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Segmentation is the process of subdivision of an image into, usually, nonoverlapping regions. The pixels within a region are required to possess some specified properties of homogeneity or similarity. Segmentation techniques can be classified according to different criteria. The typical classification is to divide segmentation algorithms as follows: • pixel-based algorithms or histogram-based algorithms if individual pixel values form the only information used to perform segmentation; • edge-based algorithms when segmentation is based on the detection of the edges present within the given image; and • region-based algorithms when both pixel values and the surrounding information are utilized to form different regions. In this chapter, we shall study several segmentation techniques for application to color images based upon the approaches listed above. 5.1 Histogram-based Thresholding The histogram of an image is a graph whose axes are the possible pixel values and the frequency of occurrence of each pixel value; see Sections 1.3 and 4.5 for discussions on and illustrations of histograms. Typically, a histogram is composed of modes, with each mode representing a meaningful object region. An image with a nearly uniform intensity has a histogram with a single mode. An image with a single object or several objects of similar values within a narrow range of intensities, placed against a background with a nearly uniform intensity of a different value, has a histogram with two modes; such a histogram is known as a bimodal histogram. Real-life images, however, have several objects comprising multiple values on varied backgrounds; the histograms of such images will be multimodal [6]. Furthermore, the ranges of values of multiple, spatially separated, and distinct objects may overlap; such a situation makes it difficult to analyze and interpret a histogram.

Several types of noise and artifacts affect the quality of images obtained even with imaging systems of the highest quality and under the most carefully designed experimental conditions. As a consequence, the removal of noise and artifacts is an important preprocessing step in the analysis of images; see Rangayyan [6] for detailed discussions on various sources of noise and methods to filter grayscale or scalar images. Some of the sources and types of noise and artifacts that affect images are described in the following list [6, 19]. • The Poisson nature of the detection of photons of light. • Thermal noise in the detector (for example, the dark current in CCD detectors). • Photoelectronic noise in electronic detectors. • Shot noise due to inactive elements in an electronic detector. • Noise due to quantization. • Noise due to lossy data compression or transmission, amplification, filtering, or other types of imperfect signal processing procedures. • Punctate, impulsive, or shot noise due to dust or fine particles on the object being imaged or the detector, leading to pixels that are of a widely different color than their neighbors. • Scratches on the object being imaged or on the detector (especially film) that could appear as intense line segments. • Salt-and-pepper noise due to impulsive noise, leading to black or white pixels at the extreme ends of the pixel-value range in grayscale or intensity images, or colors that are unrelated to those of neighboring pixels. • Film-grain noise due to scanning of films with high spatial resolution. In several algorithms for filtering color images, the observed noise is modeled as an additive, white, Gaussian noise process that affects each color component independently; it is assumed that the noise process is independent of the image-generating process. However, impulsive noise, modeled as sparse "spikes" that appear in the images, may also corrupt color images. For the sake of generality, it may be appropriate to assume that color images are corrupted by a combination of these two types of noise. Regardless, it should be noted that some processes can involve multiplicative noise and nonlinear effects [6].

Color is an important and often pleasant part of the visual domain; however, color is not a physical quantity but a human sensation. Color is the visual perception generated in the brain in response to the incidence of light, with a particular spectral distribution of power, on the retina. The retina is composed of photoreceptors sensitive to the visible range of the electromagnetic (EM) spectrum [21,36-38]. In general, different spectral distributions of power produce distinct responses in the photoreceptors, and therefore, different color sensations in the brain. See Table 1.1 for a representation of the EM spectrum and its parts related to various modalities of imaging, and Figure 1.1 for a display of the visible color spectrum as a part of the EM spectrum [1,39]. The diffraction of sunlight by water shows the visible color spectrum in the form of a rainbow; see Figure 1.2 for an example. When a surface is illuminated with a source of light, it absorbs some parts of the incident energy and reflects the remaining parts. When a surface is identified with a particular color, for example, red, it means that the surface reflects light energy in the particular range of the visible spectrum associated with the sensation of red and absorbs the rest of the incident energy. Therefore, the color of an object varies with the illumination. An object that reflects a part of the light that is incident upon it may be considered a secondary source of light. To reproduce and describe a color, a color representation model or color space is needed. Many color spaces have been proposed and designed so as to reproduce the widest possible range of colors visible to or sensed by the human visual system (HVS). The choice of a particular color space is determined by the application.

