Conocimientos declarativos

For the purpose of standard image processing, multiple blank and dark images were acquired. Raw images were corrected according to Corrected image= (Raw image – Dark image) / (Blank image – Dark image), prior to scatter correction.

5.2.4.1 Scatter interpolation

A scatter correction algorithm was applied to estimate the scatter maps. Though fundamentally similar to previous beam pass corrections [83] [84] [85], this algorithm performs three separate scatter interpolations. Preliminary studies of the method used a single interpolation over the entire image which demonstrated visible artifacts in transitional regions. [86] Refinement of the algorithm included segmentation of the full field image to create three ROI, the object, background, and skin line. Scatter maps for each region are calculated independently and merged. Figures 5-6 to 5-9 illustrate the process for each step.

As shown in Figure 5-6, the full field image was first segmented to find the skin line and establish the boundaries for skin line interpolation, or skin line mask. The segmentation was performed within the algorithm, binarizing the image based on a threshold computed via the MATLAB function graythresh. The PSD image was then segmented to define the primary sample locations. This image was also binarized in the algorithm using a manually-adjustable threshold. The binary image was automatically checked for over- or under-sized sample regions and the user prompted to adjust the threshold, if necessary. Object and background masks were generated using fixed samples of nine pixel diameter to eliminate sampling in penumbral regions.

Figure 5-6: Flow chart showing steps for segmenting the images into the three ROI: skin, object, and background.

Figure 5-7 depicts the use of these masks to sample the PSD image and normal projection image to generate a map of the scatter samples. Discrete values of the primary signal, P, were computed by averaging the signal intensity over circular regions (d = 9 pixels) at the center of each PSD hole. The corresponding pixels were averaged within the full field projection (without PSD) to compute the total signal (scatter + primary), T. Values for the scatter signal in these hole locations were computed using 𝑆 = 𝑇 − 𝑃, producing scatter sampling maps for the object and background regions.

PSD Image

Figure 5-7: Flow chart showing steps for obtaining scatter samples from PSD and full field image using masks generated via the process in figure 4.

These scatter sampling maps were then used for two separate biharmonic spline interpolations, in the object and background regions, as shown in Figure 5-8. These interpolations were sampled using the skin line mask to generate a data set of two concentric silhouettes, the inner sampled from the object interpolation and the outer sampled from the background interpolation. These two lines were then interpolated to generate a smooth transition from the object to background regions. All three interpolated images were cropped to their region of interest and combined to generate the first estimate of scatter in all pixels, 𝑆𝑖𝑛𝑡. The interpolated scatter map could have been used at this point to increase the contrast by

subtracting the low-frequency scatter profile from the full field image. This method is referred to as the scatter interpolation (SI) scatter correction.

Figure 5-8:Skin line interpolation is a result of sampling from the object and background interpolations. Object, skin line, and background scatter are cropped into their respective ROI and combined into one scatter map. The scatter map is combined with the full field image to generate the SPR, which is then filtered. Note that the window/level values of these images are non-uniform. They have been adjusted

for feature visibility.

5.2.4.2 Filtered scatter-to-primary ratio (f-SPR)

Since 𝑆𝑖𝑛𝑡 is a smooth varying function, subtraction results in a loss of signal, adversely affecting the signal-difference-to-noise ratio (SdNR) as the noise in the images is not reduced. It is desirable to increase both the contrast and SdNR, so the scatter correction must include a high-frequency scatter component. The full field image contains noise, including noise from scatter, to which the amount of

local fluctuation may correlate. To capture this we apply additional processing, also shown in Figure 5-9. The scatter-to-primary ratio (SPR) is calculated at each pixel location using 𝑆𝑃𝑅 = 𝑆𝑖𝑛𝑡/(𝑇 − 𝑆𝑖𝑛𝑡). The SPR map was then filtered via convolution with a low-pass Gaussian to generate the filtered SPR, 𝑆𝑃𝑅𝑓. The Gaussian convolution kernel was a rotationally symmetric matrix of 9x9 pixel size with a standard deviation of =2 pixels. The filtration produces a smoother SPRf image, which when mathematically recombined with T, produces a fluctuating scatter map. The final processing steps are shown in Figure 7, wherein the final estimate of the scatter, 𝑆𝑓𝑠𝑝𝑟, is re-computed from the 𝑆𝑃𝑅𝑓 using 𝑆𝑓𝑠𝑝𝑟= 𝑇 ∙

𝑆𝑃𝑅𝑓/(1 + 𝑆𝑃𝑅𝑓). The final scatter map, 𝑆𝑓𝑠𝑝𝑟, includes a smooth varying scatter component and part of local fluctuations associated with the full field image, T. When 𝑆𝑓𝑠𝑝𝑟 is subtracted from the full image, 𝑇, there is a corresponding reduction of high frequency local fluctuation, in addition to the elimination of the low frequency object-specific scatter map. Compared with using the interpolated scatter, 𝑆𝑖𝑛𝑡, this method improves both the contrast and SdNR significantly. This technique is referred to as the filtered scatter-to- primary ratio (f-SPR) scatter correction.

Figure 5-9: The filtered SPR is recombined with the full field image to generate the final scatter map, used to generate the scatter corrected final image.

5.2.5 Phantom imaging