Arthur E. Burgess

Human observer detection experiments with mammograms and power-law noise

We determined contrast thresholds for lesion detection as a function of lesion size in both mammograms and filtered noise backgrounds with the same average power spectrum, P(f)=B/f3. Experiments were done using hybrid images with digital images of tumors added to digitized normal backgrounds, displayed on a monochrome monitor. Four tumors were extracted from digitized specimen radiographs. The lesion sizes were varied by digital rescaling to cover the range from 0.5 to 16 mm. Amplitudes were varied to determine the value required for 92% correct detection in two-alternative forced-choice (2AFC) and 90% for search experiments. Three observers participated, two physicists and a radiologist. The 2AFC mammographic results demonstrated a novel contrast-detail (CD) diagram with threshold amplitudes that increased steadily (with slope of 0.3) with increasing size for lesions larger than 1 mm. The slopes for prewhitening model observers were about 0.4. Human efficiency relative to these models was as high as 90%. The CD diagram slopes for the 2AFC experiments with filtered noise were 0.44 for humans and 0.5 for models. Human efficiency relative to the ideal observer was about 40%. The difference in efficiencies for the two types of backgrounds indicates that breast structure cannot be considered to be pure random noise for 2AFC experiments. Instead, 2AFC human detection with mammographic backgrounds is limited by a combination of noise and deterministic masking effects. The search experiments also gave thresholds that increased with lesion size. However, there was no difference in human results for mammographic and filtered noise backgrounds, suggesting that breast structure can be considered to be pure random noise for this task. Our conclusion is that, in spite of the fact that mammographic backgrounds have nonstationary statistics, models based on statistical decision theory can still be applied successfully to estimate human performance.

The Rose model, revisited.

In 1946 and 1948, three very important papers by Albert Rose [J. Soc. Motion Pict. Eng. 47, 273 (1946); J. Opt. Soc. Am. 38, 196 (1948); L. Marton, ed. (Academic, New York, 1948)] were published on the role that photon fluctuations have in setting fundamental performance limits for both human vision and electronic imaging systems. The papers were important because Rose demonstrated that the performance of imaging devices can be evaluated with an absolute scale (quantum efficiency). The analysis of human visual signal detection used in these papers (developed before the formal theory of signal detectability) was based on an approach that has come to be known as the Rose model. In spite of its simplicity, the Rose model is a very good approximation of a Bayesian ideal observer for the carefully and narrowly defined conditions that Rose considered. This simple model can be used effectively for back-of-the-envelope calculations, but it needs to be used with care because of its limited range of validity. One important conclusion arising from Roses investigations is that pixel signal-to-noise ratio is not a good figure of merit for imaging systems or components, even though it is still occasionally used as such by some researchers. In the present study, (1) aspects of signal detection theory are presented, (2) Roses model is described and discussed, (3) pixel signal-to-noise ratio is discussed, and (4) progress on modeling human noise-limited performance is summarized. This study is intended to be a tutorial with presentation of the main ideas and provision of references to the (dispersed) technical literature.

Mammographic structure : data preparation and spatial statistics analysis

Detection of tumors in mammograms is limited by the very marked statistical variability of normal structure rather than image noise. This presentation reports investigation of the statistical properties of patient tissue structures in digitized x-ray projection mammograms, using a database of 105 normal pairs of craniocaudal images. The goal is to understand statistical properties of patient structure, and their effects on lesion detection, rather than the statistics of the images per se, so it was necessary to remove effects of the x-ray imaging and film digitizing procedures. Work is based on the log-exposure scale. Several algorithms were developed to estimate the breast image region corresponding to a constant thickness between the mammographic compression plates. Several analysis methods suggest that the tissue within that region, assuming second- order stationarity, is described by a power law spectrum of the form P(f) equals A/f(beta ), where f is radial spatial frequency and (beta) is about 3. There is no evidence of a flattening of the spectrum at low frequencies. Power law processes can have a variety statistical properties that seem surprising to an intuition gained using mildly random processes such as smoothed Gaussian or Poisson noise. Some of these will be mentioned. Since P(f) is approximately a 3rd order pole at zero frequency, spectral estimation is challenging.