2.1 Basics of Color Image Acquisition The initial task in the processing and analysis of color images is the acquisition of color image data with the highest quality achievable. The output of an image-acquisition system is an electronic signal that represents the distribution of light energy across the field or the spatial extent of the image. In this chapter, we study the aspects of color image processing involved in a digital still-image-acquisition system (such as a DSC). Still-image cameras are the main sources of color images used in day-to-day practice. Scanners represent another source of still color images, but they will not be considered in this chapter. The general scheme followed by a digital camera is shown in Figure 2.1; each block of this scheme is explained in detail in the following sections. 2.1.1 Color image sensors The main purpose of the sensors in a camera is to convert the incoming light into electrical or electronic signals that represent the color image at each spatial position within the field of view (FOV). All practical DSCs use either charge-coupled devices (CCDs) or complementary metal-oxide semiconductor (CMOS) sensors in 2D arrays [158]. CCD sensors can attain high signal-to-noise ratios (SNRs), whereas CMOS sensors have the advantage of being fabricated in a single integrated circuit along with other components. In addition, CMOS sensors consume far less power than CCDs due to their higher level of integration. For these reasons, CMOS is usually the chosen technology for miniature cameras, such as those built into cellular phones; however, such cameras offer limited image quality [159]. On the contrary, CCD chips are the most commonly used sensors in consumer and professional cameras.

In spite of the availability of advanced imaging devices with high sensitivity, high resolution, and built-in image-data processing procedures, images are often acquired with quality that is unsatisfactory or inadequate for certain purposes. When considering methods to modify such images with the aim of enhancing their quality, it is important to recognize and understand the several notions and factors that affect and determine the quality of an image; see Sections 2.2 and 2.3 as well as Rangayyan [6]. If further analysis of the processed image is to be performed by a human observer, the subjective and qualitative nature of such analysis needs to be taken into consideration. On the other hand, if subsequent analysis of the image is relegated to yet another computational procedure, the objective or quantitative requirements of the procedure should be taken into account in the design of the enhancement procedure. Thus, the nature and extent of enhancement to be effected on an image depend upon further use of the processed image. In most cases, the enhancement sought in an image would be aimed to achieve one or more of the following desired characteristics: • uniform or balanced brightness across the image, which may require dark areas to be made lighter and areas of excessive brightness to be made less bright; • good contrast and visibility of detail; • sharp and well-defined edges and borders of objects or regions in the image; • clean and clear representation of the original objects or scene with no noise or blemishes; • faithful reproduction of hues or shades of color, with particular attention to skin tone and hue in images of humans; and • good color balance to result in a pleasant appearance. Several digital image-processing techniques have been proposed to address the requirements stated above in the case of grayscale images [1, 6]. However, the extension of techniques designed for grayscale or monochromatic images to process color or vector images is neither straightforward nor always appropriate; the methods described in Chapter 3 to remove noise in color images illustrate some related concepts and methods.

This paper presents methods for the detection of architectural distortion in mammograms of interval-cancer cases taken prior to the diagnosis of breast cancer, using Renyi entropy. Initial candidates for sites of architectural distortion were detected using a bank of Gabor filters and phase portrait analysis. A total of 4,224 regions of interest (ROIs) were automatically obtained from 106 prior mammograms of 56 interval-cancer cases, including 301 true-positive ROIs, and from 52 mammograms of 13 normal cases. Each ROI was represented by the Renyi entropy of angular histograms composed with the Gabor magnitude response, angle, coherence, orientation strength, and the angular spread of power in the Fourier spectrum. Using the stepwise logistic regression and leave-one-image-out methods for feature selection, the best results achieved, in terms of the area under the receiver operating characteristic curve, are 0.72 with Fisher linear discriminant analysis and the Bayesian classifier, and 0.75 with an artificial neural network based on radial basis functions. Analysis of the free-response receiver operating characteristics indicated a sensitivity of 0.80 at 7.1 false positives per image.

