholding. We propose a filter design procedure and provide experimental results.

Performance of digital discrete-time implementations of non-Foster circuit elements

There is renewed interest in the use of non-Foster circuit elements in a variety of important applications such as wideband impedance matching and artificial magnetic conductors. Although non-Foster devices such as negative capacitors and negative inductors can be realized using current conveyors and Linvill circuits, a digital design approach may offer an important alternative in some applications. Therefore, digital discrete-time implementations of non-Foster circuit elements are investigated, and simulation results are presented for the implementation of a discrete-time negative inductor and a discrete-time negative capacitor.

Segmentation of optical coherence tomography images for differentiation of the cavernous nerves from the prostate gland

The cavernous nerves course along the surface of the prostate and are responsible for erectile function. Improvements in identification, imaging, and visualization of the cavernous nerves during prostate cancer surgery may improve nerve preservation and postoperative sexual potency. Two-dimensional (2-D) optical coherence tomography (OCT) images of the rat prostate were segmented to differentiate the cavernous nerves from the prostate gland. To detect these nerves, three image features were employed: Gabor filter, Daubechies wavelet, and Laws filter. The Gabor feature was applied with different standard deviations in the x and y directions. In the Daubechies wavelet feature, an 8-tap Daubechies orthonormal wavelet was implemented, and the low-pass sub-band was chosen as the filtered image. Last, Laws feature extraction was applied to the images. The features were segmented using a nearest-neighbor classifier. N-ary morphological postprocessing was used to remove small voids. The cavernous nerves were differentiated from the prostate gland with a segmentation error rate of only 0.058+/-0.019. This algorithm may be useful for implementation in clinical endoscopic OCT systems currently being studied for potential intraoperative diagnostic use in laparoscopic and robotic nerve-sparing prostate cancer surgery.