【ShapeWorks】2. 工作流的三板斧 - How to Groom Your Dataset?

No.	Content
1	【ShapeWorks】1. 软件介绍及安装
2	【ShapeWorks】2. 工作流的三板斧 - How to Groom Your Dataset?
3	【ShapeWorks】3. 工作流的三板斧 - How to Optimize Your Shape Model?
4	【ShapeWorks】4. 工作流的三板斧 - How to Analyze Your Shape Model?
5	【ShapeWorks】5. 典型例子 Ellipsoid 的运行及解析

ShapeWorks needs suitable distance transforms or meshes for establishing shape correspondence. The groom stage has the pipeline to generate aligned distance transforms from binary segmentations or groomed meshes from unaligned meshes. Common grooming steps are outlined below. For descriptions of the ShapeWorks commands used, see: ShapeWorks Commands.

1. Common Pre-Processing Steps for Segmentations

1. Resampling images and segmentations

This grooming step resamples all the binary volumes, whch in a raw setting could be in different physical spaces (different dimensions and voxel sapcing). This grooming step brings all segmentations to the same voxel spacing, typically isotropic spacing (e.g., 1,1,1).

A smaller voxel spacing than the original spacing improves the resolution of the sementations and reduces the aliasing (i.e., staircase) artifact resulting from the thresholding/binarization process.

Resampling both images and segmentations
If your dataset contains both images (e.g., CTs, MRIs) and binary segmentations, it is recommended that resampling is performed on both to keep them aligned for subsequent analyses that might entail/need imaging data.

Since image resampling entails interpolation, directly resampling binary segmentations will not result in a binary segmentation, but rather an interpolated version that does not have two distinct labels (i.e., foreground and background).

To mitigate this behavior, we need first to convert the binary segmentations (with zero-one voxels) to a continuous-valued (gray-scale) image. This can be done by either anti-aliasing the segmentations, which smooths the foreground-background interface, or converting a segmentation to a signed distance transform, where each voxel encodes the physical distance to the closest surface point (zero-one interface) with the sign indicating whether the voxel is inside or outside the foreground region.

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Here is a resampling pipeline example for binary segmentation that uses anti-aliasing:

• antialias the binary segmentation to convert it to a smooth continuous-valued image
• resample the antialiased image using the same (and possible smaller) voxel spacing for all dimensions
• binarize (aka thersholding) the resampled image to results in a binary segmentation with the desired voxel spacing

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Here is an example of resamping an ellipsoid with spacing (1,1,2) to have spacing (1,1,1):

antialias_iterations = 30
shape_seg            = sw.Image(in_shape_filename)

shape_seg.antialias(antialias_iterations)
shape_seg.resample([1,1,1], sw.InterpolationType.Linear)
shape_seg.binarize().write(out_shape_filename)

Resampling image
Images are already given as a continued-valued grid of pixels. Hence, images can be directly resampled without any pre- or post-processing steps.

Resampling images reduces pixelation and smooths out intensity noise.

Resampling segmentations smooths out shape boundaries and reduces binarization aliasing.

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2. Aligning segmentations

Rigidly aligning a cohort of shapes entail removing differences across these shapes pertaining to global transformations, i.e., translation and rotation. This step requires a reference coordinate frame to align all shapes to, where one of the shapes can be selected as a reference.

Rigid alignment (aka registration) is an optimization process that might get stuck in a bad local minima if shapes are significantly out of alignment. To bring shapes closer, we can remove translation differences using center-of-mass alignment. This factors out translations to reduce the risk of misalignment and allow for a medoid sample to be automatically selected as the reference for subsequent rigid alignment.

Applying transformation segmentations
Applying a transformation to segmentations entails interpolation due to image resampling in the new coordinate frame. Similar to the resampling workflow, we will first anti-alias the segmentation to convert it to a continuous-valued image with a smooth foreground-background interface, then apply the transformation, and finally binarize the tranformed image.

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Hence, the shapes alignment pipeline includes the following steps:

• Center-of-mass alignment for segmentations:
  – antialias the binary segmentation to convert it to a smooth continuous-valued image
  – translate the binary segmentation so that the center of the image doamin is the center of mass of the shape.
  – binarize (aka thresholding) to get a binary segmentation

• recenter moves the center of the image (which is now the center of mass) to (0,0,0)

• Reference shape selection: One option for a reference is to select the shape that is closest to all other samples in the given cohort, i.e., the medoid shape. If shape instances are misaligned (i.e., do not share the same coordinate frame), translational and rotational differences should be factored out before reference selection.
  – Use the pymodule function find_reference_image_index that perform pairwise rigid registration using the iterative closest point method and selects the sample that is closest to all other samples after factoring out global transformation differences.

