Fig. 1. Diagram of LBP principles. (a) Encoding process of original LBP: (a1) grayscale image; (a2) gray value of a 3×3 neighborhood in the grayscale image; (a3) binary thresholding result of the neighboring pixels; (a4) corresponding weight of each pixel position; (a5) LBP value of the central pixel; (a6) LBP feature mapping image of the grayscale image. (b) Circular neighborhood corresponding to different values of P and R. (c) ULBP patterns including two 0/1 transitions and two special cases in LBP.

Fig. 2. Schematic diagram of CFFPM method. (a), (b) LR full-color donor and HR grayscale acceptor image. (a1)–(a4) ULBP feature mapping; L, a, and b channel images of a typical tile in the donor image. (b1), (b2) ULBP feature mapping and L channel image of the corresponding tile in the acceptor image; (b3), (b4) color transfer results of a and b channels for the tile calculated by the trilateral filtering algorithm. (c) Reconstruction result of the typical tile and whole image with CFFPM method. (d) Replacing green channel of whole image with CFFPM method. Dashed and solid boxes in (a)–(d) represent the block processing strategy. First, obtain the gray similarity factor Gs, spatial proximity factor Gr, and feature similarity factor Gt contained in the color transfer probability function GσCT. Second, find the point in the color image with the highest color similarity with the grayscale image. Finally, transfer colors to grayscale images through Lab space. Each iteration replaces the green channel of the CFFPM reconstructed image with the HR grayscale receptor image; convert it to gray scale and continue to the next iteration. See the video of Visualization 1 for detailed process.

Fig. 3. Detailed settings of CFFPM parameters. (a1) LR color image and magnified image for the part of interest; (a2) CFFPM reconstructed image with feature similarity factor; (a3) CFFPM reconstructed image with gray similarity factor and gray similarity factor; (a4) CFFPM reconstructed image. (b1) LR grayscale image within the filter range; (b2) LBP feature mapping of LR color image within the filter range. (c1) HR grayscale image within the filter range; (c2) LBP feature mapping of HR grayscale image within the filter range. (d1)–(d4) Visualization diagrams of Gs, Gr, Gt, and GσCT; (d5) typical spatial proximity factor.

Fig. 4. Experimental results of stained resting sporangia. (a) LR color image with the entire FOV of a 4×/0.1  NA objective; (b) FPM grayscale reconstructed image under green channel (515.0 nm); (c) ground truth with the entire FOV of a 10×/0.3  NA objective. (a1) Magnified image of the specific area in (a); (b1) magnified image of the specific area in (b); (c1) magnified image of the specific area in (c). (d) Staining image via conventional R/G/B method; (e) staining image via multiplexing method; (f) staining image via CFPM; (g) staining image via CFFPM. RMSE, IHCS, and runtime values are marked below the corresponding image.

Fig. 5. Experimental results of stained emphysema. (a) LR color image with the entire FOV of a 4×/0.1  NA objective; (b) FPM grayscale reconstructed image under green channel (515.0 nm); (c) ground truth with the entire FOV of a 10×/0.3  NA objective. (a1) Magnified image of the specific area in (a); (b1) magnified image of the specific area in (b); (c1) magnified image of the specific area in (c). (d) Staining image via conventional R/G/B method; (e) staining image via multiplexing method; (f) staining image via CFPM; (g) staining image via CFFPM. RMSE, IHCS, and runtime values are marked below the corresponding image.

Fig. 6. Curves of RMSE value with the number of iterations in CFFPM method for (a) stained resting sporangia sample in Fig. 4 and (b) stained emphysema sample in Fig. 5. The dotted lines represent the RMSE value of the conventional R/G/B sequential method.

Fig. 7. Statistical comparison results of four colorization methods. (a) RMSE curves of three methods for 26 tested samples at a statistical level. (b1), (c1) Respective ground truth of the No. 3 and No. 14 stained biological samples. (b2), (c2); (b3), (c3); (b4), (c4); (b5), (c5) Respective reconstructed results obtained by conventional R/G/B method, multiplexing method, CFPM, and CFFPM. RMSE values are marked below the corresponding results.

Fig. 8. Block size and overlapping rate. (a1) Effects of filter size and sliding step size on stained resting sporangia; (a2) effects of σr/σs and σt/σs on stained resting sporangia; (b1) effects of filter size and sliding step size on stained emphysema; (b2) effects of σr/σs and σt/σs on stained emphysema.