Integrated wavelets for enhancement of microcalcifications in digital mammography

This paper presents a new algorithm for enhancement of microcalcifications in mammograms. The main novelty is the application of techniques we have developed for construction of filterbanks derived from the continuous wavelet transform. These discrete wavelet decompositions, called integrated wavelets, are optimally designed for enhancement of multiscale structures in images. Furthermore, we use a model based approach to refine existing methods for general enhancement of mammograms resulting in a more specific enhancement of microcalcifications. We present results of our method and compare them with known algorithms. Finally, we want to indicate how these techniques can also be applied to the detection of microcalcifications. Our algorithm was positively evaluated in a clinical study. It has been implemented in a mammography workstation designed for soft-copy reading of digital mammograms developed by IMAGETOOL, Germany.     

Automated seeded lesion segmentation on digital mammograms

Segmenting lesions is a vital step in many computerized mass-detection schemes for digital (or digitized) mammograms. The authors have developed two novel lesion segmentation techniques-one based on a single feature called the radial gradient index (RGI) and one based on simple probabilistic models to segment mass lesions, or other similar nodular structures, from surrounding background. In both methods a series of image partitions is created using gray-level information as well as prior knowledge of the shape of typical mass lesions. With the former method the partition that maximizes the RGI is selected. In the latter method, probability distributions for gray-levels inside and outside the partitions are estimated, and subsequently used to determine the probability that the image occurred for each given partition. The partition that maximizes this probability is selected as the final lesion partition (contour). The authors tested these methods against a conventional region growing algorithm using a database of biopsy-proven, malignant lesions and found that the new lesion segmentation algorithms more closely match radiologists' outlines of these lesions. At an overlap threshold of 0.30, gray level region growing correctly delineates 62% of the lesions in the authors' database while the RGI and probabilistic segmentation algorithms correctly segment 92% and 96% of the lesions, respectively     

Detection of microcalcifications in digital mammograms usingwavelets

This paper presents an approach for detecting micro-calcifications in digital mammograms employing wavelet-based subband image decomposition. The microcalcifications appear in small clusters of few pixels with relatively high intensity compared with their neighboring pixels. These image features can be preserved by a detection system that employs a suitable image transform which can localize the signal characteristics in the original and the transform domain. Given that the microcalcifications correspond to high-frequency components of the image spectrum, detection of microcalcifications is achieved by decomposing the mammograms into different frequency subbands, suppressing the low-frequency subband, and, finally, reconstructing the mammogram from the subbands containing only high frequencies. Preliminary experiments indicate that further studies are needed to investigate the potential of wavelet-based subband image decomposition as a tool for detecting microcalcifications in digital mammograms     

A novel approach to microcalcification detection using fuzzy logictechnique

Breast cancer continues to be a significant public health problem in the United States. Approximately, 182,000 new cases of breast cancer are diagnosed and 46,000 women die of breast cancer each year. Even more disturbing is the fact that one out of eight women in the United States will develop breast cancer at some point during her lifetime. Since the cause of breast cancer remains unknown, primary prevention becomes impossible. Computer-aided mammography is an important and challenging task in automated diagnosis. It has great potential over traditional interpretation of film-screen mammography in terms of efficiency and accuracy. Microcalcifications are the earliest sign of breast carcinomas and their detection is one of the key issues for breast cancer control. In this study, a novel approach to microcalcification detection based on fuzzy logic technique is presented. Microcalcifications are first enhanced based on their brightness and nonuniformity. Then, the irrelevant breast structures are excluded by a curve detector. Finally, microcalcifications are located using an iterative threshold selection method. The shapes of microcalcifications are reconstructed and the isolated pixels are removed by employing the mathematical morphology technique. The essential idea of the proposed approach is to apply a fuzzified image of a mammogram to locate the suspicious regions and to interact the fuzzified image with the original image to preserve fidelity. The major advantage of the proposed method is its ability to detect microcalcifications even in very dense breast mammograms. A series of clinical mammograms are employed to test the proposed algorithm and the performance is evaluated by the free-response receiver operating characteristic curve. The experiments aptly show that the microcalcifications can be accurately detected even in very dense mammograms using the proposed approach     

