William E. Higgins

Optimal Gabor filters for texture segmentation

Texture segmentation involves subdividing an image into differently textured regions. Many texture segmentation schemes are based on a filter-bank model, where the filters, called Gabor filters, are derived from Gabor elementary functions. The goal is to transform texture differences into detectable filter-output discontinuities at texture boundaries. By locating these discontinuities, one can segment the image into differently textured regions. Distinct discontinuities occur, however, only if the Gabor filter parameters are suitably chosen. Some previous analysis has shown how to design filters for discriminating simple textures. Designing filters for more general natural textures, though, has largely been done ad hoc. We have devised a more rigorously based method for designing Gabor filters. It assumes that an image contains two different textures and that prototype samples of the textures are given a priori. We argue that Gabor filter outputs can be modeled as Rician random variables (often approximated well as Gaussian rvs) and develop a decision-theoretic algorithm for selecting optimal filter parameters. To improve segmentations for difficult texture pairs, we also propose a multiple-filter segmentation scheme, motivated by the Rician model. Experimental results indicate that our method is superior to previous methods in providing useful Gabor filters for a wide range of texture pairs.

Texture segmentation using 2-D Gabor elementary functions

Many texture-segmentation schemes use an elaborate bank of filters to decompose a textured image into a joint space/spatial-frequency representation. Although these schemes show promise, and although some analytical work has been done, the relationship between texture differences and the filter configurations required to distinguish them remain largely unknown. This paper examines the issue of designing individual filters. Using a 2-D texture model, we show analytically that applying a properly configured bandpass filter to a textured image produces distinct output discontinuities at texture boundaries; the analysis is based on Gabor elementary functions, but it is the bandpass nature of the filter that is essential. Depending on the type of texture difference, these discontinuities form one of four characteristic signatures: a step, ridge, valley, or a step change in average local output variation. Accompanying experimental evidence indicates that these signatures are useful for segmenting an image. The analysis indicates those texture characteristics that are responsible for each signature type. Detailed criteria are provided for designing filters that can produce quality output signatures. We also illustrate occasions when asymmetric filters are beneficial, an issue not previously addressed. >

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.

Symmetric region growing

Of the many proposed image segmentation methods, region growing has been one of the most popular. Research on region growing, however, has focused primarily on the design of feature measures and on growing and merging criteria. Most of these methods have an inherent dependence on the order in which the points and regions are examined. This weakness implies that a desired segmented result is sensitive to the selection of the initial growing points. We define a set of theoretical criteria for a subclass of region-growing algorithms that are insensitive to the selection of the initial growing points. This class of algorithms, referred to as symmetric region growing algorithms, leads to a single-pass region-growing algorithm applicable to any dimensionality of images. Furthermore, they lead to region-growing algorithms that are both memory- and computation-efficient. Results illustrate the methods efficiency and its application to 3D medical image segmentation.

Three-dimensional path planning for virtual bronchoscopy

Multidetector computed-tomography (MDCT) scanners provide large high-resolution three-dimensional (3-D) images of the chest. MDCT scanning, when used in tandem with bronchoscopy, provides a state-of-the-art approach for lung-cancer assessment. We have been building and validating a lung-cancer assessment system, which enables virtual-bronchoscopic 3-D MDCT image analysis and follow-on image-guided bronchoscopy. A suitable path planning method is needed, however, for using this system. We describe a rapid, robust method for computing a set of 3-D airway-tree paths from MDCT images. The method first defines the skeleton of a given segmented 3-D chest image and then performs a multistage refinement of the skeleton to arrive at a final tree structure. The tree consists of a series of paths and branch structural data, suitable for quantitative airway analysis and smooth virtual navigation. A comparison of the method to a previously devised path-planning approach, using a set of human MDCT images, illustrates the efficacy of the method. Results are also presented for human lung-cancer assessment and the guidance of bronchoscopy.

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.

Shape-based interpolation of tree-like structures in three-dimensional images

Many three-dimensional (3-D) medical images have lower resolution in the z direction than in the x or y directions. Before extracting and displaying objects in such images, an interpolated 3-D gray-scale image is usually generated via a technique such as linear interpolation to fill in the missing slices. Unfortunately, when objects are extracted and displayed from the interpolated image, they often exhibit a blocky and generally unsatisfactory appearance, a problem that is particularly acute for thin treelike structures such as the coronary arteries. Two methods for shape-based interpolation that offer an improvement to linear interpolation are presented. In shape-based interpolation, the object of interest is first segmented (extracted) from the initial 3-D image to produce a low-z-resolution binary-valued image, and the segmented image is interpolated to produce a high-resolution binary-valued 3-D image. The first method incorporates geometrical constraints and takes as input a segmented version of the original 3-D image. The second method builds on the first in that it also uses the original gray-scale image as a second input. Tests with 3-D images of the coronary arterial tree demonstrate the efficacy of the methods.

Extraction of the hepatic vasculature in rats using 3-D micro-CT images

High-resolution micro-computed tomography (CT) scanners now exist for imaging small animals. In particular, such a scanner can generate very large three-dimensional (3-D) digital images of the rats hepatic vasculature. These images provide data on the overall structure and function of such complex vascular trees. Unfortunately, human operators have extreme difficulty in extracting the extensive vasculature contained in the images. Also, no suitable tree representation exists that permits straightforward structural analysis and information retrieval. This work proposes an automatic procedure for extracting and representing such a vascular tree. The procedure is both computation and memory efficient and runs on current PCs. As the results demonstrate, the procedure faithfully follows human-defined measurements and provides far more information than can be defined interactively.

Computer-based system for the virtual-endoscopic guidance of bronchoscopy

The standard procedure for diagnosing lung cancer involves two stages: three-dimensional (3D) computed-tomography (CT) image assessment, followed by interventional bronchoscopy. In general, the physician has no link between the 3D CT image assessment results and the follow-on bronchoscopy. Thus, the physician essentially performs bronchoscopic biopsy of suspect cancer sites blindly. We have devised a computer-based system that greatly augments the physicians vision during bronchoscopy. The system uses techniques from computer graphics and computer vision to enable detailed 3D CT procedure planning and follow-on image-guided bronchoscopy. The procedure plan is directly linked to the bronchoscope procedure, through a live registration and fusion of the 3D CT data and bronchoscopic video. During a procedure, the system provides many visual tools, fused CT-video data, and quantitative distance measures; this gives the physician considerable visual feedback on how to maneuver the bronchoscope and where to insert the biopsy needle. Central to the system is a CT-video registration technique, based on normalized mutual information. Several sets of results verify the efficacy of the registration technique. In addition, we present a series of test results for the complete system for phantoms, animals, and human lung-cancer patients. The results indicate that not only is the variation in skill level between different physicians greatly reduced by the system over the standard procedure, but that biopsy effectiveness increases.

3D CT-Video Fusion for Image-Guided Bronchoscopy

Bronchoscopic biopsy of the central-chest lymph nodes is an important step for lung-cancer staging. Before bronchoscopy, the physician first visually assesses a patients three-dimensional (3D) computed tomography (CT) chest scan to identify suspect lymph-node sites. Next, during bronchoscopy, the physician guides the bronchoscope to each desired lymph-node site. Unfortunately, the physician has no link between the 3D CT image data and the live video stream provided during bronchoscopy. Thus, the physician must essentially perform biopsy blindly, and the skill levels between different physicians differ greatly. We describe an approach that enables synergistic fusion between the 3D CT data and the bronchoscopic video. Both the integrated planning and guidance system and the internal CT-video registration and fusion methods are described. Phantom, animal, and human studies illustrate the efficacy of the methods.