Fig 1.
Illustration of the datasets that will be used to compare the tracing algorithms. (a) Second Harmonic Generation Collagen (SHG). (b) Fluorescent Fibronectin (FF). (c) Breast Cancer Biopsy slide (BCB). (d) Disease Mimicking Extra Cellular Matrix (DME). (e-h) Regions of interest (ROI) of the images in (a-d). (i-l) Manually delineated ground truth (GT) for the ROIs of images in (e-h). White lines correspond to the GT and intensities are displayed in a colormap with hot colours (black-red-orange-yellow-white).
Fig 2.
Illustration of the U-Net architecture used to segment the fibres. The architecture consists of three encoder levels and 3 decoder levels.
Fig 3.
Illustration of the data augmentation approaches used to train the U-Net. (a) Original patch (b) Horizontally flipped (c) Vertically flipped (d) Rotation by 90 degrees (e) Gaussian blurred, with zero mean and a standard deviation of 0.05. (f–j) labels corresponding to augmented patches. It should be noted that (j) is the same as (f) as the Gaussian blur does not affect the label.
Fig 4.
Illustration of the Trace Ridges methodology. (a) Region of interest of one SHG image that shows some strong ridges and a region with some noise highlighted with a green rectangle. (b) Output of a Watershed transform, which traces the strong ridges but also some smaller ones that are not of interest. (c) Edges detected with Canny’s algorithm highlight the sides of the strong ridges. (d) The combination of Edge Detection (red lines) with Watershed (yellow lines). White pixels correspond to the overlap of both techniques. The watershed will be broken by removing these overlapping pixels.
Fig 5.
Illustration of three cases of two lines where the pixel-wise metrics of true positives, true negatives, false positives, false negatives are identical, yet the distance between the lines is different.
Fig 6.
Illustration of the distance error measurement between the two lines of (Fig 5c). (a, d) Two lines that overlap only at a single point. (b) Distance map computed from the red line in (a). Distances follow a hot colour map: black-red-orange-yellow-white. (c) Product of the distance map shown in (e) with the line shown in (a). (e) Distance map computed from the yellow line in (d). (f) Product of the distance map shown in (b) with the yellow line shown in (d).
Fig 7.
Illustration of the calculation of the error distance maps on the Second Harmonic Generation image shown in (Fig 1a). (a) One representative image with a variety of fibres. (b) Distance map calculated from the traces calculated with Trace Ridges. (c) Product of the ground truth and the distance map of (b). (d) Comparison between the results of Trace Ridges and the ground truth. White lines indicate pixels from GT and trace. Blue lines correspond to Trace Ridges. Red lines are from the GT. (e) Distance map calculated from the ground truth. (f) Product of the traces from Trace Ridges and the distance map of (e). It should be noticed how the cases where the lines overlap (white) in (d) do not appear in any of the distance maps (c, f) whilst the lines that do not overlap (blue and red) appear in the distance maps with increased brightness as they are further away from the lines generated by the opposite method.
Table 1.
Quantitative Comparison by total error distance in pixels of the following Tracing methods: Edge Detection (ED), CT Fire (CTF), Scale Space (SS), Twombli (TW), U-Net, Graph based (GB) and Trace Ridges (TR), with three filtering options on the following images: Disease Mimicking ECM (DME), Second Harmonic (SHG), Fluorescent Fibronectin (FF) and Breast Cancer Biopsy (BCB) images. In addition to the errors per image, average per filtering option, average of the methodology and rank are presented. Results are sorted by rank with the worst results at the top (7) and best results at the bottom (1).
Table 2.
Quantitative Comparison by average error distance in pixels of the following Tracing algorithms; Edge Detection (ED), CT Fire (CTF), Scale Space (SS), Twombli (TW), U-Net, Graph based (GB) and Trace Ridges (TR) with three filtering options on Disease Mimicking ECM (DME), Second Harmonic (SHG), Fluorescent Fibronectin (FF) and Breast Cancer Biopsy (BCB) images. In addition to errors per image, average per filtering option, average of the methodology and rank are presented. Results are sorted by rank with the worst results at the top (7) and best results at the bottom (1).
Table 3.