• Rigid alignment:
  – antialias the binary segmentation and reference to convert them to a smooth continuous-valued image
  – createTransform: compute the rigid transformation parameters that would align a segmentation to the reference shape
  – applyTransform: apply the rigid transformation to the segmentation and make it have the same cooridnate system as the reference
  – binarize (aka thresholding) to get a binary segmentation

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Here is an example of performing center of mass alignment on one ellipsoid:

shape_seg            = sw.Image(in_shape_filename)
antialias_iterations = 30
translation_vector   =  shape_seg.center() - shape_seg.centerOfMass() 

shape_seg.antialias(antialias_iterations)
         .translate(translation_vector)
         .binarize().recenter()
         .write(out_shape_filename)

3. Clip segmentations

In some cases, binary segmentations need to be clipped with a cutting plane so that only the desired part of the shape is reflected in the shape model. To perform this step, you can use clip defined the cutting plane defined using three points.

4. Cropping and padding segmentations

In many cases, image boundaries are not tight around shapes. This leaves too much irrelevant background voxels that might increase the memory footprint when optimizing the shape model. We can remove this irrelevant background while keeping our segmentations intact and avoid cropped segmentations to touch image boundaries, which results in artifical holes in the shape boundary and does not allow particles to be distributed in regions touching the image boundary.

5. Converting segmentations to smooth signed distance transforms

For numerical computations for correspondences optimization, we need to convert binary segmentations to a continuous-valued image that satisfies the following requirements.

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2. Common Pre-Processing Steps for Meshes

1. Reflect meshes

It is common in medical imaging data to have a left and right anatomy. To align and model all such shapes, we must reflect some meshes so that all are oriented the same.

• reflect: reflects the mesh across the given axis (typically x-axis for anatomy)

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Here is an example of reflecting a mesh:

shape_mesh = sw.Mesh(in_mesh_filename)
shape_mesh.reflect(sw.X).write(out_mesh_filename)

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2. Meshes to volumes

Meshes can be converted to binary segmentations if desired so that grooming can be done on segmentations and optimization on distance transforms.

The steps to convert meshes to volumes are:

• toImage convert the mesh to a signed distance transform
• binarize (aka thresholding) to get a binary segmentation

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Example of turning a mesh to a segmentation:

shape_mesh = sw.Mesh(in_mesh_filename)
shape_seg  = shape_mesh.toImage()
                       .binarize()
                       .write(out_shape_filename)

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For list of commands, check out ShapeWorks Commands

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3. Remesh

Remeshing creates meshes with evenly spaced vertices. - remeshPercent remeshes the mesh to have a given percent of the current number of vertices

mesh.remeshPercent(percentage=0.80, adaptivity=1.0)

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4. Aligning meshes

Rigidly aligning a cohort of shapes entails removing differences across these shapes pertaining to global transformations, i.e., translation and rotation. This step requires a reference coordinate frame to align all shapes to, where one of the shapes can selected as a reference.

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5. Extract Shared Boundary

In this step, we ingest the two original shapes and the output consists of three new shapes, two of which correspond to the original shapes and one for the shared boundary. Let us designate the original meshes as Lo and Ro. Then:

1. Find all the triangles in Lo that are close to Ro, and construct a mesh with these triangles called Ls. A triangle with vertices $v_0$, $v_1$ and $v_2$ is considered close to a mesh if the shortest euclidean distance to the mesh for all the three vertices is below a small threshold. We similarly find all the triangles in Ro that are close to Lo and designate this mesh as Rs.
2. Find the remainder of the mesh in Lo after removing the triangles in Ls and designate this as Lr.
3. Arbitrary desiged Rs as the shared surface M.
4. Snap all the points on the boundary loop of Lr to the boundary loop of M.
5. Return three new shapes Lr, M and Rr.

extracted_l, extracted_r, extracted_s = sw.MeshUtils.shareBoundaryExtractor(mesh_l, mesh_r, tol)

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• Input shapes with shared surface
  

• Output extracted surfaces

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6. Extract Contour

The boundary loop of the shared surface M obtained using the sharedBoundaryExtractor is computed.

output_contor = sw.MeshUtils.boundaryLoopExtractor(extracted_shared_meshes)

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7. Smoothing

Laplacian Smoothing allows you to reduce noise on a mesh’s surface with minimal changes to its shape. The effect is to “relax” the mesh, making the cells better shaped and the vertices more evenly distribued.

mesh.smooth(iterations, relaxation)

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Ref

1. How to Groom Your Dataset?