KEYWORDS: Signal to noise ratio, Sensors, Tissues, Signal detection, Breast, Optical spheres, Mammography, Digital mammography, X-rays, Interference (communication)
The purpose of this work was to evaluate the effect of detector element size on detection and discrimination of small objects in digital mammograms in the presence of quantum noise, stochastic breast structure {P (f) = K/f3)} and system (electronic) noise. Theoretical analysis was done using the Fourier domain approximation of Albert and Maidment (Medical Physics, Vol. 27, pp 2417-2434, 2000), including averaging over random but known signal locations and aliasing. Realistic CsI-based indirect detection system operating parameters were used with 4 detector element sizes (25, 50, 75 and 100 microns). Detailed results depended on selected input exposure and system noise level (10 mR and 100 photons/del equivalent photon input were used). Results will be described using size thresholds based on human decision performance estimates -- typical threshold SNRs were about 6 to 7 at 95% decision accuracy. The selected tasks and approximate threshold sizes were: searching for a microcalcification in a 1 cm2 cluster (140 microns), two-alternative forced-choice microcalcification discrimination of shape (220 microns) and edge gradient (290 microns), and searching for a spiculation (cylinder model) around the perimeter of a known mass. MC task threshold variations with del size were small (usually less than 5% variation). Spiculation thresholds depended on length and surrounding tissue composition -- del size and system noise had little effect. For 15 mm spiculations, the threshold diameters were about 0.5 mm in fatty tissue and 1.3 mm in 50% glandular tissue.
KEYWORDS: LCDs, Signal detection, Signal to noise ratio, Visualization, Calibration, Switching, Image processing, Medical devices, Performance modeling, Data modeling
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 Lambert's
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.
Observer models based on linear classifiers with basis functions (channels) are useful for evaluation of detection performance with medical images. They allow spatial domain calculations with a covariance matrix of tractable size. The term “channelized Fisher-Hotelling observer” will be used here. It is also called the “channelized Hotelling observer” model. There are an infinite number of basis function (channel ) sets that could be employed. Examples of channel sets that have been used include: difference of Gaussian (DOG) filters, difference of Mesa (DOM) filters and Laguerre-Gauss (LG) basis functions. Another option, sums of LG functions (LGS), will also be presented here. This set has the advantage of having no DC response. The effect of the number of images used to estimate model observer performance will be described, for both filtered 1/f3 noise and GE digital mammogram backgrounds. Finite sample image sets introduce both bias and variance to the estimate. The results presented here agree with previous work on linear classifiers. The LGS basis set gives a small but statistically significant reduction in bias. However, this may not be of much practical benefit. Finally, the effect of varying the number of basis functions included in the set will be addressed. It was found that four LG bases or three LGS bases are adequate.
Normal mammographic image backgrounds have approximately isotropic power spectra of the form, P(f) =K/fe, where f is radial frequency. The values ofthe exponent, 3, range from 1.5 to 3.5 with an average of about 2.8. The ideal observer model predicts that, for signals with certain properties, the log-log contrast-detail (CD) diagram slope, m, is given by: m = O.5(3-2). Previously, we reported results for detection of a model mass (designer nodule) in filtered noise with an exponent of 3. The model and human observer CD slopes were 0.5 and 0.45 respectively. Here, we report preliminary results for human and model observer 2AFC detection of a simple signal in filtered noise with exponents from 1.5 to 3.5. Our results are in good agreement with the prediction of the above equation. We will also describe results of 2AFC detection experiments done using "twin" noise backgrounds with identical noise realizations in the two backgrounds. We could not replicate the results ofJohnson et al. For '1/f3' noise, they found a CD slope of—O.59 while we found +0.37.
KEYWORDS: Mammography, Signal detection, Mathematical modeling, Performance modeling, Medical imaging, Digital imaging, Databases, Imaging systems, Systems modeling, Mathematics
Kundel et al. Suggested the use of circle cues to assist human observers during signal-known-exactly (SKE) detection experiments. The circles were bipolar (with concentric black and white rings) and centered on potential locations of simulated masses added to mammographic backgrounds. They used a large circle cue (diameter 6.4 cm) and a background size of 7.7 cm (referred to the initial mammogram). They found significant detection performance improvement compared to the no cue conditions. In our previous experiments, we use mammographic background sizes of 6.1 cm and smaller circles with sizes dependent on lesion size. Our circle sizes were selected to subjectively optimize utility but choices may not have been the best. Also, detectability may also depend on background size. In this work, we present human observer results for detecting a realist mass added to mammographic backgrounds using 30 conditions (all combinations of the mass scaled to 3 sizes, 2 background sizes and 5 circle sizes). Performance did not depend on background size. For the smallest mass size (1 mm, 8 pixels), detectability decreased as circle size increased. There may be an optimum near a circle/mass size ratio of 4. The optimum size ratio for the 4 mm mass was 3. For the 16 mm mass, detectability decreased as steadily as circle size increased. The smallest size ratio used was 1.2.