Monitoring the openness of the inferior and the superior temporal arcades (ITA and STA) in retinal fundus images and how they change over time can facilitate improved diagnosis and optimized treatment of myopia and retinopathy of prematurity. We propose methods for the detection and modeling of the ITA and the STA, including Gabor filters to detect retinal vessels, and the generalized Hough transform to detect and parameterize semi-parabolic forms. Results obtained with 40 images of the DRIVE database, compared with traces of the temporal arcade drawn by an expert ophthalmologist, indicate a low mean distance to the closest point error of 12.33 pixels (0.25 mm). The proposed methods should facilitate quantitative analysis of the ITA and the STA and overcome limitations associated with subjective manual analysis.

The two-dimensional (2D) S-transform can provide a more localized measure of image texture than is possible with the Fourier transform (FT). However there is a considerable time penalty: Order(N4 log N) when compared to an Order(N2 log N) FT implementation via the fast Fourier transform (FFT). We investigate the characteristics of the textural features identified when using a 2D variant of the fast discrete S-transform, an implementation which executes in a time comparable to the FFT. Results from both simulations and the comparison of the features of a benign breast mass and a malignant tumour are presented.

We present methods for the detection of architectural distortion in mammograms of interval-cancer cases taken prior to the diagnosis of breast cancer using measures of angular distribution derived from Gabor filter responses in magnitude and angle, coherence, orientation strength, and the angular spread of power in the Fourier spectrum. A total of 4224 regions of interest (ROIs) were automatically obtained using Gabor filters and phase portrait analysis from 106 prior mammograms of 56 interval-cancer cases with 301 ROIs related to architectural distortion, and from 52 mammograms of 13 normal cases. Images of coherence and orientation strength were derived from the Gabor responses in magnitude and orientation. Each ROI was represented by the entropy of the angular histogram composed with the Gabor magnitude response, angle, coherence, and orientation strength; the entropy of the angular spread of power in the Fourier spectrum was also computed. Using stepwise logistic regression for feature selection and the leave-one-image-out method in feature selection and pattern classification, the area under the receiver operating characteristic curve of 0.76 was obtained with an artificial neural network based on radial basis functions. Analysis of the free-response receiver operating characteristics indicated 82% sensitivity at 7.2 false positives per image.

The electrocardiographic (ECG) signal is a transthoracic manifestation of the electrical activity of the heart and is widely used in clinical applications. This chapter describes an unbiased linear adaptive filter (ULAF) to attenuate high-frequency random noise present in ECG signals. The ULAF does not contain a bias in its summation unit and the filter coefficients are normalized. During the adaptation process, the normalized coefficients are updated with the steepest-descent algorithm to achieve efficient filtering of noisy ECG signals. A total of 16 ECG signals were tested in the adaptive filtering experiments with the ULAF, the least-mean-square (LMS), and the recursive-least-squares (RLS) adaptive filters. The filtering performance was quantified in terms of the root-mean-squared error (RMSE), normalized correlation coefficient (NCC), and filtered noise entropy (FNE). A template derived from each ECG signal was used as the reference to compute the measures of filtering performance. The results indicated that the ULAF was able to provide noise-free ECG signals with an average RMSE of 0.0287, which was lower than the second-best RMSE obtained with the LMS filter. With respect to waveform fidelity, the ULAF provided the highest average NCC (0.9964) among the three filters studied. In addition, the ULAF effectively removed more noise, measured by FNE, in comparison with the LMS and RLS filters in most of the ECG signals tested. The issues of adaptive filter setting for noise reduction in ECG signals are discussed at the end of this chapter.

