Mixture Modeling for Digital Mammogram Display and Analysis

To determine the preferences of radiologists among eight different image processing algorithms applied to digital mammograms obtained for screening and diagnostic imaging tasks. Twenty-eight images representing histologically proved masses or calcifications were obtained by using three clinically available digital mammographic units. Images were processed and printed on film by using manual intensity windowing, histogram-based intensity windowing, mixture model intensity windowing, peripheral equalization, multiscale image contrast amplification (MUSICA), contrast-limited adaptive histogram equalization, Trex processing, and unsharp masking. Twelve radiologists compared the processed digital images with screen-film mammograms obtained in the same patient for breast cancer screening and breast lesion diagnosis. For the screening task, screen-film mammograms were preferred to all digital presentations, but the acceptability of images processed with Trex and MUSICA algorithms were not significantly different. All printed digital images were preferred to screen-film radiographs in the diagnosis of masses; mammograms processed with unsharp masking were significantly preferred. For the diagnosis of calcifications, no processed digital mammogram was preferred to screen-film mammograms. When digital mammograms were preferred to screen-film mammograms, radiologists selected different digital processing algorithms for each of three mammographic reading tasks and for different lesion types. Soft-copy display will eventually allow radiologists to select among these options more easily.

Spectral Phase Based Medical Image Processing 1

This paper proposes a data-driven approximation of the Cumulative Distribution Function using the Finite Mixtures of the Cumulative Distribution Function of Logistic distribution. Since it is not possible to solve the logistic mixture model using the Maximum likelihood method, the mixture model is modeled to approximate the empirical cumulative distribution function using the computational intelligence algorithms. The Probability Density Function is obtained by differentiating the estimate of the Cumulative Distribution Function. The proposed technique estimates the Cumulative Distribution Function of different benchmark distributions. Also, the performance of the proposed technique is compared with the state-of-the-art kernel density estimator and the Gaussian Mixture Model. Experimental results on κ−μ distribution show that the proposed technique performs equally well in estimating the probability density function. In contrast, the proposed technique outperforms in estimating the cumulative distribution function. Also, it is evident from the experimental results that the proposed technique outperforms the state-of-the-art Gaussian Mixture model and kernel density estimation techniques with less training data.

In rarefied gas flows, discontinuity phenomena such as velocity slip and temperature jump commonly appear in the gas layer adjacent to a solid boundary. Due to the physical complexity of the interactions at the gas-solid interface, particularly in the case of systems with local nonequilibrium state, boundary models with limited number of parameters cannot completely describe the reflection of gas molecules at the boundary. In this work, the Gaussian mixture (GM) model, which is an unsupervised machine learning technique, is employed to construct a statistical gas-solid surface scattering model based on the collisional data obtained from molecular dynamics (MD) simulations. The GM model is applied to study Couette flow for different inert gases (Ar and He) confined between two parallel infinite gold walls at different temperatures. A direct comparison between the results obtained from the GM model and the Cercignani-Lampis-Lord (CLL) scattering kernel against the MD collisional data in terms of the distribution of the predicted postcollisional velocities, and accommodation coefficients has shown that the results from the GM model are an excellent match with the MD results outperforming the CLL scattering kernel. As an example, for He gas, while the predicted energy accommodation coefficient by the CLL model is more than two times higher than the MD predictions, the value computed by the GM model is in excellent agreement with the MD results. This superior performance of the GM model confirms its high potential to derive a generalized boundary condition in systems encountered with highly nonequilibrium and complex gas flow conditions.

This work presents a deep learning approach based on autoencoder to improve the detection of architectural distortion (AD) in digital mammography. AD can be the earliest sign of breast cancer, appearing before the formation of any mass or calcification. However, it is very diffcult to be detected and almost 50% of the cases are missed by the radiologists. Thus, we designed an autoencoder, based on a convolutional neural network (CNN), to work as a feature descriptor in a computer-aided detection (CAD) pipeline with the objective of detecting AD in digital mammography. This model was trained with 140,000 regions-of-interest (ROI) extracted from clinical mammograms. These samples were divided in two groups, with and without AD, according to the radiologist's report. Validation was done comparing the classifier performance when using the proposed autoencoder and other well-known feature descriptors, commonly used for the task of detecting AD in digital mammograms. The results showed that the performance of the autoencoder is slightly higher than that of other descriptors. However, the complexity and the computational cost of the autoencoder is much higher when compared to the hand-crafted descriptors.