Detection of mass lesions in mammograms is essentially limited by image variation due to normal patient structure, which has an average power-spectrum of the form `1/f3'. Image noise plays little role in limiting mass detection. The contrast-detail (CD) diagram for lesion detection in mammographic structure is novel, for both human and model observers. Contrast thresholds increase with increasing signal size for signals larger than about 1 mm, with CD slopes of about 0.3 for humans and 0.4 for model observers. Similar results were obtained in search experiments. The work was done using hybrid images, with of tumor masses (extracted from specimen radiographs) added to digitized mammographic backgrounds. We have been able to explain the results using a number of observer models. These results demonstrate that CD diagrams based on image noise-limited detection with simple phantoms are not useful for evaluation of mass detection in mammograms--so more realistic approaches are necessary in order to model mammographic imaging systems for optimization.
Two alternative forced-choice (2AFC) nodule detection performances of a number of model observers were evaluated for detection of simulated nodules in filtered power-law (1/f3) noise. The models included the ideal observer, the channelized Fisher-Hotelling (FH) model with two different basis function sets, the non-prewhitening matched filter with an eye filter (NPWE), and the Rose model with no DC response (RoseNDC). Detectability of the designer nodule signal was investigated. It has equation s((rho) )equalsA*Rect((rho) /2)(1-(rho) 2)v, where (rho) is a normalized distance (r/R), R is the nodule radius and A is signal amplitude. The nodule profile can be changed (designed) by changing the value of v. For example, the result is a sharp-edged, flat-topped disc for v equal to zero and the projection of a sphere for v equal to 0.5. Human observer experiments were done with nodules based on v equal to 0, 0.5 and 1.5. For the v equal to 1.5 case, human results could be well fitted using a variety of models. The human CD diagram slopes were -0.12, +0.27 and +0.44 for v equal to 0, 0.5 and 1.5 respectively.
Both the natural and manmade worlds abound with processes that have power-law spectra of the form, P(f)equalsK/f(beta ). Statistical properties of such processes are dramatically different from those of smoothed Gaussian random processes. There is an extreme concentration of spectral power at low frequencies and a unique correlation distance does not exist. In addition, processes that do not have a low frequency cutoff have infinite (undefined) variance for infinite data sets. The fact that mammographic structure has a power-law spectrum does not tell one a great deal about the underlying process that generated the structure. Many different processes can have the same second order statistics, example classes are: deterministic, stochastic, self-similar, self-affine, and chaotic. It will be necessary to develop or adapt a variety of analytical techniques to investigate the nature of mammographic statistics. Some examples of power-law processes will be described and some statistical properties of mammograms will be presented.
This paper is a report on very surprising results from recent work on detection of real lesions in digitized mammograms. The experiments were done using a novel experimental procedure with hybrid images. The lesions (signals) were real tumor masses extracted from breast tissue specimen radiographs. In the detection experiments, the tumors were added to digitized normal mammographic backgrounds. The results of this new work have been both novel and very surprising. Contrast thresholds increased with increasing lesion size for lesions larger than approximately 1 mm in diameter. Earlier work with white noise, radiographic image noise, computed tomography (CT) noise and some types of patient structure have accustomed us to a particular relationship between lesion size and contrast for constant detectability. All previous contrast/detail (CD) diagrams have been similar, the contrast threshold decreases as lesion size increases and flattens at large lesion sizes. The CD diagram for lesion detection in mammographic structure is completely different. It will be shown that this is a consequence of the power-law dependence of the projected breast tissue structure spectral density on spatial frequency. Mammographic tissue structure power spectra have the form P(f) equals B/f(beta ), with an average exponent of approximately 3 (range from 2 to 4), and are approximately isotropic (small angular dependence). Results for two-alternative forced-choice (2AFC) signal detection experiments using 4 tumor lesions and one mathematically generated signal will be presented. These results are for an unbiased selection of mammographic backgrounds. It is possible that an additional understanding of the effects of breast structure on lesion detectability can be obtained by investigating detectability in various classes of mammographic backgrounds. This will be the subject of future research.
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.
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.
Blindness is nature is fatal. In biology and physiology one finds many situations where nature has obtained neat solutions to problems, solutions that ar every nearly the best possible. Many of the design parameters for the eye are not arbitrarily selected, but are constrained to a narrow range of values by physics and information theory considerations. As Helmholtz mentioned more than a century ago 'the eye has every possible defect that can be found in an optical instrument and even some which are peculiar to itself; but they are all so interacted, that the inexactness of the image which results from their presence very little exceeds, under ordinary conditions of illumination, the limits which are set to the delicacy of sensation by the dimensions of the retinal cones.' Helmholtz was particularly prescient in his reference to cone dimension because, as we will see, many eye properties are completely determined once cone diameter is selected. The ideas presented in this paper are based on the working assumption that the eye does the best possible job within physical limits. This idea originated with Horace Barlow more than 40 years ago. Once excellent reference is the proceedings of a conference organized to honor Barlow's retirement with presentations by his many collaborators over the years. The list includes practically everyone referenced in this paper, which explores the design and optimization of the optics of the eye, retinal transduction and coding of visual data.