We present pattern classification methods based upon nonlinear and combinational optimization techniques, specifically, radial basis functions (RBF) and simulated annealing (SA), to classify masses in mammograms as malignant or benign. Combinational optimization is used to pre-estimate RBF parameters, namely, the centers and spread matrix. The classifier was trained and tested, using the leave-one-out procedure, with shape, texture, and edge-sharpness measures extracted from 57 regions of interest (20 related to malignant tumors and 37 related to benign masses) manually delineated on mammograms by a radiologist. The classifier’s performance, with pre-estimation of the parameters, was evaluated in terms of the area Az under the receiver operating characteristics curve. Values up to Az = 0.9997 were obtained with RBF-SA with pre-estimation of the centers and spread matrix, which are better than the results obtained with pre-estimation of only the RBF centers, which were up to 0.9470. Overall, the results with the RBF-SA method were better than those provided by standard multilayer perceptron neural networks

We propose a detection and classification system for the analysis of mammo-graphic calcifications. First, a new multi-tolerance region growing method is proposed for the detection of potential calcification regions and extraction of their contours. The method employs a distance metric computed on feature sets including measures of shape, centre of gravity, and size obtained for various growth tolerance values in order to determine the most suitable parameters. Then, shape features from moments, Fourier descriptors, and compactness are computed based upon the contours of the regions. Finally, a two-layer perceptron is utilized for the purpose of classification of calcifications with the shape features. A new leave-one-out algorithm-based parameter determination procedure is included in the neural network training step. In our preliminary study, detection rates were 81% and 85±3%, and correct classification rates were 94% and 87% with a test set of 58 benign calcifications and 241±10 malignant calcifications, respectively. The proposed system should provide considerable help to radiologists in the diagnosis of breast cancer.

Pain over the anterior portion of the knee joint is a common clinical complaint. A condition known as 'chondromalacia patella' (softening of the cartilage under the patella), which frequently causes anterior knee pain is difficult to diagnose and monitor. Vibrations detected by a contact transducer over the patellofemoral joint may be useful in the assessment of chondromalacia patella. This paper utilised this technique known as vibroarthrography (VAG), to study two potential sources of variability of the normal patellofemoral joint signal. The effect of increased muscular force on the VAG signal was measured by externally loading the joint. The effect of load history (cyclic loading) on the VAG signal was determined by comparing signals before, during, and after application of weights under similar cyclic loading conditions. Results indicated that external loading of the patellofemoral joint caused only minor signal variation. Cyclical loading of the joint, on the other hand, was determined to be a major source of variability of the normal patellofemoral joint signal, which must be controlled in future VAG tests.

The authors present some simplifications to the method of computing two-dimensional (2-D) linear prediction coefficients (LPCs) directly from image data using an extension of the multichannel Burg algorithm. This simplification results from imposing the structure of the Burg algorithm. The method can also be used for computing prediction errors directly from the data. Results of applying the method to 2-D LP coding of images and 2-D autoregressive (AR) spectral estimation are presented. >

We report on a morphological study of 192 breast masses as seen in mammograms, with the aim of discrimination between benign masses and malignant tumors. From the contour of each mass, we computed the fractal dimension (FD) and a few shape factors, including compactness, fractional concavity, and spiculation index. We calculated FD using four different methods: the ruler and box-counting methods applied to each 2-dimensional (2D) contour and its 1-dimensional signature. The ANOVA test indicated statistically significant differences in the values of the various shape features between benign masses and malignant tumors. Analysis using receiver operating characteristics indicated the area under the curve, A z , of up to 0.92 with the individual shape features. The combination of compactness, FD with the 2D ruler method, and the spiculation index resulted in the highest A z value of 0.93.

