Fig 1.
Overview of the SLAVV approach.
The purpose of SLAVV is to vectorize vascular objects from raw three dimensional images. The first step of the method is to linearly filter the input image to form “energy” and “size” images, which enhance vessel centerlines and estimate vessel sizes, respectively. Next, vertices along the blood vessels are extracted as local minima of the three-dimensional energy image. Vertices are then connected by edges, which follow minimal energy trajectories. Finally, a graph theoretic representation of the vascular network is generated from the vertices and edges.
Fig 2.
Example projections of original two-photon images, intermediate outputs, and vector renderings of manually assisted SLAVV applied to Image 2.
The green chevron is directly underneath a medium sized vessel which bleeds into the original projection volume for the plasma-labeled Image 2 but not the endothelial-labeled Image 1. A. Either Image 1 or 2 could be the input (Image 2 outputs shown here, Image 1 outputs are similar (S1 Fig). The original image is subject to multiscale, LoG, matched filtering to obtain three-dimensional energy and size images. The energy image is used to estimate vertex centers and the size image to estimate their radii. Vertices are used as genesis and terminus points for energy image exploration in the centerline extraction algorithm. Finally, estimated vessel radii are recalled from the size image to form the volume-filled vector rendering. Gray-scale coloring in the vector renderings corresponds to the energy values and thus vector probabilities. B. Three-dimensional visual output of SLAVV. Colors represent strands, which are defined as non-bifurcating vessel segments. Each strand is assigned a random color. The image is 125 μm in z and 460 in x and y. The projection volume used in the other panels is shown as a gray box in the center of the larger volume. The blue chevron marks the vessel that bleeds into Image 2 at the green chevron. C. Depth and direction outputs from SLAVV. Vector volumes are rendered over the original projection at a quarter of their original radius to facilitate the visualization of the underlying vessels. Direction is calculated by spatial difference quotient with respect to edge trajectory. The centerline for the vessel above the green chevron lies above the projection volume.
Table 1.
Runtimes of automated processing steps in seconds.
Processing computer specifications: Intel Xeon CPU E5–2687 v3 @3.10 GHz, 32 GB RAM, 64-bit operating system, and 10 independent cores for parallel processing.
Table 2.
Bulk network statistics of interest.
Table 3.
Summary of human effort toward manual vector classification on the graphical curator interface in the demonstration of SLAVV.
Selections were point-and-click classifications of objects either individually or over a rectangular volume.
Fig 3.
Example statistics of the microvasculature calculated from manually assisted SLAVV applied to Image 3.
A. Three-dimensional rendering of strand objects similar to Fig 2B. Size of the image is 600 μm in z, 1350 in x, and 940 y. Projection of the first 70 μm of the original image is shown with the same perspective. B. Cartoon depiction of consecutive cylinder representation of a vessel segment used in calculations. C. Histograms of depth, radius, and inclination (angle from the xy plane). The large peak in the inclination histogram at horizontal alignment is due to low axial resolution (5 μm). Contributions of cylinders to the bins are weighted by their lateral areas. D. Depth-resolved anatomical statistics output from SLAVV. Cylinders are binned by depth. Their heights, lateral areas, and volumes are summed and divided by the image volume apportioned to each bin to yield length, area, and volume densities of vasculature. Average radius and inclination in each depth bin are lateral area-weighted averages.
Fig 4.
Objective performance of fully-automated SLAVV software.
A. Simulated images of varying quality are generated from the vector set from Image 3 shown in Fig 3. Image quality is swept along contrast and noise axes, independently. Example maximum intensity projections are shown for three extremes of image quality (triangle: best quality, 4-point star: high noise, 5-point star: lowest contrast). The legend shows the labels for the four segmentation methods used in B-D. Images are vectorized using SLAVV with different amounts of Gaussian filter, fG (60, 80, or 100% of matched filter length). B. Vasculature is segmented from three simulated images using four automated approaches: thresholding either voxel intensity or maximum energy feature on edge objects produced by three automated vectorizations. Voxel-by-voxel classification strengths of thresholded vectorized objects or voxel intensities are shown as ROC curves for three of the seven input images. Note that the ROC curves for the energy feature of vectors do not have support for every voxel, because not every voxel is contained in an extracted vector volume. Operating points with maximal classification accuracy are indicated by circles in the bottom row of B and plotted in the top row of C&D across all input images. C&D. Bulk network statistics (length, area, volume, and number of bifurcations) were extracted from vectors or binary images resulting from maximal accuracy operating points. Performance metrics were plotted against CNR (image quality) for a (C) contrast or (D) noise sweep. Thresholding vectorized objects to segment vasculature demonstrated a greater robustness to image quality than thresholding voxel intensities. Surface area, length, and number of bifurcations were not extracted from binary images, because these images were topologically very inaccurate.
Table 4.
Descriptions of 2PM input images used in SLAVV demonstration.
Note that the endothelium (vessel wall) was labeled in Image 1.
Fig 5.
One-dimensional simplification of linear filtering step.
To form the energy image E at scales 1…n…N, the original image I(x) is convolved with a LoG filter and an Ideal kernel. The Ideal kernel is a linear combination of spherical and annular pulses to match the fluorescent signal shape of vessels. σ2 is the variance of the Gaussian, r is the radius of the Ideal kernel, so R2 = σ2 + r2 is the square “radius” of the LoG, matched filter. The resulting multiscale energy image is projected along the scale coordinate to form two three-dimensional images that depict energy and size (not shown here, example in Fig 2. In this example, the kernel weighting factor was chosen so that the sums of all the spherical and annular kernels were all equal, the ratio r/σ was chosen to be 1, and a vertex was found at location v with radius Rn and energy En(v).
Table 5.
Processing parameters used to vectorize the three experimental images and the set of synthetic images derived from Image 3.
The smallest and largest radii delimit the range of the characteristic radii of the convolutional matching kernels used, and the “scales per octave” parameter determined the sampling density in the scale coordinate.