Efficient similarity search for uncertain data is a challenging task in many modern data mining applications like image retrieval, speaker recognition and stock market analysis. A common way to model the uncertainty of data objects is using probability density functions in the form of Gaussian Mixture Models (GMMs), which have an ability to approximate arbitrary distribution. However, due to the possible unequal length of mixture models, the use of existing index techniques has serious problems for the objects modeled by GMMs. Either the techniques cannot handle GMMs or they have too many limitations. Hence, we propose a dynamic index structure, Gaussian Component based Index (GCI), for GMMs. GCI decomposes GMMs into the single, pairs, or n-lets of Gaussian components, stores these components into well studied index trees such as U-tree and Gauss-Tree, and refines the corresponding GMMs in a conservative but tight way. GCI supports both k-most-likely queries and probability threshold queries by means of Matching Probability. Extensive experimental evaluations of GCI demonstrate a considerable speed-up of similarity search on both synthetic and real-world data sets.

A semi-automated prototype compression paddle system has been designed to enable co-registered acquisition of tomosynthesis and 3D breast ultrasound images. The system retrofits to a digital mammography system (Senographe 2000D, GE Medical Systems). A high frequency, linear, multirow transducer is positioned in mechanical alignment above the paddle. The two-dimensional transducer motion in a plane above the digital mammography detector is controlled and synchronized through dedicated software that resides on a stand-alone computer, that also interfaces with a LOGIQ700 ultrasound system (GE Medical Systems). Following tomosynthesis or standard projection digital mammography exposure, a full-breast ultrasound scan is acquired with multiple linear sweeps of the transducer positioned above the compressed breast. The digital mammograms and sonograms are thus acquired with the same views of the breast, as determined by mechanical design. The images are then transformed into a common coordinate system and reformatted views in orthogonal or oblique planes may be visualized in various ways to compare regions of interest on the two sets of images for combined evaluation. Initial results on 2D ad 3D mammograms combined with 3D ultrasound for anthropomorphic breast phantoms and 2D mammograms combined with 3D ultrasound for patients demonstrate promising potential of this system towards improved breast imaging.

Synthesized 2D (s2D) mammography is rapidly replacing digital mammography in breast imaging with digital breast tomosynthesis (DBT) to reduce radiation dose and maintain screening outcomes. We illustrate variations in the appearance of s2D and digital mammograms to aid in implementation of this technology. Despite subjective differences in the appearance of s2D and digital mammograms, early outcomes of screening using s2D mammography and DBT are not inferior to those achieved with digital mammography and DBT. Understanding these variations may aid in implementing this technique and improving patient outcomes.

Medical-image segmentation is of primary importance in the development of computer assisted detection (CAD) of mammographic masses. Image segmentation is used for finding regions of interest (ROI) within mammograms that are further processed to estimate their likelihood of being a potential lesion or mass. This task can be stated as follows: €œA gray-scale image is represented as a 1D array X = (x1, x2,...,xN), where xn is an input feature for pixel n and N is the total number of pixels in the image. The input feature vector xn may be a D dimensional vector or simply the gray-scale value of the pixel n. Let the underlying true segmentation of the image be denoted as Y = (y1, y2,..., yN). It is assumed that the number of classes is predetermined as a set of known class labels I‰l, where l Iµ {1,..., L{ and therefore the class label of pixel n is indicated as y n ∈{I‰ l } L l=1 . The task is to predict the A·n estimate of the segmentation for each pixel. In an automated system, such likelihood estimates are generated using a classifier that takes as input some features that describe region properties, e.g., image texture. The segmentation of digital mammograms is a difficult task. A number of different approaches have been adopted in this area with varying success. Broadly speaking, image segmentation can be carried out either as: (1) image preprocessing step with the main objective of identifying regions of interest (spatially coherent collection of pixels within the image) and a subsequent feature extraction and classification step is required to characterize a given region of interest as either €œnormal€ or €œsuspicious€; or (2) part of the overall classification scheme, where the likelihood of each pixel being €œsuspicious is calculated to generate a probability image using pixel-based features as input to a classifier. The probability image is thereafter thresholded to give both the segmentation and classification output. The main difference between (1) and (2) is that in the first case, image segmentation is needed before classification can be performed; whereas in the second case, classification and segmentation are both based on thresholding probability estimates of pixels and are achieved at the same time. The image segmentation approaches, with the aim of finding regions of interest, were first attempted in digital mammography with varying techniques, including global thresholding, region growing, region clustering, template matching, edge operators and filtering, and edge-based hybrid methods. Image segmentation is developed from pixel-based probability estimation is underpinned by modeling features using parametric methods, Gaussian mixture modeling, Markov random fields, and other methods. A detailed discussion on mammogram-based image segmentation with their algorithms is available in Singh and Bovis. Experience shows that it is quite difficult to select an outright winning image-segmentation method, since different approaches have been shown to be suitable for different data sets and show varied performance under different experimental conditions. However, there is a consensus that image segmentation in medical imaging is most successful when explicitly using a priori information about the problem to be studied.