A few recent studies have proposed computed-aided methods for the detection and analysis of vertebral bodies in radiographic images. This paper presents a method based on Gabor filters. Forty-one lateral lumbar spinal X-ray images from different patients were included in the study. For each image, a radiologist manually delineated the vertebral plateaus of L1, L2, L3, and L4 using a software tool for image display and mark-up. Each original image was filtered with a bank of 180 Gabor filters. The angle of the Gabor filter with the highest response at each pixel was used to derive a measure of the strength of orientation or alignment. In order to limit the spatial extent of the image data and the derived features in further analysis, a semi-automated procedure was applied to the original image. A neural network utilizing the logistic sigmoid function was trained with pixel intensity from the original image, the result of manual delineation of the plateaus, the Gabor magnitude response, and the alignment image. The average overlap between the results of detection by image processing and manual delineation of the plateaus of L1–L4 in the 41 images tested was 0.917. The results are expected to be useful in the analysis of vertebral deformities and fractures.

Diagnostic measures related to the deterioration of the articular cartilage surfaces of knee joints due to arthritis and other abnormalities may be derived from vibroarthrographic (VAG) signals. In the present work, we explore fractal analysis to parameterize the temporal and spectral variability of normal and abnormal VAG signals. The power spectrum analysis method was used with the 1/f model to derive estimates of the fractal dimension. Classification accuracy of up to A z = 0.74 was obtained, in terms of the area under the receiver operating characteristics curve, with a database of 89 VAG signals. The result compares well with the performance of other features derived in previous related works and could help in the detection and monitoring of knee-joint pathology.

Monitoring the openness of the temporal arcade and how it changes over time can facilitate improved diagnosis and optimized treatment of plus disease and retinopathy of prematurity. We propose methods for the detection and parametric modeling of the temporal arcade, including Gabor filters to detect retinal vessels and the Hough transform to detect and parameterize parabolic forms. Results obtained with 40 images compared with parabolic models fitted to hand-drawn traces of the temporal arcade indicate a correlation coefficient of 0.97 for the openness and a mean error of 15 pixels (0.3 mm) in the vertex.

A new algorithm for image restoration in the presence of additive white Gaussian noise is presented. This algorithm is based on a new, adaptive method to estimate the additive noise. The basic idea in this technique is to identify uniform structures or objects in the image by use of an adaptive neighborhood and to estimate the noise and the signal content in these areas separately. The noise is then subtracted selectively from the seed pixel of the adaptive neighborhood, and the process is repeated at every pixel in the image. The algorithm is compared with the adaptive two-dimensional least-mean-squares and the adaptive rectangular-window least-mean-squares algorithms for noise suppression. The results from the application of these algorithms to synthesized images and natural scenes are presented along with mean-squared-error measures. The new algorithm performs better than the other two methods both in terms of visual presentation and mean-squared error.

Contours of benign breast masses and malignant tumors in mammograms differ substantially in their shape and complexity; the former are usually round and smooth, whereas the latter are typically spiculated and irregular. We demonstrate the usefulness of fractal analysis via a frequency domain approach applied to one-dimensional signatures of the two-dimensional contours of breast masses. The 1/ƒ model was applied to power spectra of signatures to estimate the fractal dimension. Tests with a dataset of 111 contours, including those of 65 benign masses and 46 malignant tumors, indicated a high classification performance of 0.89 in terms of the area under the receiver operating characteristic curve.

Ulcered lesions on the legs and feet caused by venous insufficiency and other conditions require long-term clinical treatment and follow-up. To facilitate the analysis of the tissue composition of a lesion, we propose color imaging and image processing methods. Methods considering the bottom tissues are proposed for the segmentation of a given image into regions corresponding to red granulation, yellow fibrin, black scar, and white hyperkeratotic tissue (callous). Tests with 172 images and comparison with visual analysis by a dermatologist indicated an average root-mean-squared error of 22.7% in tissue composition. In retrospective analysis, the dermatologist indicated that the results were accurate for 31.4% and acceptable for 14% of the images. Comparison between the lesion area obtained automatically and the same lesion region manually drawn by a dermatologist indicated an average superposition of 0.61.

