Resizing an image
The invention notably relates to computer-implemented method for resizing an image I. The method comprises the steps of: providing the image I to resize; and providing an image significance by computing a significance of each pixel in the image to resize. An original spatial domain (Ω) of the significance image is extracted. A transformation T θ , parameterized as an interpolating spline by a set of control points, is provided from Ω to a resized spatial domain Ω′; subdividing Ω into cells, each cell being defined by a subset of control points of the set. For each cell, a weighted average of the significance of the pixels in the cell is computed, the weighted average being computed using the interpolating spline. The cells of Ω are deformed by displacing one or more control points of the cells having a lesser weighted average. The transformation T θ over a spatial domain of the image I is computed using the displaced one or more control points. A resized image J is computed by applying the computed transformation T θ to the spatial domain of the image I to resize.
1. A computer-implemented method for resizing an image I, the method comprising the steps of:
providing (S 10 ) the image I to resize;
providing an image significance (S 20 ) by computing a significance of each pixel in the image to resize;
extracting (S 30 ) an original spatial domain (Ω) of the significance image;
providing (S 40 ) a transformation T θ , parameterized as an interpolating spline by a set of control points, from the original spatial domain (Ω) to a resized spatial domain (Ω′);
subdividing (S 50 ) the original spatial domain (Ω) into cells, each cell being defined by a subset of control points of the set;
computing (S 60 ), for each cell, a weighted average of the significance of the pixels in the cell, the weighted average being computed using the interpolating spline;
deforming (S 70 ) the cells of the original spatial domain (Ω) by displacing one or more control points of the cells having a lesser weighted average;
computing (S 80 ) the transformation T θ over a spatial domain of the image I using the displaced one or more control points; and
computing (S 90 ) a resized image J by applying the computed transformation T θ to the spatial domain of the image I to resize.
2. The computer-implemented method of claim 1 , wherein the provided transformation T θ is a diffeomorphic transformation T θ such that J(x)=I(T θ −1 (x)), wherein 1 is the image to be resized, J is the resized image, x is the position of a given pixel in the original spatial domain (Ω).
3. The computer-implemented method of claim 2 , wherein the diffeomorphic transformation T θ is defined by the equation T θ =x+u θ (x), wherein x is the position of a given pixel in the original spatial domain (Ω), and u θ (x) is a displacement function wherein u is a mapping from the original spatial domain (Ω) to the resized spatial domain (Ω′).
4. The computer-implemented method of claim 3 , wherein the transformation T θ is parameterized as a free form deformation interpolating spline, and wherein displacement function u θ (x) is defined by the equation
u
θ
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k
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wherein B 0 , B 1 , B 2 , B 3 are Cubic B-splines functions, θ is a function representing the control points, s w is the spacing between two control points in an horizontal direction, s h is the spacing between two control points in a vertical direction, x w is the position of a pixel in the original spatial domain (Ω) on an horizontal axis, x h is the position of a pixel in the original spatial domain (Ω) on a vertical axis.
5. The computer-implemented method of claim 4 , wherein the set of control points form a grid and θ is the function representing the grid of control points.
6. The computer-implemented method of claim 4 , wherein the step of computing, for each cell, a weighted average of the significance of the pixels in the cell is carried out with the function
SI
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S
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wherein Ω (i,j) is a partition of the original spatial domain (Ω), S(x) represents the provided significance image.
7. The computer-implemented method of claim 6 , wherein the partition Ω (i,j) is the domain covered by the cells.
8. The computer-implemented method of claim 1 , wherein the original spatial domain (Ω) extracted from the significance image is the same as the spatial domain (Ω) of the image I to resize.
9. The computer-implemented method of claim 1 , wherein the step of computing a resized image J comprises reducing or increasing the image size.