We present an unsupervised segmentation algorithm combining the mean shift procedure and deterministic annealing expectation maximization (DAEM) called MS-DAEM algorithm. We use the mean shift procedure to determine the number of components in a mixture model and to detect their modes of each mixture component. Next, we have adopted the Gaussian mixture model (GMM) to represent the probability distribution of color feature vectors. A DAEM formula is used to estimate the parameters of the GMM which represents the multi-colored objects statistically. The experimental results show that the mean shift part of the proposed MS-DAEM algorithm is efficient to determine the number of components and initial modes of each component in mixture models. And also it shows that the DAEM part provides a global optimal solution for the parameter estimation in a mixture model and the natural color images are segmented efficiently by using the GMM with components estimated by MS-DAEM algorithm.

Scattering kernels are of paramount importance in modeling gas–surface interactions for rarefied gas flows. However, most existing empirical models need one or several accommodation coefficients (ACs) to be determined before applications. In this paper, an unsupervised machine learning technique, known as the Gaussian mixture (GM) model, is applied to establish a new scattering kernel based on the simulated data collected by molecular dynamics (MD) simulations. The main work is devoted to the scattering of diatomic molecules under thermal non-equilibrium conditions. Correspondingly, different MD simulations on the scattering process of nitrogen molecules from a platinum surface have been performed involving rotational and translational excitation. Here, we evaluate the performance of the GM and Cercignani–Lampis–Lord models against the MD approach by comparing the velocity correlation distributions and the relevant outgoing velocity probability density function as well as the computed ACs. The presented comparisons have demonstrated the superiority of the GM model in matching with MD results. Therefore, in the case of diatomic gases, the GM model can be employed as a promising strategy to derive the generalized boundary conditions.

In many modern applications such as biometric identification systems, sensor networks, medical imaging, geology, and multimedia databases, the data objects are not described exactly. Therefore, recent solutions propose to model data objects by probability density functions(pdf). Since a pdf describing an uncertain object is often not explicitly known, approximation techniques like Gaussian mixture models(GMM) need to be employed. In this paper, we introduce a method for efficiently indexing and querying GMMs allowing fast object retrieval for arbitrary shaped pdf. We consider probability ranking queries which are very important for probabilistic similarity search. Our method stores the components and weighting functions of each GMM in an index structure. During query processing the mixture models are dynamically reconstructed whenever necessary. In an extensive experimental evaluation, we demonstrate that GMMs yield a compact and descriptive representation of video clips. Additionally, we show that our new query algorithm outperforms competitive approaches when answering the given probabilistic queries on a database of GMMs comprising about 100.000 single Gaussians.