Spectral analysis may be used to monitor process measurement accuracy and provide verification of an experimentally derived acoustical impulse response function (AIRF) of a music performance hall. First, it is necessary to derive a transducer system inverse filter in order to remove the residual effects of the measurement hardware from the AIRF. Second, through the use of a test signal, spectral analysis of the AIRF of the actual hall may be performed and compared with that of the experimentally derived AIRF. In this manner, the present work illustrates how power spectral density analysis may be used for the numerical quantification and verification of the measured AIRF of a music performance hall.

Diagnosis and monitoring of kidney diseases and transplants is supported by microscopic analysis of needle-core biopsy samples. The current methods of analysis are affected by inconsistencies, bias, and inaccuracies. We propose and evaluate image processing methods for automatic segmentation of cell nuclei in digital images of renal biopsy samples. The methods evaluated include automatic thresholding, adaptive thresholding, and morphological granulometry. The results are compared to annotations made by an expert pathologist of more than 1500 cells in 18 images from different patients. The three methods provided true-positive ratios in the range 0.80 to 0.93.

In Western countries, women have a higher than 1-in-8 chance of developing breast cancer during their lives. Breast cancer represents the most frequently diagnosed cancer in women. The National Cancer Institute of U.S.A. estimates that, based on current rates, 13.2% of women born today will be diagnosed with breast cancer at some time in their lives. In order to reduce mortality, early detection of breast cancer is important, because therapeutic actions are more likely to be successful in the early stages of the disease. For women whose tumors were discovered early by mammography, the five-year survival rate was about 82% as opposed to 60% for the cases where the tumors were not found early. Mammography is currently the best radiological technique available for early detection of nonpalpable breast cancer. However, it is difficult for radiologists to provide both accurate and uniform evaluations for the large number of mammograms that they have to interpret in screening programs where most of the cases are normal; it has been observed that 10-30% of breast lesions are missed during routine screening. The situation is even more challenging since the early malignancies have small size and subtle contrast when compared with normal breast structures. Double reading (as carried out, for example, by two radiologists) helps to reduce the number of false negatives by 5-15%. Digital image-processing techniques represent useful tools for helping radiologists to improve their diagnosis with the aid of computer systems. In this sense, different CAD (computer-aided diagnosis) tools have been developed for improving image quality, identifying malignant signs, enhancing mammographic features, etc. On the average, the reader's sensitivity can be increased by 10% with the assistance of CAD systems. Some works have studied this potential of CAD to improve radiologists' performance in detecting clustered microcalcifications. There are a number of different classes of abnormality that may be observed in mammograms. One of the most significant types of mammographic abnormality is microcalcification. Microcalcifications are tiny granule like deposits of calcium. They are relatively bright (dense) in comparison with the surrounding normal tissue, and are up to about 1 mm in diameter, with an average diameter of 0.3 mm. Microcalcifications are of particular clinical significance when found in clusters of three or more within a square-centimeter region of a mammogram. Lanyi has described microcalcifications as “the most important leading symptom in mammographic detection of preclinical carcinomas.” Sickles noted that more than 50% of nonpalpable cancers had mammographically visible calcifications, and in 36% of nonpalpable cancers, calcifications were the only sign of abnormality. In an important study of cancers missed in screening mammography, it was observed that the presence of microcalcifications was the predominant feature in 18% of the missed cancers.

Mammography is used in screening for the early detection of breast cancer in asymptomatic women. The Alberta Cancer Board (Canada) has been operating Screen Test: Alberta Program for the Early Detection of Breast Cancer since 1990. The program attracts the participation of about 21,000 women per year. In order for screening to be cost effective, means need to be developed to achieve high diagnostic accuracy. Mammograms are difficult images to interpret, especially in the screening context. Ambiguous cases with suspicious features detected on mammograms are evaluated further with adjunctive imaging procedures, such as supplementary views, ultrasonography, magnification mammography, and magnetic resonance imaging, depending on the characteristics of the abnormality. Biopsy is recommended if the imaging methods do not lead to a definite diagnosis but indicate a high suspicion for malignancy, or for confirmation of malignancy. Objective methods for the analysis of mammographic features are needed for the development of computer-aided methods to assist radiologists in the evaluation of ambiguous features. Current research is directed toward the development of digital imaging and image-analysis systems that can detect mammographic features, classify them, and give visual prompts to the radiologist.

