M-rep modeled kidney with its medial mesh, liver, and male pelvis (two bones, bladder, rectum, prostate). The kidney model also shows the underlying representation of a sampled medial surface and a tiled boundary.
An interior through section of a single-figure kidney.
The boundary-relative stencil region and the intensity profiles that make up the template stencil for measuring geometry-to-image match (a) in 2D, both before and after deformation. (b) In 3D, the mesh showing the object boundary and the grey scale in the collar showing the image intensities there in two orthogonal slices. (c) Intensity profiles for the kidney (trained from kidney images). (d) Locations where each profile is dominant. In (c) and (d) light grey indicates a light to dark profile, between the kidney and surrounding general tissue; black indicates a dark to light profile, between the kidney and an adjacent organ, e.g., the liver or spleen; medium grey indicates a light to dark to light notch profile, between the kidney, through adjacent general tissue, and then into an adjacent organ.
Stage by stage progress of deformable m-rep segmentation of the kidney. Top: rendered 3D view, after the stage indicated. Bottom: results on axial, sagittal, and coronal CT slices. Each image compares progress through consecutive stages via overlaid curves: H, initial (hand-placed) position; M, postfigural model stage; A, postfigural section (atom) stage; B, at end, i.e., postboundary displacement stage.
M-reps for kidney, liver, and male pelvis. Top row: mesh of atom hubs; middle row; mesh of medial atoms (including spokes); bottom row: the implied boundaries shown with atom mesh(es).
Left two: medial atoms, made from a hub position and two spokes of equal length . The atom on the left is for an internal mesh position, implying two boundary sections. The atom on the right is for a mesh edge position, implying a section of boundary crest. An atom is represented by the medial hub position ; the length of the spokes; a frame made from the unit-length bisector of the spokes, the -orthogonal unit vector in the plane of the spokes, and the complementary unit vector ; and the “object angle” between and each spoke. The implied figure section is slablike, and the local implied boundary is incident to and orthogonal to the spoke ends. Right: the figure/subfigure arrangement, with the subfigure (6 medial atoms appearing, 3 of which form the “hinge”) on top, the host figure (4 medial atoms showing) below, and the blend region shown darker.
A single-figure m-rep for a kidney (left) and the boundary points implied by its spoke ends (middle). Right: interpolated boundary mesh, from which surface rendering can be done.
Correspondence over deformation via figural correspondence. In each pair of marked points connected by lines, the two points have the same value of the figural coordinate .
M-reps for segmenting the male pelvis in CT images in later radiotherapy fractions. Top left: m-rep for pubic bones, used to register the later day fraction images with the first day fraction. Top right: the m-rep for the bladder, prostate and rectum. Bottom left: a visualization of the bladder, prostate rectum m-rep’s implied boundaries relative to a slice of the associated 3D CT image. Bottom middle and right: the segmentation result in a later fraction, shown in one of the image slices first vs the grey scale CT image and then vs the human segmentation shown in white.
Left: A subset of our population of training kidneys. Right: the mean of the population and the mean standard deviation in each of the first two principal geodesic modes.
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