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The second of two examples of the application of the segmentation and analysis framework to images reconstructed from numerical ultrasound reflection data is presented. Similar to the first example, the aim is to extract knowledge related to the breast’s internal structure from the ultrasound reconstruction, and to incorporate this prior structural information into the reconstruction algorithm implemented for microwave imaging. Accordingly, the focus of the analysis is the delineation of dense tissue regions rather than tumor detection. The dense tissue regions are comprised of glandular, transition, and in this case, malignant tissues; the non-dense tissue regions are comprised of fatty (or adipose) tissue.

A more challenging scenario, relative to the first example, is examined by using a numerical ultrasound model of a dense breast with one tumor embedded in the glandular tissue [9]. The model is illuminated with a circular array of equally spaced ultrasound transducers. An ultrasound image is reconstructed by applying a multi-static delay-and-sum method to the backscattered fields over all transducer locations.

The ultrasound propagation speed (or velocity) component of the forward model that was used to generate the numerical data serves as ground truth. For the analysis, it is used as the reference image, whereas the ultrasound image reconstructed from the backscattered fields serves as the test image. The reference and test images that are input to the workflow are shown in Figure 1.

Figure 1. Velocity (or speed of propagation) component of forward model used as reference image (left). Test image (right) represents the backscattered energy reconstructed from numerical reflection data generated from the forward model [9].

The reference and test images shown in Figure 1 are input to a workflow displayed in Figure 2. The workflow is comprised of segmentation and analysis steps. In the first step of the segmentation process, the reference and test images are partitioned into immersion medium, breast interior, and a region-of-interest. An approximation of the skin region is also formed.

The region-of-interest is partitioned further into dense and non-dense (or fatty) tissue regions. The region-of-interest of the reference image is partitioned with a thresholding segmentation technique; an unsupervised machine learning technique is applied to the region-of-interest of the test image. The segmentation steps of the reference and test images are described in more detail in sections 8.1 and 8.2, respectively. The interface and geometric property analysis steps are described in more detail in sections 8.3 and 8.4, respectively.

Figure 2. Segmentation and image analysis workflow.

8.1 Segmentation of reference image

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The first step of the segmentation procedure uses a thresholding technique to delineate the breast interior within the reference image which allows the formulation of masks for the immersion medium and interior. Similar to the first ultrasound example that is described in section 7.1, a closed contour that bounds the interior mask is used to model the skin surface and to construct a region-of-interest mask. A skin mask is also formed by subtracting the region-of-interest mask from the breast interior mask.

The region-of-interest mask is applied to the reference image and a simple thresholding segmentation delineates the region-of-interest into dense and non-dense (or fatty) tissues as described in section 7.1. The resulting dense and fatty tissue masks are shown in the left column of Figure 3. The breast interior mask formed in the first step is also shown in the top row of Figure 3.

The tissue and immersion medium masks are mapped to labels to form the respective tissue type regions as described in section 7.1. A tissue type image is formed by the disjoint union of the tissue type regions, and is a shown in the left panel of the middle row of Figure 4.

Figure 3. Segmentation masks constructed from reference (left column) and test images (right column).

Figure 4. Reference image representing forward model (top left) and test image representing reconstructed ultrasound image (top right) of a dense breast with corresponding tissue types identified via segmentation (middle row). Cluster map of final iteration (bottom row) of unsupervised machine learning segmentation algorithm that is used to segment test image. The reference image is segmented using a thresholding technique.

8.2 Segmentation of test image

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The test image is preprocessed to construct masks of the breast interior and immersion medium by applying a *k-*means clustering technique [28] to the image. As already described in in section 7.2, a closed contour that bounds the interior mask is used to model the skin surface and to construct a region-of-interest mask. The difference between the breast interior and region-of-interest masks leads to a skin mask.

Once the region-of=interest mask is formed in the preprocessing step, an automatic segmentation algorithm is applied to the region-of-interest within the test image to delineate the dense tissue regions as described in section 7.2. When the segmentation algorithm is terminated, the region-of-interest is partitioned into $5$ clusters. The resulting cluster map is shown in the right hand side of the bottom row of Figure 4. Note that each cluster within the image can be identified using the provided color bar.

The clusters are mapped to Dense and Fatty tissue masks, and the masks are subsequently mapped to tissue type regions as described in section 7.2. The disjoint union of the tissue type regions leads to a tissue type image shown in the middle of the right column of Figure 4. The labels assigned to the corresponding tissue type region are shown with the color bar.

The tissue type images constructed from the reference and test images serve as a visualization tool that may assist with the interpretation of the ultrasound images. The analysis component of the workflow applies metrics to the Interior mask, the Dense tissue masks, and the closed contour that bounds the interior. The metrics measure discrepancies between regions within the test and reference images and is described next.

Figure 5. Estimated (blue line) and actual (red line) interface that delineates the breast interior (left) and dense tissue regions (right). The interfaces are superimposed onto the test image.

8.3 Interface analysis

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The boundary of each dense tissue mask constructed from the test image is sampled uniformly. This leads to a set of edge points that collectively estimate points along each interface that delineates the dense tissue. A closed contour is fitted to the points and is superimposed onto the test image along with the corresponding contour of the reference mask.

The skin surface contour that was formulated in the preprocessing step to delineate the breast interior is also superimposed onto the test image. The test image adds context to the test and reference contours, and so the image is helpful to visually evaluate the quality of the interface extracted from the data. Contours of the reference and test interfaces extracted from the skin surface and dense tissue masks are shown in Figure 5. The reference contour is shown in red while the reconstructed (or test) contour is represented with the blue line.

Figure 6. Analysis of skin surface contour that delineates the interior.

The estimated points sampled from the boundary of a test mask are compared with the corresponding boundary of the reference mask in order to measure how accurately the skin surface or a dense tissue interface is extracted by the reconstruction algorithm. More specifically, the distance each edge point on a test interface is to the nearest point on the corresponding reference contour (refer to section 1) is measured. A negative distance implies that the estimated point is within the reconstructed region, while a positive distance implies the opposite.

In Figures 6-7, selected points of the estimated test interface along with the errors are superimposed onto the reference contour to help visualize how the errors are spatially distributed along the interface. A quantitative analysis of the errors is provided by plotting the error distribution along with an estimate of the mean and variance (or spread) of the errors. This information is shown in the right hand panels of Figures 6-7.

Figure 7. Analysis of interfaces associated with each of the reconstructed dense tissue regions.

8.4 Geometric property analysis

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The interior region bound by the skin surface and the regions bound by each of the dense tissue interfaces are compared with the corresponding region within the reference image. A comprehensive geometric property analysis is performed on each of the reconstructed regions using metrics 1, 2, 3, 4, 5, 6, 7, 8, 16 described in section 1. The subset of overlap metrics are primarily used to measure how accurately the skin surface and dense tissue regions are reconstructed relative to the reference region. Accordingly, the measured values are most meaningful when the ground truth is used as the reference image (as in this case). Results of the analysis are shown in Figures 8 and 9.

Figure 8. Geometric property analysis of skin surface and the region bound by this closed contour.

Figure 9. Geometric property analysis of each region of dense tissue extracted from test image.