Clinical ROC Studies of Digital Stereo Mammography

The objective of this study was to explore and document the diagnostic utility of digital stereo mammography for the detection of localized breast cancer in women. In it we character­ized the ability of experienced mammographers, general radiologists, and non-radiologists to detect three types of tumor masses embedded within a heterogeneous background of normal tis­sue elements in numerically simulated digital mammograms. The simulated mammograms were displayed to the subjects on a high resolution video display, both in stereo mode and in mono mode. Half of the mammograms contained a single tumor, ranging from 0.3 to 0.8 cm in maxi­mal diameter. Each reader rated 120 images (60 in stereo and 60 in mono) as to the probability of abnormality on scale of 1-5. Observer responses were evaluated using receiver operating characteristic (ROC) analysis to characterize any difference in diagnostic performance between the two viewing modes. The synthesized mammograms and the digital display were highly rated by the participant radiologists as promising tools for future research. The results of ROC analysis, however, indicated no significant difference in tumor detection when the same readers utilized the stereo mode versus the mono mode (Az mono = 0.833 versus, Az stereo = 0.826). The results were similar for readers of all 3 experience levels--mammographers, general radiolo­gists, and non-radiologists

Visible Light and X-Ray Ray Tracing of Generalized Cylinders

A new algorithm for ray tracing generalized cylinders whose axis is an arbit:rary three dimensional space curve and whose cross-sectional contour can be varied accortding to a general sweeping rule is presented. The only restriction placed on the class of generalized cylinders that can be ray-traced is that the sweeping rule of the generalized cylinder must be invertible. This algorithm handles a broader class of generalized cylinders than ainy other reported ray tracer. It has been integrated into a general geometric modeling systenn that can render objects utilizing visible light as well as simulated X-rays. Generalized cylinders are often used in modeling systems because they cornpactly represent objects. Many commonly occurring objects including snakes, horses, airplanes, flower vases, and organ,s of the human abdomen such as the stomach and liver can be described naturally and conveniently in terms of one or more generalized cylinder primitives. By extending the class of generalized cylinders that can be conveniently modeled, the presented algorithm enhances the utility of modeling systems based on generalized cylinders. X-ray images of the internal bone structure of a knee joint, and a visible light image of a fan blade assembly are presented

Invariant Reconstruct ion of Curves and Surfaces using a First Order Regularization

This paper describes the application of a first order regularization technique to the problem of reconstruction of curves and surfaces from sparse data. The reconstruction methods achieve approximate invariance, sharp preservation of discontinuities and are robust to the smoothing parameter A. The robustness property to X allows a free choice of the smoothing parameter X without struggling to determine an optimal X that provides the best reconstrilction. A new approximately invariant first order stabilizing function for surface reconstruction is obtained by employing a first order Taylor expansion of a nonconvex invariant stabilizing function that is expanded at the estimated value of the squared gradient instead of at zero. The data compatibility measure used is the squared perpendicular distance between the reconstructed surface and the constraint surface. This combination of stabilizing function and data compatibility measure is necessary to achieve invariance with respect to rotations and translations of the surfaces being reconstructed. Sharp preservation of discontinuities is achieved by a weighted sum of adjacent pixels such that the adjacent pixels that are more likely to be in different regions are less weighted. The ideas employed for surface reconstruction are also applied to curve reconstruction. The results indicate that the proposed methods for curve and surface reconstruction perform well on sparse noisy range data. Curved surfaces (or curved sections in the case of curve reconstruction) are well reconstructed even though a first order model is employed. In addition, the volume between two surfaces normalized by the surface area is proposed as an invariant measure for the comparison of reconstruction results. Similarly, the area between two curves normalized by the arc length is proposed for comparing curve reconstruction results

Recognition and Localization of a Flat Symmetric Object from a Single Perspective Image

A flat symmetric object viewed under perspective (orthographic) projectiorl yields a convergent (skew) symmetry. Unlike skew symmetry where the axes constrain the orientation of the underlying object to lie on a hyperbola in the gradient space, for convergent symmetry the object orientation can be uniquely determined from the axis and convergent point except for some special cases. However, detection of the axis and convergent point of a convergent symmetry has not yet received much attention. We present a technique which can detect the axis and convergent point of a convergent symmetric contmour in an image using distinguished points such as bitangents, corners, and inflection points on the contour. In addition to recovering the orientation of an object directly from the axis and convergent point of its convergent symmetry, when a model database is available, our technique is also able to recognize and locate the object by using the cross ratio as an indexing function. The orientation information is also used for verification purposes. Our technique is simple, efficient, and accurate. It is also robust to noise and partial occlusion. Experimental results on real images are shown