Quantitative Comparison by maximum error distance in pixels of the following Tracing algorithms; Edge Detection (ED), CT Fire (CTF), Scale Space (SS), Twombli (TW), U-Net, Graph based (GB) and Trace Ridges (TR) with three filtering options on Disease Mimicking ECM (DME), Second Harmonic (SHG), Fluorescent Fibronectin (FF) and Breast Cancer Biopsy (BCB) images. In addition to errors per image, average per filtering option, average of the methodology and rank are presented. Results are sorted by rank with the worst results at the top (7) and the best results at the bottom (1).
Table 4.
Quantitative Comparison by time taken in seconds of the following Tracing algorithms; Edge Detection (ED), CT Fire (CTF), Scale Space (SS), Twombli (TW), U-Net, Graph based (GB) and Trace Ridges (TR) with three filtering options on Disease Mimicking ECM (DME), Second Harmonic (SHG), Fluorescent Fibronectin (FF) and Breast Cancer Biopsy (BCB) images. In addition to time taken per image, average per filtering option, average of the methodology and rank are presented. Results are sorted by rank with the worst results at the top (7) and the best results at the bottom (1).
Fig 8.
Comparison of tracing algorithms on SHG image (full view) [40]. Image was applied to algorithms with three different filters: Original/no filtering, Gaussian and DnCnn. Data corresponds to the tracing images; GT is the manually delineated ground truth. For the evaluation of Tracing Algorithms, the GT fibres are represented in red, algorithm tracing is depicted in blue and areas where they overlap is white.
Fig 9.
Comparison of tracing algorithms on FF image (full view). Image was applied to algorithms with three different filters: Original/no filtering, Gaussian and DnCnn. Data corresponds to the images traced; GT is the manually delineated ground truth. For the evaluation of Tracing Algorithms, the GT fibres are represented in red, algorithm tracing is depicted in blue and areas where they overlap is white.
Fig 10.
Comparison of tracing algorithms on Picrosirius red Breast Cancer Biopsy image (full view) [38]. Image was applied to algorithms with three different filters: Original/no filtering, Gaussian and DnCnn. Data corresponds to the images traced; GT is the manually delineated ground truth. For the evaluation of Tracing Algorithms, the GT fibres are represented in red, algorithm tracing is depicted in blue and areas where they overlap is white.
Fig 11.
Comparison of tracing algorithms on DME image (full view) [42]. Image was applied to algorithms with three different filters: Original/no filtering, Gaussian and DnCnn. Data corresponds to images traced; GT is the manually delineated ground truth. For the evaluation of Tracing Algorithms, the GT fibres are represented in red, algorithm tracing is depicted in blue and areas where they overlap is white.
Fig 12.
Comparison of tracing algorithms on SHG image (region of interest) [40]. Image was applied to algorithms with three different filters: Original/no filtering, Gaussian and DnCnn. Data corresponds to the images traced; GT is the manually delineated ground truth. For the evaluation of Tracing Algorithms, the GT fibres are represented in red, algorithm tracing is depicted in blue and areas where they overlap is white.
Fig 13.
Comparison of tracing algorithms on FF image (region of interest). Image was applied to algorithms with three different filters: Original/no filtering, Gaussian and DnCnn. Data corresponds to images traced; GT is the manually delineated ground truth. For the evaluation of Tracing Algorithms, the GT fibres are represented in red, algorithm tracing is depicted in blue and areas where they overlap is white.
Fig 14.
Comparison of tracing algorithms on Picrosirius red Breast Cancer Biopsy image (region of interest) [38]. Image was applied to algorithms with three different filters: Original/no filtering, Gaussian and DnCnn. Data corresponds to images traced; GT is the manually delineated ground truth. For the evaluation of Tracing Algorithms, the GT fibres are represented in red, algorithm tracing is depicted in blue and areas where they overlap is white.
Fig 15.
Comparison of tracing algorithms on DME image (region of interest) [42]. Image was applied to algorithms with three different filters: Original/no filtering, Gaussian and DnCnn. Data corresponds to images traced; GT is the manually delineated ground truth. For the evaluation of Tracing Algorithms, the GT fibres are represented in red, algorithm tracing is depicted in blue and areas where they overlap is white.