Wavelet transforms for detecting microcalcifications in mammograms

Clusters of fine, granular microcalcifications in mammograms may be an early sign of disease. Individual grains are difficult to detect and segment due to size and shape variability and because the background mammogram texture is typically inhomogeneous. The authors develop a 2-stage method based on wavelet transforms for detecting and segmenting calcifications. The first stage is based on an undecimated wavelet transform, which is simply the conventional filter bank implementation without downsampling, so that the low-low (LL), low-high (LH), high-low (HL), and high-high (HH) sub-bands remain at full size. Detection takes place in HH and the combination LH+HL. Four octaves are computed with 2 inter-octave voices for finer scale resolution. By appropriate selection of the wavelet basis the detection of microcalcifications in the relevant size range can be nearly optimized. In fact, the filters which transform the input image into HH and LH+HL are closely related to prewhitening matched filters for detecting Gaussian objects (idealized microcalcifications) in 2 common forms of Markov (background) noise. The second stage is designed to overcome the limitations of the simplistic Gaussian assumption and provides an accurate segmentation of calcification boundaries. Detected pixel sites in HH and LH+HL are dilated then weighted before computing the inverse wavelet transform. Individual microcalcifications are greatly enhanced in the output image, to the point where straightforward thresholding can be applied to segment them. FROG curves are computed from tests using a freely distributed database of digitized mammograms.     

Optimization of wavelet decomposition for image compression and feature preservation

A neural-network-based framework has been developed to search for an optimal wavelet kernel that can be used for a specific image processing task. In this paper, a linear convolution neural network was employed to seek a wavelet that minimizes errors and maximizes compression efficiency for an image or a defined image pattern such as microcalcifications in mammograms and bone in computed tomography (CT) head images. We have used this method to evaluate the performance of tap-4 wavelets on mammograms, CTs, magnetic resonance images, and Lena images. We found that the Daubechies wavelet or those wavelets with similar filtering characteristics can produce the highest compression efficiency with the smallest mean-square-error for many image patterns including general image textures as well as microcalcifications in digital mammograms. However, the Haar wavelet produces the best results on sharp edges and low-noise smooth areas. We also found that a special wavelet whose low-pass filter coefficients are 0.32252136, 0.85258927, 1.38458542, and -0.14548269) produces the best preservation outcomes in all tested microcalcification features including the peak signal-to-noise ratio, the contrast and the figure of merit in the wavelet lossy compression scheme. Having analyzed the spectrum of the wavelet filters, we can find the compression outcomes and feature preservation characteristics as a function of wavelets. This newly developed optimization approach can be generalized to other image analysis applications where a wavelet decomposition is employed.     

A CAD system for the automatic detection of clustered microcalcifications in digitized mammogram films

Clusters of microcalcifications in mammograms are an important early sign of breast cancer. This paper presents a computer-aided diagnosis (CAD) system for the automatic detection of clustered microcalcifications in digitized mammograms. The proposed system consists of two main steps. First, potential microcalcification pixels in the mammograms are segmented out by using mixed features consisting of wavelet features and gray level statistical features, and labeled into potential individual microcalcification objects by their spatial connectivity. Second, individual microcalcifications are detected by using a set of 31 features extracted from the potential individual microcalcification objects. The discriminatory power of these features is analyzed using general regression neural networks via sequential forward and sequential backward selection methods. The classifiers used in these two steps are both multilayer feedforward neural networks. The method is applied to a database of 40 mammograms (Nijmegen database) containing 105 clusters of microcalcifications. A free-response operating characteristics (FROC) curve is used to evaluate the performance. Results show that the proposed system gives quite satisfactory detection performance. In particular, a 90% mean true positive detection rate is achieved at the cost of 0.5 false positive per image when mixed features are used in the first step and 15 features selected by the sequential backward selection method are used in the second step. However, we must be cautious when interpreting the results, since the 20 training samples are also used in the testing step.     