10. A computer program product comprising:
a non-transitory computer readable storage medium having thereon a computer program for resizing an image I; and
computer instructions embodied on the computer readable storage medium supporting execution of the computer program by a processor and causing the processor to:
provide the image I to resize;
provide an image significance by computing a significance of each pixel in the image to resize;
extract an original spatial domain (Ω) of the significance image;
provide a transformation T θ , parameterized as an interpolating spline by a set of control points, from the original spatial domain (Ω) to a resized spatial domain (Ω′);
subdivide the original spatial domain (Ω) into cells, each cell being defined by a subset of control points of the set;
compute, for each cell, a weighted average of the significance of the pixels in the cell, the weighted average being computed using the interpolating spline;
deform the cells of the original spatial domain (Ω) by displacing one or more control points of the cells having a lesser weighted average;
compute the transformation T θ over a spatial domain of the image I using the displaced one or more control points; and
compute a resized image J by applying the computed transformation T θ to the spatial domain of the image I to resize.
11. A computer system comprising:
a processor; and
a memory, the processor being operatively coupled to the memory and the memory having recorded thereon instructions configuring the processor to implement a resizing of an image I by:
providing the image I to resize;
providing an image significance by computing a significance of each pixel in the image to resize;
extracting an original spatial domain (Ω) of the significance image;
providing a transformation T θ , parameterized as an interpolating spline by a set of control points, from the original spatial domain (Ω) to a resized spatial domain (Ω′);
subdividing the original spatial domain (Ω) into cells, each cell being defined by a subset of control points of the set;
computing, for each cell, a weighted average of the significance of the pixels in the cell, the weighted average being computed using the interpolating spline;
deforming the cells of the original spatial domain (Ω) by displacing one or more control points of the cells having a lesser weighted average;
computing the transformation T θ over a spatial domain of the image using the displaced one or more control points; and
computing a resized image J by applying the computed I transformation T θ to the spatial domain of the image I to resize.
12. The computer system as claimed in claim 11 , wherein the provided transformation T θ is a diffeomorphic transformation T θ such that J(x)=I(T θ −1 (x)), wherein I is the image to be resized, J is the resized image, x is the position of a given pixel in the original spatial domain (Ω).
13. The computer system as claimed in claim 12 , wherein the diffeomorphic transformation T θ is defined by the equation T θ =x+u θ (x), wherein x is the position of a given pixel in the original spatial domain (Ω), and u θ (x) is a displacement function wherein u is a mapping from the original spatial domain (Ω) to the resized spatial domain (Ω′).
14. The computer system as claimed in claim 13 , wherein the transformation T θ is parameterized as a free form deformation interpolating spline, and wherein displacement function u θ (x) is defined by the equation
u
θ
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x
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=
∑
k
=
0
3
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l
=
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3
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k
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x
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)
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l
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x
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θ
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x
w
s
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+
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+
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wherein B 0 , B 1 , B 2 , B 3 are Cubic B-splines functions, θ is a function representing the control points, s w is the spacing between two control points in an horizontal direction, s h is the spacing between two control points in a vertical direction, x w is the position of a pixel in the original spatial domain (Ω) on an horizontal axis, x h is the position of a pixel in the original spatial domain (Ω) on a vertical axis.
15. The computer system as claimed in claim 14 , wherein the set of control points form a grid and θ is the function representing the grid of control points.
16. The computer system as claimed in claim 14 , wherein the step of computing, for each cell, a weighted average of the significance of the pixels in the cell is carried out with the function
SI
(
y
)
=
∑
k
=
0
3
∑
l
=
0
3
∫
Ω
(
i
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j
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k
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x
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l
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x
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S
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x
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ⅆ
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,
wherein Ω (i,j) is a partition of the original spatial domain (Ω), S(x) represents the provided significance image.
17. The computer system as claimed in claim 16 , wherein the partition Ω (i,j) is the domain covered by the cells.
18. The computer system as claimed in claim 11 , wherein the original spatial domain (Ω) extracted from the significance image is the same as the spatial domain (Ω) of the image I to resize.
19. The computer system as claimed in claim 11 , wherein the step of computing a resized image J comprises reducing or increasing the image size.