On the noise variance of a digital mammography system

A recent paper by Cooper et al. [Med. Phys. 30, 2614-2621 (2003)] contains some apparently anomalous results concerning the relationship between pixel variance and x-ray exposure for a digital mammography system. They found an unexpected peak in a display domain pixel variance plot as a function of 1/mAs (their Fig. 5) with a decrease in the range corresponding to high display data values, corresponding to low x-ray exposures. As they pointed out, if the detector response is linear in exposure and the transformation from raw to display data scales is logarithmic, then pixel variance should be a monotonically increasing function in the figure. They concluded that the total system transfer curve, between input exposure and display image data values, is not logarithmic over the full exposure range. They separated data analysis into two regions and plotted the logarithm of display image pixel variance as a function of the logarithm of the mAs used to produce the phantom images. They found a slope of minus one for high mAs values and concluded that the transfer function is logarithmic in this region. They found a slope of 0.6 for the low mAs region and concluded that the transfer curve was neither linear nor logarithmic for low exposure values. It is known that the digital mammography system investigated by Cooper et al. has a linear relationship between exposure and raw data values [Vedantham et al., Med. Phys. 27, 558-567 (2000)]. The purpose of this paper is to show that the variance effect found by Cooper et al. (their Fig. 5) arises because the transformation from the raw data scale (14 bits) to the display scale (12 bits), for the digital mammography system they investigated, is not logarithmic for raw data values less than about 300 (display data values greater than about 3300). At low raw data values the transformation is linear and prevents over-ranging of the display data scale. Parametric models for the two transformations will be presented. Results of pixel variance measurements made on raw data images will be presented. The experimental data are in good agreement with those of Cooper et al. It will be shown that the slope of 0.6 found by Cooper et al. for the log-log plot at low exposure is not due to transfer function nonlinearity, it occurs because of an additive variance term-possibly due to electronic noise. It will also be shown, using population statistics from clinical images, that raw data values below 300 are rare in tissue areas. Those tissue areas with very low raw data values are within about a millimeter of the chest wall or in very dense muscle at comers of images.

Visual signal detection with two-component noise: low-pass spectrum effects

Detection of signals in natural images and scenes is limited by both noise and structure. The purpose of this study is to investigate phenomenological issues of signal detection in two-component noise. One component had a broadband (white) spectrum designed to simulate image noise. The other component was filtered to simulate two classes of low-pass background structure spectra: Gaussian-filtered noise and power-law noise. Measurements of human and model observer performance are reported for several aperiodic signals and both classes of background spectra. Human results are compared with two classes of observer models and are fitted very well by suboptimal prewhitening matched filter models. The nonprewhitening model with an eye filter does not agree with human results when background-noise-component power spectrum bandwidths are less than signal energy bandwidths.

Visual Perception Studies and Observer Models in Medical Imaging

Most academic radiologists will be familiar with receiver operating characteristic (ROC) studies. Fundamental studies of human observer performance are now usually performed by forced-choice methods. Both methods are based on signal detection theory. The ROC method gives an operating curve of true-positive versus false-positive probabilities. The area under the curve, A(Z), can be used a summary performance measure. In the forced-choice method, observers are given 2 or more images with one containing the signal. The observers task is to select the option most likely to contain the signal. The percentage of correct responses, PC, is a summary performance measure. Precise comparison of the 2 methods is limited to very controlled experiments in which signals (simulated lesions for example) are carefully designed and detection or discrimination is limited by true random noise. Under these conditions, theory predicts a simple relationship between summary measures and human results are consistent with theory. There will be a description of forced-choice experimental methods and data analysis. There has also been considerable work on development of theoretic observer models. Human experiment results have used to evaluate the models. Models that correlate well with human performance in turn can be used for preliminary design of new imaging systems and for selection of image quality metrics for comparing equipment performance, this article will provide a summary of work during the last 30 years on evaluating human signal detection capabilities, observer models and image quality metrics.