In this chapter, the present status and future possibilities for computer-aided-detection (CAD) in breast imaging is considered. Xeromammography and later, conventional x-ray mammography, were among the earliest medical imaging modalities to benefit from the use of computers to assist radiologists in detecting lesions, especially cancers. At present, mammography is the preferred method to screen asymptomatic women for breast cancer. Breast cancer itself is a heterogeneous disease with no cure; the earlier the cancer is detected, the better the prognosis. The principal thrust of CAD research in recent years has therefore been to detect early signs of the disease, such as microcalcifications, small masses, and subtle lesions, especially those most likely to be missed by radiologists, so that any cancer present may be detected at the earliest possible stage of the disease. In this chapter, CAD in breast imaging is reviewed, and the possible lines of future research and development speculated on. The major unresolved problems are identified and, in some cases, promising trends and possible solutions are outlined. Mammography has certain structural deficiencies that have propelled research into alternative imaging modalities for breast cancer detection. Some of these emerging imaging modalities that could either be adjuncts to mammography or supplant it in the future are reviewed. The possible roles for CAD for these alternative modalities are also examined. Certain generic problems of CAD, such as accurate segmentation, registration, lesion detection, and assessment of algorithm performance are then considered. The technology of CAD, in the context of mammography, generally stands for computer-aided detection of lesions and suspicious regions, meriting careful scrutiny by a radiologist. If a patient's history and the radiologist's findings are taken into account, together with the computer-aided detection data that provides diagnostic output, a computer-aided diagnosis (CADx) system exists. Sometimes, a computer-aided diagnosis system is also confusingly referred to by the acronym CAD. In an attempt to overcome such confusion, a computer-aided detection system is sometimes referred to as a CADe system. In this chapter, computer-aided detection is referred to as CAD, and computer-aided diagnosis as CADx.

Most of the concepts used in image processing and computer vision for oriented pattern analysis have their roots in neurophysiological studies of the mammalian visual system. Campbell and Robson suggested that the human visual system decomposes retinal images into a number of filtered images, each of which contains intensity variations over a narrow range of frequency and orientation. Marcelja, and Jones and Palmer demonstrated that simple cells in the primary visual cortex have receptive fields that are restricted to small regions of space and are highly structured, and that their behavior corresponds to local measurements of frequency. According to Daugman, one suitable model for the 2D receptive field profiles measured experimentally in mammalian cortical simple cells is the parameterized family of 2D Gabor functions. Jones and Palmer and Daugman showed that a majority of cortical cells have 2D receptive field profiles that can be fitted well, in the sense of a statistical test, by members of the family of 2D Gabor elementary functions. Another important characteristic of Gabor functions or filters is their optimal joint resolution in both space and frequency, which suggests that Gabor filters are appropriate operators for tasks requiring simultaneous measurement in the two domains. Except for the optimal joint resolution possessed by the Gabor functions, the difference of Gaussian (DOG) and difference of offset Gaussian (DOOG) filters used by Malik and Perona have similar properties. Gabor filters have been presented in several works on image processing; however, most of these works are related to segmentation and analysis of texture. Rolston and Rangayyan, and Rolston proposed methods for directional decomposition and analysis of linear components in images using multiresolution Gabor filters. Multiresolution analysis using Gabor filters has natural and desirable properties for analysis of directional information in images; most of these properties are based on biological vision studies as described previously. Other multiresolution techniques have also been used with success in addressing related topics such as texture analysis and segmentation, and image enhancement. Chang and Kuo, for instance, developed a new method for texture classification that uses a tree-structured wavelet transform for decomposing an image. In their work, image decomposition is performed by taking into account the energy of each subimage instead of decomposing subsignals in the low-frequency channels. If the energy of a subimage is higher than a certain fixed threshold value C, then the decomposition procedure is applied again; otherwise, the decomposition is stopped in that region.