Statistical textural features for detection of microcalcificationsin digitized mammograms

Clustered microcalcifications on X-ray mammograms are an important sign for early detection of breast cancer. Texture-analysis methods can be applied to detect clustered microcalcifications in digitized mammograms. In this paper, a comparative study of texture-analysis methods is performed for the surrounding region-dependence method, which has been proposed by the authors, and conventional texture-analysis methods, such as the spatial gray-level dependence method, the gray-level run-length method, and the gray-level difference method. Textural features extracted by these methods are exploited to classify regions of interest (ROI's) into positive ROI's containing clustered microcalcifications and negative ROI's containing normal tissues. A three-layer backpropagation neural network is used as a classifier. The results of the neural network for the texture-analysis methods are evaluated by using a receiver operating-characteristics (ROC) analysis. The surrounding region-dependence method is shown to be superior to the conventional texture-analysis methods with respect to classification accuracy and computational complexity.     

基于多尺度空间滤波和l1范数最近邻分类的乳腺图像微钙化点检测

钙化信息是乳腺癌早期诊断的一个重要依据,针对钙化点检测检出率较低和假阳性较高的问题,提出一种基于多尺度空间滤波和l1范数最近邻分类的乳腺图像微钙化点检测算法.首先利用多尺度空间滤波方法得到原图像的多尺度显著特征图,然后通过基于人眼视觉特性的钙化点分割方法得到粗检测钙化点的二值图像,并送入l1范数最近邻分类器去除假阳性点...     

Segmentation of microcalcifications in mammograms

A systematic method for the detection and segmentation of microcalcifications in mammograms is presented. It is important to preserve size and shape of the individual calcifications as exactly as possible. A reliable diagnosis requires both rates of false positives as well as false negatives to be extremely low. The proposed approach uses a two-stage algorithm for spot detection and shape extraction. The first stage applies a weighted difference of Gaussians filter for the noise-invariant and size-specific detection of spots. A morphological filter reproduces the shape of the spots. The results of both filters are combined with a conditional thickening operation. The topology and the number of the spots are determined with the first filter, and the shape by means of the second. The algorithm is tested with a series of real mammograms, using identical parameter values for all images. The results are compared with the judgement of radiological experts, and they are very encouraging. The described approach opens up the possibility of a reproducible segmentation of microcalcifications, which is a necessary precondition for an efficient screening program.     

A class of square root and division free algorithms andarchitectures for QRD-based adaptive signal processing

The least squares (LS) minimization problem constitutes the core of many real-time signal processing problems, such as adaptive filtering, system identification and adaptive beamforming. Recently efficient implementations of the recursive least squares (RLS) algorithm and the constrained recursive least squares (CRLS) algorithm based on the numerically stable QR decomposition (QRD) have been of great interest. Several papers have proposed modifications to the rotation algorithm that circumvent the square root operations and minimize the number of divisions that are involved in the Givens rotation. It has also been shown that all the known square root free algorithms are instances of one parametric algorithm. Recently, a square root free and division free algorithm has also been proposed. In this paper, we propose a family of square root and division free algorithms and examine its relationship with the square root free parametric family. We choose a specific instance for each one of the two parametric algorithms and make a comparative study of the systolic structures based on these two instances, as well as the standard Givens rotation. We consider the architectures for both the optimal residual computation and the optimal weight vector extraction. The dynamic range of the newly proposed algorithm for QRD-RLS optimal residual computation and the wordlength lower bounds that guarantee no overflow are presented. The numerical stability of the algorithm is also considered. A number of obscure points relevant to the realization of the QRD-RLS and the QRD-CRLS algorithms are clarified. Some systolic structures that are described in this paper are very promising, since they require less computational complexity (in various aspects) than the structures known to date and they make the VLSI implementation easier     

