Rapid quantification of pixel-wise fiber orientation data in micrographs

Abstract

Defining fiber orientation at each pixel within a medical image has traditionally been computationally intensive and prone to systematic errors. A weighted orientation vector summation algorithm capable of detecting fiber orientation simultaneously at each pixel within an image is presented. As a result, pixel-specific fiber orientation information with 2 deg to 3 deg accuracy can be determined within seconds, enabling the practical use of pixel-wise orientation data for characterizing structural anisotropy. This analysis technique has applicability and potential diagnostic utility for a variety of modalities, including second harmonic generation, scanning electron microscopy and immunohistochemical imaging is demonstrated.

Fig. 1

Summary of vector summation technique for pixel-wise fiber orientation measurements. The vector lengths in (b) and (c) represent the relative weighting factors for each orientation. The average vector orientation corresponds to the direction with the lowest variation in pixel intensity values ($a_i$).

Fig. 2

Error in fiber orientation measurements with respect to fiber thickness and window size used for the vector summation measurements. Beyond a thickness of 5 pixels, error in fiber orientation measurements began increasing exponentially when fiber thickness increased beyond the window size used for detection. Standard deviation of the average difference in angles was on the same order of magnitude as the mean value, but is not plotted in the graph in order to aid in viewing the overall effects of thickness and window size.

Fig. 3

Error in orientation detection using the vector summation method for a simulated image containing regions with diverging orientations. (a) The average absolute value of the difference between measured and actual pixel-wise orientations noticeably decreases with increasing window sizes of $3\times 3$ to $11\times 11$ using a simulated image (b) of circles at different locations, diameters, and thicknesses. (c) With increasing window size, error initially decreases and then becomes localized to regions where fibers are in close proximity to each other. (d) A magnified view of the error in the area indicated by red outline in (b) demonstrates an increase in error between $11\times 11$ and $25\times 25\text{\hspace{0.17em}\hspace{0.17em}pixel}$ windows for specific regions with multiple nearby fibers.

Fig. 4

Comparison of the computational times for a pixel-wise Fourier detection of fiber orientation and the vector summation approach. (a) The vector summation approach ranges from 5.25-fold faster for a 0.01 megapixel image to 10.34-fold faster for a 5 megapixel image compared to Fourier approaches for a range of image sizes using an $11\times 11$ window size. (b) Smaller window sizes produce a more pronounced difference in the computational time of the two methods. Using a $960\times 960$ image, computational time of the vector summation method was 74.4-fold faster using a $3\times 3$ window, but reduced to a 3.2-fold difference using a $25\times 25$ window.

Fig. 5

Fiber orientation detection via vector summation performed on (a) fluorescence microscopy image of DRG neurites, (b) scanning electron microscopy image of silk fibers, (c) second harmonic generation image of collagen in engineered bone, (d) picosirius red stained collagen fibers surrounding MCF10A cells (reproduced with permission²⁴). For the orientation maps in the middle row, pixel-wise fiber angle measurements were color coded to the HSV color map in MATLAB, and these color maps were then multiplied by the grayscale intensity image to produce a final image.