Previous experiments using highpass nose have either suggested that humans cannot compensate for anti-correlated noise in images or were inconclusive. These results may have been misleading because of the use of a single noise component. For large exponents of fn, image noise within the bandwidth of the signal amplitude for detection. This situation does not correspond to CT or SPECT imaging cases where patient structure with a lowpass spectrum is also present and limits detection accuracy. In addition, humans have two forms of internal noise that limit detection and this may have been the source of poor human performance. So, in this work, experiments were done with two noise components - one broadband to ensure that task performance was always limited by external noise. The experiments were designed to be more precise test of compensation for anti- correlated noise and to provide a more sensitive test of existing observer models. In all cases, separate experiments were done to estimate observer internal noise. The new results show a marked asymmetry between lowpass and highpass noise effects and are consistent withthe view that internal noise is the cause of poor highpass noise performance.
Historically, gray scale has been the standard method of displaying univariate medical images. With the advent of digital imaging, color scales have been used for display of quantitative nuclear medicine images and for quantitative overlays in ultrasound images. There has been no interest shown in using color for anatomically based imaging such as radiography or CT. The one exception has been attempts to do multi-spectral (T1, T2, (rho) ) image display in MRI. A few color scales have been proposed and evaluated, but have had little acceptance by radiologists. It is possible that carefully designed scales might give lesion detection performance that equals gray scale and improves performance of other tasks. We investigated 13 display scales including the physically linear gray scale, the popular rainbow scale, and 11 perceptually linearized scales. One was the heated object scale and the other 10 were spiral trajectories in the CIELAB uniform color space. The experiments were performed using signals added to white noise and a statistically defined (lumpy) background. In general, the best performance was obtained using the gray scale and the heated object scale. Performance for the spiral trajectory scales was typically 25% lower. Performance for the rainbow scale was very poor (about 30% of gray scale performance).
KEYWORDS: Signal detection, Interference (communication), Eye models, Performance modeling, Signal to noise ratio, Lung, Data modeling, Fractal analysis, Eye, Medical imaging
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.
Recent investigations of human signal detection performance for noise limited tasks have used statistically defined signal or image parameters. The Bayesian ideal observer procedure is then nonlinear and analysis becomes mathematically intractable. Linear, but suboptimal, observer models have been proposed for mathematical convenience. Experiments by Rolland and Barrett involving detection of completely defined signals in white noise superimposed on statistically defined (Lumpy) backgrounds showed that the Fisher-Hotelling model gave a good fit while the simple nonprewhitening (NPW) matched filter gave a poor fit. Burgess showed that the NPW model can be modified to fit their data by adding a spatial frequency filter with response similar to the human contrast sensitivity function. New experimental results will be presented demonstrating that neither model is satisfactory. The results of our experiments done with a variety of spectral densities for the background can be described by a Fisher-Hotelling model modified to include simple circularly symmetric spatial frequency channels as proposed by Myers and Barrett. However, results of our variable viewing distance experiments do not agree with predictions of this simple channelized model. It will be necessary to use a more complex F model with physiologically reasonable spatial frequency channels.
Investigation of human signal-detection performance for noise- limited tasks with statistically defined signal or image parameters represents a step towards clinical realism. However, the ideal observer procedure is then usually nonlinear, and analysis becomes mathematically intractable. Two linear but suboptimal observer models, the Hotelling observer and the non- prewhitening (NPW) matched filter, have been proposed for mathematical convenience. Experiments by Rolland and Barrett involving detection of signals in white noise superimposed on statistically defined backgrounds showed that the Hotelling model gave a good fit while the simple NPW matched filter gave a poor fit. It will be shown that the NPW model can be modified to fit their data by adding a spatial frequency filter of shape similar to the human contrast sensitivity function. The best fit is obtained using an eye filter model, E(f) equals f1.3 exp(-cf2) with c selected to give a peak at 4 cycles per degree.
The problem of image assessment is examined for several cases of parameter uncertainty. Several ideal and
sub-ideal observers are considered and figures of merit (FOM) for describing their performance are
considered. Advantages and disadvantages of these FOMs are enumerated. The spectrum of noise
equivalent quanta, NEQ(f), appears to be the most useful for evaluating a broad class of practical problems
since the performance of the best-linear as well as the ideal non-linear observers considered here is
monotonic with its components. However, more work is required within this context to quantify the effects
of the "null space," or regions in object space for which NEQ = 0. These regions derive from incomplete
measurement sets and may lead to severe image degrading artifacts that are not adequately covered by any
FOMs considered here.
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