Optimal filter-based detection of microcalcifications

This paper deals with the problem of texture feature extraction in digital mammograms. We use the extracted features to discriminate between texture representing clusters of microcalcifications and texture representing normal tissue. Having a two-class problem, we suggest a texture feature extraction method based on a single filter optimized with respect to the Fisher criterion. The advantage of this criterion is that it uses both the feature mean and the feature variance to achieve good feature separation. Image compression is desirable to facilitate electronic transmission and storage of digitized mammograms. In this paper, we also explore the effects of data compression on the performance of our proposed detection scheme. The mammograms in our test set were compressed at different ratios using the Joint Photographic Experts Group compression method. Results from an experimental study indicate that our scheme is very well suited for detecting clustered microcalcifications in both uncompressed and compressed mammograms. For the uncompressed mammograms, at a rate of 1.5 false positive clusters/image our method reaches a true positive rate of about 95%, which is comparable to the best results achieved so far. The detection performance for images compressed by a factor of about four is very similar to the performance for uncompressed images.     

Scale-space signatures for the detection of clustered microcalculations in digital mammograms

A method is described for the automated detection of microcalcifications in digitized mammograms. The method is based on the Laplacian scale-space representation of the mammogram only. First, possible locations of microcalcifications are identified as local maxima in the filtered image on a range of scales. For each finding, the size and local contrast is estimated, based on the Laplacian response denoted as the scale-space signature. A finding is marked as a microcalcification if the estimated contrast is larger than a predefined threshold which depends on the size of the finding. It is shown that the signature has a characteristic peak, revealing the corresponding image features. This peak can be robustly determined. The basic method is significantly improved by consideration of the statistical variation of the estimated contrast, which is the result of the complex noise characteristic of the mammograms. The method is evaluated with the Nijmegen database and compared to other methods using these mammograms. Results are presented as the free-response receiver operating characteristic (FROC) performance. At a rate of one false positive cluster per image the method reaches a sensitivity of 0.84, which is comparable to the best results achieved so far.     

Nonparametric fixed-interval smoothing with vector splines

A computationally efficient algorithm for nonparametric smoothing of vector signals with general measurement covariances is presented. This algorithm provides an alternative to the optimal smoothing algorithms that hinge on (possibly inaccurate) parametric state-space models. Automatic procedures that use the measurements to determine how much to smooth are developed and compared. This adaptation allows the data to speak for itself without imposing a Gauss-Markov model structure. A nonparametric approach to covariance estimation for the case of independently identically distributed (i.i.d.) measurement errors is presented. Monte Carlo simulations demonstrate the performance of the algorithm     

多传感器多目标跟踪算法性能分析

多假设与联合概率数据互联算法都能很好地解决杂波环境下的多目标跟踪问题。随后 ,人们在此基础上又将单传感器多假设、联合概率数据互联算法推广至集中式多传感器系统与分布式多传感器系统。近来 ,也有文献提出将广义S D分配算法动态化 ,实时地应用到集中式多传感器系统对杂波中的多目标进行跟踪。这些算法各有特点 ,因而它们在不同的情况下 ,算法的跟踪精度、实时性等方面各有优劣。然而 ,至今尚未见到有文献对这些算法在统一环境下进行分类比较 ,文中假定多种典型的多目标运动环境 ,对上述算法在这些环境下进行仿真实验 ,并根据仿真结果对它们各方面的性能进行综合分析     