Nodule detection in two component noise : toward patient structure

It is common, in discussions of lesion (signal) detection in radiology, to refer to patient anatomy as structured noise. This is, of course, a gross over-simplification -- because it does not take issues of phase coherence/incoherence into account. However, there are benefits from investigating phenomenological issues of signal detection in two component noise -- with one component being broad band (white) noise designed to simulate image noise and the other (background) component filtered to match the power spectrum of some aspect of imaged patient anatomy. The purpose of the experiments described in this paper is to develop an understanding of how the power spectrum of simulated patient structure affects detectability of simulated lesions. We report results of a number of investigations of human and model observer performance. Example tasks are: detection of simulated lung nodules in noise filtered to simulate background lumpy structure at a variety of scales, detection of nodules in fractal-like power law noise, and detection of simulated microcalcification clusters and simulated breast mass lesions in power law noise designed to simulate mammographic parenchymal structure. Human results are compared to three observer models and are fitted very well by a channelized Fisher-Hotelling model. The nonprewhitening model with eye filter does not agree with human results over much of the parameter ranges.

Mass discrimination in mammography

Abstract Rationale and Objectives. In a previous publication concerning detection of masses in mammograms it was shown that the amplitude (contrast) required for detection increased as mass size increased. The work presented here was designed to measure the variation of amplitude threshold for discrimination between masses as a function of lesion size. Materials and Methods. A hybrid image method with digitized masses added to digitized normal mammograms was used. The masses were extracted from surgical specimen radiographs. Observer experiments were performed using the two-alternative forced-choice method with images displayed on a computer monitor. There were two tasks: (1) discrimination between a ductal carcinoma and a fibroadenoma, and (2) discrimination between two ductal carcinomas. Masses were scaled to cover the linear size range from 1 to 16 mm. Three observers took part, two physicists and a radiologist. Results. The discrimination contrast-detail (CD) diagrams were found to have minimum threshold amplitudes at lesion sizes near 4 mm. The detection results had demonstrated an unusual contrast-detail diagram form with threshold amplitudes monotonically increasing with lesion size for lesions larger than 1 mm, which was opposite the usual result for image noise. Discrimination thresholds or masses larger than 4 mm were approximately 1.5–2 times those reported for detection of the lesions. Conclusion. The detection results had been explained using a relatively simple model based on signal detection theory with some characteristics of the human visual system included. The observer model cannot explain the discrimination results, so additional complexity must be introduced to the observer model.

Effect of viewing angle on visual detection in liquid crystal displays

Display devices for medical diagnostic workstations should have a diffuse emission with apparent luminance independent of viewing angle. Such displays are called Lambertian, or they obey Lamberts law. Actual display devices are never truly Lambertian; the luminance of a pixel depends on the viewing angle. In active-matrix liquid crystal displays (AMLCD), the departure from the Lambertian profile depends on the gray level and complex pixel designs having multiple domains, in-plain switching or vertically-aligned technology. Our previous measurements established that the largest deviation from the desired Lambertian distribution occurs in the low luminance range for the diagonal viewing direction. Our purpose in this work is to determine the effect that non-uniform changes of the angular emission have on the detection of low-contrast signals in noisy backgrounds. We used a sequential two-alternative forced choice (2AFC) approach with test images displayed at the center of the screen. The observer location was fixed at different viewing angles: on-axis and off-axis. The results are expressed in terms of percent-correct for each observer and for each experimental condition (viewing angle and luminance). Our results show that for the test images used in this experiment with human observers, the changes in detectability between on-axis and off-axis viewing are smaller than the observer variability. Model observers are consistent with these results but also indicate that different background and signal levels can lead to meaningful performance differences between on-axis and off-axis viewing.

Producing lesions for hybrid mammograms: extracted tumors and simulated microcalcifications

Experimental and theoretical investigations of signal detection in medical imaging have been increasingly based on realistic images. In this presentation, techniques for producing realistic breast tumor masses and microcalcifications will be described. The mass lesions were obtained from 24 specimen radiographs of surgically removed breast tissue destined for pathological evaluation. A variety of masses were represented including both lobular and spiculated ductal carcinomas as well as fibroadenomas. Mass sizes ranged from 4 to 18 mm. The specimens included only a small amount of attached normal tissue, so tumor boundaries could be identified subjectively. A simple, interactive quadratic surface generating method was used for background subtraction -- yielding an isolated tumor image. Individual microcalcifications were generated using a 3D stochastic growth algorithm. Starting with a central seed cell, adjacent cells were randomly filled until the 3D object consisted of a randomly selected number of filled cells. The object was then projected to 2D, smoothed and sampled. It is possible to generate a large variety of realistic shapes for these individual microcalcifications by varying the rules used to control stochastic growth. MCCs can then randomly generated, based on the statistical properties of clusters described by LeFebvre et al.