Classification images for localization performance in ramp-spectrum noise

Abstract

Purpose: This study investigates forced localization of targets in simulated images with statistical properties similar to trans-axial sections of x-ray computed tomography (CT) volumes. A total of 24 imaging conditions are considered, comprising two target sizes, three levels of background variability, and four levels of frequency apodization. The goal of the study is to better understand how human observers perform forced-localization tasks in images with CT-like statistical properties.

Methods: The transfer properties of CT systems are modeled by a shift-invariant transfer function in addition to apodization filters that modulate high spatial frequencies. The images contain noise that is the combination of a ramp-spectrum component, simulating the effect of acquisition noise in CT, and a power-law component, simulating the effect of normal anatomy in the background, which are modulated by the apodization filter as well. Observer performance is characterized using two psychophysical techniques: efficiency analysis and classification image analysis. Observer efficiency quantifies how much diagnostic information is being used by observers to perform a task, and classification images show how that information is being accessed in the form of a perceptual filter.

Results: Psychophysical studies from five subjects form the basis of the results. Observer efficiency ranges from 29% to 77% across the different conditions. The lowest efficiency is observed in conditions with uniform backgrounds, where significant effects of apodization are found. The classification images, estimated using smoothing windows, suggest that human observers use center-surround filters to perform the task, and these are subjected to a number of subsequent analyses. When implemented as a scanning linear filter, the classification images appear to capture most of the observer variability in efficiency (r² = 0.86). The frequency spectra of the classification images show that frequency weights generally appear bandpass in nature, with peak frequency and bandwidth that vary with statistical properties of the images.

Conclusions: In these experiments, the classification images appear to capture important features of human-observer performance. Frequency apodization only appears to have a significant effect on performance in the absence of anatomical variability, where the observers appear to underweight low spatial frequencies that have relatively little noise. Frequency weights derived from the classification images generally have a bandpass structure, with adaptation to different conditions seen in the peak frequency and bandwidth. The classification image spectra show relatively modest changes in response to different levels of apodization, with some evidence that observers are attempting to rebalance the apodized spectrum presented to them.

Keywords: classification images; noise; noise power spectrum; observer performance.

Figure 1

Signal transfer components. The four levels of frequency apodization are shown (a) and the total system MTF (b), composed of the product of the apodization function and the intrinsic system MTF. Note that the plot of MTF1 represents the intrinsic system MTF since apodization is constant at this level.

Figure 2

Target panel. The panel shows the two target sizes (1 mm and 4 mm diameter) at the four levels of apodization used in the experiments at 100% object contrast. Note that for the smaller target, partial volume effects reduce the target contrast, particularly at higher levels of apodization.

Figure 3

Noise components. The effect of apodization on the Ramp‐noise power spectrum is shown (a), along with unapodized (level 1) power spectra showing the effect of background variability in addition to noise (b).

Figure 4

Image background panel. The panel shows the various background image textures used in the experiments, which are affected by the amount of background variability as well as the level of apodization.

Figure 5

Stimulus display. This image shows the central portion of the image display window that subjects use in the psychophysical experiments. The reference image of the noiseless target can be seen at the top of the figure, as well as hash marks indicating the search region. The gray border extends out further in the actual display.

Figure 6

Task performance data. Performance data from the 24 experimental conditions are shown with 95% confidence intervals across subjects, as a function of target size, amount of background variability, and level of apodization. The target amplitude data (a) are the result of the threshold estimation procedure. The task performance data (b) show that the observed proportion of correct localizations was reasonably close to the 80% threshold (dotted line) used for threshold estimation. Task efficiency with respect to the ideal observer (c) shows a considerable dependence across conditions with notably large confidence intervals due to inter‐subject variability.

Figure 7

Pointing errors. The average RMSE across subjects is plotted as a function of the number of localization refinement passes (0 passes represent the original unmodified localization responses). The experimental conditions are separated into two groups based on the size of the target. Confidence intervals (95%) are derived from the standard error across subjects.

Figure 8

Classification images averaged across subjects. Subject averaged classification images for large (a) and small (b) targets, estimated according to the procedure in Eq. (11), are shown for each of the 24 tasks.

Figure 9

Scatterplot of observer efficiency and template efficiency. The average efficiency of human observers in each task is plotted against efficiency of the average template in each condition. Note the legend indicates the signal size (Sm. or Lg.) and the relative magnitude of background variability (BV = 0%, 50% or 100%). The data are reasonably well fit (r ² = 0.86) by an offset of 12.4% in efficiency (gray line).

Figure 10

Classification image spectra. The plots show radial averages of the classification images for large (a) and small (b) targets and for each level of background variability. These use the same data as was used to generate the spatial profiles shown in Figure 8, except that no frequency window is applied.

Figure 11

Peak frequency vs bandwidth plots. For each combination of target size (Small, Large) and apodization level (A1–A4), a plot shows template bandwidth as a function peak spatial frequency, plotted across the three levels of background variability. Increasing background variability generally leads to higher peak frequency and lower bandwidth. Error bars represent ±1SE derived from bootstrapping across subjects (200 resamples).

Figure 12

Template Similarity. Normalized template differences are plotted for six possible comparisons of the four apodization levels. Results are averaged across background variability in the small‐target conditions and across subjects. Error bars are the standard error across subjects. Significant differences (paired t‐test) after correction for multiple comparisons are indicated with an asterisk (*).