Effects of the different steps involved in image thresholding for (a) model image consisting of bright sticks that model collagen fibers and 20% Gaussian noise, (f) an acquired collagen fiber image with low signal to noise ratio, and (k) an acquired collagen fiber image with high signal to noise ratio. Adaptive thresholding is performed on those images to achieve the corresponding fields shown on panels (b), (g), and (l). The results of eliminating any pixels that do not belong to a cluster of at least 15 interconnected “on” pixels is shown on panels (c), (h), and (m). Only panel (h) meets the requirements for further processing, which involves erosion and dilation (i) stretching, thresholding, and a final erosion and dilation step (j). The corresponding fiber densities are displayed at the bottom left corner of each panel. Scale
Schematic of the steps followed for the extraction of the OI for a model SHG image. Initially, the 2D Fourier transform of the image shown in panel (a) is calculated, as shown in (b). The coordinates of the Fourier image are transformed so that the spatial frequency is lowest at the origin and increases as we move toward the image edges (c). The frequency components along different orientations are represented by the amplitude along a specific angle from the horizontal (d). The information in each map can be compacted into a line plot of the spatial frequency averaged intensity as a function of the angle (e). From such plots the OI of each image is calculated.
OI and entropy distributions for model images consisting of sticks (collagen fibers) arranged in a (a) highly random or (d) aligned orientation. The corresponding spatially frequency averaged angular power spectral density distributions are shown in (b) and (e), while the probability distributions from the Hough-transform-based analysis are shown in (c) and (f). The distributions are broad and exhibit strong fluctuations for the randomly oriented sticks, while they consist of a well-defined peak in the highly aligned configuration. Scale represents .
Schematic of the steps followed for the extraction of the entropy for a model SHG image, included in (a). Initially, the image is segmented into tiles (b), so that each tile is likely to consist of a fairly linear segment of a collagen fiber (C is a magnified version of a single tile). The Hough transform is performed on each tile to determine the dominant direction of the collagen fiber segments present. If we consider two points in space, there is an infinite number of lines that go through these points represented by red and blue linear segments (panel D). All the lines intersecting point shown in blue are represented by a line (also shown in blue) in the space representing the slopes and intercepts of these lines (panel E). The lines intersecting the second point are represented by the red line. The point where the red and blue lines cross in panel E represents the intercept and slope of the line that connects the two points in space (shown in black in panel D). To avoid the need to include infinite slope numbers to represent vertical lines, we use a parametric description of a line through a point such that , where is the angle from the horizontal direction and represents the distance from the origin. So, the set of lines going through a point is represented by a curved line in space (panel F). The point where the two lines in F intersect represents the line connecting the two points in panel D. Thus, for each tile the points where most of the lines intersect represents the dominant direction of the lines present in the tile. This is represented by the red arrows in panel G. The probability of finding the dominant direction along a particular angle for a given tile of the image is shown in H. The entropy of this distribution is used a measure of local organization of the fibers.
Representative SHG images from gels with original collagen concentration of 1.0 (A–C), 2.0 (D–F), and 3.0 (G–I) mg/ml following 1 (A, D, G), 3 (B, E, H), and 14 (C, F, I) days upon the onset of gelation. The 2D PSD for each SHG image is shown as an inset. .
Representative area normalized distributions of determined from the 2D Fourier transform of the images are shown for day 1 (blue), 3 (red), and 14 (green) of observation from collagen gels with initial collagen concentration of (a) 1, (b) 2, and (c) 3 mg/ml. Note that the shape of these distributions does not change significantly over time.
Representative area normalized distributions of the probability that the dominant direction of the linear segments within each image tile is along a particular direction as assessed by the Hough transform. Data is shown for day 1 (blue), 3 (red), and 14 (green) of observation from collagen gels with initial collagen concentration of (a) 1, (b) 2, and (c) 3 mg/ml.
Representative SHG images from gels with 3 mg/ml original collagen concentration seeded with 70 000 fibroblasts following (a) 1, (b) 3, (c) 7, and (d) 12 days from the onset of gelation. A significant change in the appearance of the gels is seen on day 12. The corresponding 2D PSDs are included in the insets, demonstrating a noticeably more uniform distribution for the last day of measurements. Scale .
Representative area normalized distributions extracted from the 2D Fourier transform (a) and Hough transform (b) of SHG images acquired from gels seeded with 70 000 fibroblasts following 1 (blue), 3 (red), 7 (green), and 12 (brown) days from the onset of gelation. Note the change in distribution observed for the day 12 measurements.
Representative SHG images from gels with 3 mg/ml original collagen concentration seeded with 150 000 fibroblasts following (a) 1, (b) 3, (c) 7, and (d) 12 days from the onset of gelation. On days 1 and 3 the gels appear similar to the gels seeded with a lower concentration of fibroblasts for 12 days. The collagen fibers detected on days 7 and 12 appear significantly longer and better aligned than the previous time points. These likely represent fibers deposited by the fibroblasts. The corresponding 2D PSDs are included in the insets, demonstrating highly nonuniform distributions for the measurements acquired on days 7 and 12. Scale .
Representative area normalized distributions extracted from the 2D Fourier transform (a) and Hough transform (b) of SHG images acquired from gels seeded with 150 000 fibroblasts following 1 (blue), 3 (red), 7 (green), and 12 (brown) days from the onset of gelation. Note the substantial changes in the distributions observed for the measurements on days 7 and 12.
Quantitative assessment of collagen fiber content and organization in acellular collagen gels.
Quantitative assessment of collagen fiber content and organization in collagen gels containing a low concentration of fibroblasts.
Quantitative assessment of collagen fiber content and organization in collagen gels containing a high concentration of fibroblasts.
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