Wavelet transform methods for object detection and recovery

We show that a biorthogonal spline wavelet closely approximates the prewhitening matched filter for detecting Gaussian objects in Markov noise. The filterbank implementation of the wavelet transform acts as a hierarchy of such detectors operating at discrete object scales. If the object to be detected is Gaussian and its scale happens to coincide with one of those computed by the wavelet transform, and if the background noise is truly Markov, then optimum detection is realized by thresholding the appropriate subband image. In reality, the Gaussian may be a rather coarse approximation of the object, and the background noise may deviate from the Markov assumption. In this case, we may view the wavelet decomposition as a means for computing an orthogonal feature set for input to a classifier. We use a supervised linear classifier applied to feature vectors comprised of samples taken from the subbands of an N-octave, undecimated wavelet transform. The resulting map of test statistic values indicates the presence and location of objects. The object itself is reconstructed by using the test statistic to emphasize wavelet subbands, followed by computing the inverse wavelet transform. We show two contrasting applications of the wavelets-based object recovery algorithm. For detecting microcalcifications in digitized mammograms, the object and noise models closely match the real image data, and the multiscale matched filter paradigm is highly appropriate. The second application, extracting ship outlines in noisy forward-looking infrared images, is presented as a case where good results are achieved despite the data models being less well matched to the assumptions of the algorithm.     

Using immunology principles for fault detection

The immune system is a cognitive system of complexity comparable to the brain and its computational algorithms suggest new solutions to engineering problems or new ways of looking at these problems. Using immunological principles, a two- (or three-) module algorithm is developed which is capable of launching a specific response to an anomalous situation for diagnostic purposes. Experimental results concerning fault detection in an induction motor are presented as an example illustrating how the immune-based system operates, discussing its capabilities, drawbacks, and future developments.     

Unsupervised image classification, segmentation, and enhancementusing ICA mixture models

An unsupervised classification algorithm is derived by modeling observed data as a mixture of several mutually exclusive classes that are each described by linear combinations of independent, non-Gaussian densities. The algorithm estimates the data density in each class by using parametric nonlinear functions that fit to the non-Gaussian structure of the data. This improves classification accuracy compared with standard Gaussian mixture models. When applied to images, the algorithm can learn efficient codes (basis functions) for images that capture the statistically significant structure intrinsic in the images. We apply this technique to the problem of unsupervised classification, segmentation, and denoising of images. We demonstrate that this method was effective in classifying complex image textures such as natural scenes and text. It was also useful for denoising and filling in missing pixels in images with complex structures. The advantage of this model is that image codes can be learned with increasing numbers of classes thus providing greater flexibility in modeling structure and in finding more image features than in either Gaussian mixture models or standard independent component analysis (ICA) algorithms.     

Development of an automated method for detecting mammographicmasses with a partial loss of region

Recently, we have been developing several automated algorithms for detecting masses on mammograms. For our algorithm, we devised an adaptive thresholding technique for detecting masses, but our system failed to detect masses with a partial loss of region that were located on the edge of the film. This is a common issue in all of the algorithms developed so far by other groups. In order to deal with this problem, we propose a new method in the present study. The partial loss masses are identified by their similarity to a sector-form model in the template matching process. To calculate the similarity, four features are applied: 1) average pixel value; 2) standard deviation of pixel values; 3) standard correlation coefficient defined by the sector-form model; and 4) concentration feature determined from the density gradient. After employing the new method to 335 digitized mammograms, the detection sensitivity for the partial loss masses jumped from 70% to 90% when the number of false positives was kept constant (0.2/image). Moreover, a combination of the existing method and the new method improved the true-positive rate up to 97%. Such results indicate that the new technique may improve the performance of our computer-aided diagnosis system for mammographic masses effectively.     

Retrieval algorithms for the EOS Microwave limb sounder (MLS)

The retrieval algorithms for the Earth Observing System Microwave Limb Sounder (MLS) on the Aura spacecraft, launched on July 15, 2004, are described. These algorithms are used to produce estimates of geophysical parameters such as vertical profiles of atmospheric temperature and composition ("Level 2" data) from the calibrated MLS observations of microwave limb radiance ("Level 1" data). The MLS algorithms are based on the standard optimal estimation approach, a weighted nonlinear least squares optimization with a priori constraints. New aspects include adaptation to a two-dimensional system, and an approach to the issues of retrieval "phasing" and error propagation that differs from that taken for previous similar instruments. Important new aspects of the software that implements these algorithms are also described, along with the algorithm configuration for the "version 1.5" dataset. Some examples are shown from MLS in-orbit observations.