This paper presents methods for the detection of architectural distortion in mammograms of interval-cancer cases taken prior to the diagnosis of breast cancer, using Gabor filters, phase portrait analysis, fractal dimension (FD), and analysis of the angular spread of power in the Fourier spectrum. In the estimation of FD using the Fourier power spectrum, only the distribution of power over radial frequency is considered; the information regarding the angular spread of power is ignored. In this study, the angular spread of power in the Fourier spectrum is used to generate features for the detection of spiculated patterns related to architectural distortion. Using Gabor filters and phase portrait analysis, a total of 4224 regions of interest (ROIs) were automatically obtained from 106 prior mammograms of 56 interval-cancer cases, including 301 ROIs related to architectural distortion, and from 52 mammograms of 13 normal cases. For each ROI, the FD and measures of the angular spread of power were computed. Feature selection was performed using stepwise logistic regression. The best result achieved, in terms of the area under the receiver operating characteristic curve, is 0.75 ± 0.02 with an artificial neural network including radial basis functions. Analysis of the performance of the methods with free-response receiver operating characteristics indicated a sensitivity of 0.82 at 7.7 false positives per image.

The authors present a restoration scheme for single photon emission computed tomography (SPECT) images that performs restoration before reconstruction (pre-reconstruction restoration) from planar (projection) images. In this scheme, the pixel-by-pixel geometric mean of each pair of opposing (conjugate) planar projections is computed prior to the reconstruction process. The averaging process is shown to help in making the degradation phenomenon less dependent on the distance of each point of the object from the camera. The restoration filters investigated are the Wiener and power spectrum equalization filters. These filters are used to obtain SPECT images of a hollow cylinder phantom, a resolution phantom, and a truncated conic phantom containing two types of cold spots-a sphere, and a triangular object. A comparison of results obtained by pre-reconstruction restoration with and without averaging is performed through measurement of root mean squared errors and contrast ratios.

By modifying the histogram of an image, a dramatic improvement in the perceptibility of details can often be achieved. However, the two commonly used methods of full-frame histogram equalization and local-area histogram equalization often fail to produce adequate enhancement when the image contains relatively small but variable-sized regions in which there are objects or features of interest with low visual contrast. A new method of adaptive-neighborhood histogram equalization that is effective in enhancing these types of images is proposed in this paper. In this method, an adaptive neighborhood is developed for each pixel in the image. The adaptive neighborhood is a compound region made up of a foreground that contains 8-connected pixels close in gray level to that of the seed pixel, and a background of neighboring pixels molded around the foreground. The histogram of this adaptive neighborhood is equalized to provide the transformation that is applied to the seed pixel. Major advantages of this method are the avoidance of block edge artifacts that are encountered in local-area histogram equalization, and improved perceptibility of image detail. Examples of images transformed using the three methods of histogram modification are presented along with a discussion of the merits of the adaptive-neighborhood method.

An image analysis technique has been developed to quantitatively describe the fine vascular patterns observed in ligament tissue. The longitudinal orientational distribution and total vessel volume of India-ink-perfused blood vessel segments in normal and healing ligaments were determined. The methods involved special vascular preparation of adult rabbit knee medial collateral ligaments (MCLs) by India-ink perfusion. Black and white microscope images of ink-perfused tissue sections were subjected to a thresholding procedure to binarize digitized ligament images, which were then skeletonized and analyzed for directional distribution based on the least-squares technique. Analysis of medial collateral ligaments in New Zealand White rabbits using this method has shown that scarred tissue is more vascular and has a more chaotic angular distribution of blood-vessel segments than normal ligament tissue. >