High-resolution images based on directional fusion of gradient

10.1007/s41095-016-0036-6.F1 Fig. 1Constructing surface.

10.1007/s41095-016-0036-6.F2 Fig. 2Flowchart of the method.

10.1007/s41095-016-0036-6.F3 Fig. 3Diffusion of gradient. The blue dots $P_{x,y}$ stand for neighboring HR pixels of $P_{i,j}$ , and the blue arrow represents the gradient direction at $P_{x,y}$ , while the red arrow indicates the gradient direction at $P_{i,j}$ . ${\beta }_{xy}$ is the angle between the gradient directions $P_{i,j}$ and $P_{x,y}$ . The dashed area defines the range of angles for which the gradient direction of $P_{x,y}$ is positively correlated with that of $P_{i,j}$ .

10.1007/s41095-016-0036-6.F4 Fig. 4Degradation mode. (a) Pixels of LR image. (b) Pixels of HR image. The solid black dots in (a) represent pixels of the LR image. The dots in (b) are pixels of the HR image, where the black dots are the known pixels of HR image $I{(2n-1,2m-1)}_{\text{H}}$ that are directly determined by the corresponding LR image pixels, blue dots stand for the case where $I{(2n,2m)}_{\text{H}}$ , while the pink points represent the cases where $I{(2n-1,2m)}_{\text{H}}$ or $I{(2n,2m-1)}_{\text{H}}$ .

10.1007/s41095-016-0036-6.F5 Fig. 5Three cases for constructing the linear surface $f_{i,j}^{\text{H}}$ . (a) represents the linear surface constructed in $Step2$ . (b) and (c) represent the linear surface constructed in $Step3$ . In the figure, black dots give known pixels of the HR image from the corresponding LR pixels, and the blue dots stand for unknown HR pixels calculated in $Step2$ .

10.1007/s41095-016-0036-6.F6 Fig. 6Weighting. (a) represents the case of what is solved in $Step\mathrm{\hspace{0.25em}2}$ . (b) and (c) are the two situations to be determined in $Step\mathrm{\hspace{0.25em}3}$ using the results of $Step\mathrm{\hspace{0.25em}2}$ . The black dots are known pixels of the HR image, and the blue dots are the unknown HR pixels. $P_{x,y}$ stands for the neighboring pixels of $P_{i,j}$ . $\stackrel{\to }{CG}$ is the gradient direction at the center pixel $P_{i,j}$ .

10.1007/s41095-016-0036-6.F7 Fig. 7Results of magnifying the boat image: (a) ground truth; (b) Bicubic; (c) CSF; (d) NEDI; (e) GGI; (f) ours.

10.1007/s41095-016-0036-6.F8 Fig. 8Results of magnifying the baboon image: (a) ground truth; (b) Bicubic; (c) CSF; (d) NEDI; (e) GGI; (f) ours.

10.1007/s41095-016-0036-6.F9 Fig. 9Enlarged image of a brain. (A) and (B) are segmented brain images produced by MICO. Images (a), (b), and (c) are results of enlarging a specified area of (A). Images (d), (e), and (f) are the results of enlarging a specified area of (B).

10.1007/s41095-016-0036-6.F10 Fig. 10Magnification of vertical edges: (a) original image and gray value; (b) ours; (c) Bicubic; (d) CSF; (e) NEDI; (f) GGI.

10.1007/s41095-016-0036-6.F11 Fig. 11Magnification of horizontal edges: (a) original image and gray value; (b) ours; (c) Bicubic; (d) CSF; (e) NEDI; (f) GGI.

10.1007/s41095-016-0036-6.F12 Fig. 12Magnification of diagonal edges: (a) original image and gray value; (b) ours; (c) Bicubic; (d) CSF; (e) NEDI; (f) GGI.

10.1007/s41095-016-0036-6.F13 Fig. 13Test images. Top row, left to right: cameraman, baboon, boat, goldhill, lake. Bottom row: peppers, couple, Lena, crowd, medical.