In this paper we seek a Gaussian mixture model (GMM) of an n-variate probability density function. Usually the parameters of GMMs are determined in the original n-dimensional space by optimizing a maximum likelihood (ML) criterion. A practical deficiency of this method of fitting GMMs is its poor performance when dealing with high-dimensional data since a large sample size is needed to match the accuracy that is possible in low dimensions. We propose a method for fitting the GMM based on the projection pursuit strategy. This GMM is highly constrained and hence its ability to model structure in subspaces is enhanced, compared to a direct ML fitting of a GMM in high dimensions. Our method is closely related to recently developed independent factor analysis (IFA) mixture models. The comparisons with ML fitting of GMM in n-dimensions and IFA mixtures show that the proposed method is an attractive choice for fitting GMMs using small sizes of training sets.

The accurate modeling of uncertain variables, such as wind power and load uncertainty, is an essential foundation for the planning operation and scheduling decisions in power systems. Currently, Gaussian mixture model (GMM) and Dirichlet process mixture model (DPMM) are the primary techniques used to characterize uncertainties in power systems, which are commonly solved by expectation-maximization (EM) algorithm. However, for the massive data of uncertain variables, the algorithm encounters challenges in accurately obtaining GMM and DPMM with a lower time consumption. To address this issue, we propose a method for GMM uncertainty modeling in power systems considering the mutual assistance of latent variables. Specifically, the GMM of uncertain variables is first constructed, and the conditional probability is employed to characterize the mutual assistance of latent variables. Then, an improved EM algorithm is developed to obtain the optimal GMM parameters, in which the expectation step (E-step) and maximization step (M-step) of the algorithm are revised using the conditional probability. Importantly, the closed-form solutions for GMM parameters are rederived in the revised E-step and M-step. Finally, the proposed uncertainty modeling method is compared with the traditional GMM and DPMM on actual wind power and load data from Australia. The proposed method performs the efficiency and accuracy in characterizing uncertainty.

The aim of this study was to implement a Dirichlet process mixture (DPM) model for automatic tumor edge identification on (18)F-fluorodeoxyglucose positron emission tomography ((18)F-FDG PET) images by optimizing the parameters on which the algorithm depends, to validate it experimentally, and to test its robustness. The DPM model belongs to the class of the Bayesian nonparametric models and uses the Dirichlet process prior for flexible nonparametric mixture modeling, without any preliminary choice of the number of mixture components. The DPM algorithm implemented in the statistical software package R was used in this work. The contouring accuracy was evaluated on several image data sets: on an IEC phantom (spherical inserts with diameter in the range 10-37 mm) acquired by a Philips Gemini Big Bore PET-CT scanner, using 9 different target-to-background ratios (TBRs) from 2.5 to 70; on a digital phantom simulating spherical/uniform lesions and tumors, irregular in shape and activity; and on 20 clinical cases (10 lung and 10 esophageal cancer patients). The influence of the DPM parameters on contour generation was studied in two steps. In the first one, only the IEC spheres having diameters of 22 and 37 mm and a sphere of the digital phantom (41.6 mm diameter) were studied by varying the main parameters until the diameter of the spheres was obtained within 0.2% of the true value. In the second step, the results obtained for this training set were applied to the entire data set to determine DPM based volumes of all available lesions. These volumes were compared to those obtained by applying already known algorithms (Gaussian mixture model and gradient-based) and to true values, when available. Only one parameter was found able to significantly influence segmentation accuracy (ANOVA test). This parameter was linearly connected to the uptake variance of the tested region of interest (ROI). In the first step of the study, a calibration curve was determined to automatically generate the optimal parameter from the variance of the ROI. This "calibration curve" was then applied to contour the whole data set. The accuracy (mean discrepancy between DPM model-based contours and reference contours) of volume estimation was below (1 ± 7)% on the whole data set (1 SD). The overlap between true and automatically segmented contours, measured by the Dice similarity coefficient, was 0.93 with a SD of 0.03. The proposed DPM model was able to accurately reproduce known volumes of FDG concentration, with high overlap between segmented and true volumes. For all the analyzed inserts of the IEC phantom, the algorithm proved to be robust to variations in radius and in TBR. The main advantage of this algorithm was that no setting of DPM parameters was required in advance, since the proper setting of the only parameter that could significantly influence the segmentation results was automatically related to the uptake variance of the chosen ROI. Furthermore, the algorithm did not need any preliminary choice of the optimum number of classes to describe the ROIs within PET images and no assumption about the shape of the lesion and the uptake heterogeneity of the tracer was required.