Automatic Gradient Threshold Determination for Edge Detection Using a Statistical Model A Description of the Model and Comparison of Algorithms

In the enhancement/thresholding method of edge detection, the gradient values of pixels exceeding a certain threshold are designated as edge pixels. However, selecting a threshold has commonly been performed through ad hoc measures. This paper describes a method for automatically selecting a threshold using a 5-parameter model. The model is based on the weighted sum of two gamma density functions corresponding to edge and ncln-edge pixels. A variety of statistical and fitting methods for finding the model parameters were evaluated by comparing their computed thresholds to perceptual thresholds determined by subjects for 16 different images. The performance of the model was also analyzed under different noise levels. Index Terms: Automatic thresholding, edge detection, gradient, Sobel operator, statistical classification

An Efficient Method for Computing Volume and Surface Area Over Grid Sampled Surfaces

In this paper, we propose the volume between two surfaces normalized by the surface area as an invariant quantitative measure for comparing surface reconstruction results. The invariant property of the volume quantity provides the same measure with respect to an arbitrary coordinate system. By normalizing the volume by the surface area, the values of the measure can be compared for different size of images. We also present a computationally simple and efficient way of computing the volume between two surfaces and the surface area using a least-square-error fit plane approximation of a surface patch defined over a rectangular grid. Experiments indicate that the method using a least-square-error fit plane approximation gives equivalent performance as other more complicated and computationally expensive methods. The advantage of this method is that computation is extremely simple and efficient. Similarly, we propose the area between two curves normalized by the arc length as an invariant measure for comparing plane curve reconstruction results

Pre-Clinical ROC Studies of Digital Stereomammography

This paper reports the diagnostic performance of observers in detecting abnormalities in computer generated mammogram-like images. A mathematical model of the human breast is defined in which breast tissues are simulated by spheres of different sizes and densities. Images ar\u27e generated by casting rays from a specified source, through the: model, and onto an image plane. Observer performance with two viewing modalities (stereo versus mono) is compared. In the stereo viewing mode, left and right images are presented to the observer (wearing liquid crystal shuttle glasses), such that the left eye sees the left image only and the right eye sees the right image only. In this way, the images can be fused by the observer to obtain a sense of depth. In the mono viewing mode, left and right images are presented side by side and the observer can see both images at the same time. Observer response data are evaluated using receiver operating characteristic (ROC) analysis to characterize any difference in detectability of abnormalities (in either the density or arrangement of simulated tissue densities) using the two viewing modes. The results indicate the clear superiority of stereo viewing for detection of arrangement abnormalities. For detection of density abnormalities, the performance of the two viewing modes is similar. These preliminary results suggest that stereomanlmography may permit easier detection of certain tissue abnormalities, perhaps providing a route to earlier tumor detection in cases of breast cancer

A Geometric Modeling Tool for Visualization of Human Anatomical Structures

A geometric modeling system for creating and visualizing models of human anatomical structures has been developed. Many structures in the human body such as blood vessels, bones, the breast, and the chest cavity can be naturally modeled using generalized cylinder and quadric primitives. These models can be accurately and efficiently rendered to form simulated transmitted x-ray and reflected visible light images of human anatomy. Stereoscopic images can be easily generated to allow 3D viewing. Representation of organs by geometric models allows easy modification of their size, shape, and grouping relations. Rotation and viewing in arbitrary direction, and anatomical manipulations such as removal of organs to reveal details of surrounding structures, can be accomplished. Some potential applications and sample images generated by our system are presented. 1 Introduction Medical imaging and visualization have been playing an ever increasing role in the diagnosis and followup care of patie..

A framework for using benefit functions in complex real-time systems

Researchers are currently investigating applying benefit, or utility functions for allocating resources in limited, soft real time systems [1,2,3]. While the future of real-time computing research and practice will likely explo it the utility of benefit-based models, this will not occur until a suitable system level benefit framework has been defined. This paper provides an overview of ongoing work to develop such an initial framework that can formalize the use of benefit functio ns in complex real time systems. It is easily shown that this framework can support traditional hard/firm/soft real-time paradigms as well as support newer proposed models for future real time operation [5,6]. We also show that our proposed framework unifies composition of benefit values derived from heterogeneous perspectives, including those derived from the application perspective.