Deviation magnification: revealing departures from ideal geometries
Geometries of the structures and objects deviate from their idealized models, while not always visible to the naked eye. Embodiments of the present invention reveal and visualize such subtle geometric deviations, which can contain useful, surprising information. In an embodiment of the present invention, a method can include fitting a model of a geometry to an input image, matting a region of the input image according to the model based on a sampling function, generating a deviation function based on the matted region, extrapolating the deviation function to an image wide warping field, and generating an output image by warping the input image according to the warping. In an embodiment of the present invention, Deviation Magnification inputs takes a still image or frame, fits parametric models to objects of interest, and generates an output image exaggerating departures from ideal geometries.
1. A method comprising:
fitting a model of a geometry to a digital input image;
matting a region of the digital input image according to the model based on a sampling function;
generating a deviation function based on the matted region, the deviation function representing a deviation of the matted region of the digital input image from the model;
extrapolating the deviation function to an image wide warping field; and
generating a digital output image by warping the digital input image according to the image wide warping field.
2. The method of claim 1 , wherein:
generating the deviation function further includes generating a function ƒ(x),
x represents coordinates of one of the axes,
the value ƒ(x) is based on a value of
∑
y
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I
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x
,
y
)
-
S
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y
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)
S
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(
y
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y
S
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y
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2
,
I(x,y) represents an intensity profile of the matted region for given co-ordinates x and y, and
S(y) represents an average of edge profiles for all values of x in relation to the matted region.
3. The method of claim 1 , wherein fitting the model of the geometry to the digital input image further includes:
receiving an approximate model of a geometry from user input; and
fitting the model of the geometry based on a best match of the approximate model to the digital input image.
4. The method of claim 1 , wherein fitting a model of a geometry to an input image includes automatically detecting at least one model of the digital input image.
5. The method of claim 1 , wherein the model can be expressed by a parametric equation.
6. The method of claim 1 , wherein the sampling function further transforms the region of the digital input image to a canonical image stripe.
7. The method of claim 1 , wherein:
fitting the model of the geometry to the digital input image includes fitting a plurality of models of at least one geometry to the digital input image;
matting the region of the digital input image further includes matting each region corresponding to each plurality of the models;
generating the deviation function further includes generating a plurality of deviation functions each based on a corresponding matted region;
extrapolating the deviation function to an image wide warping field further includes extrapolating each deviation function to a plurality of image wide warping fields; and
generating the digital output image by warping the digital input image according to each image wide warping field.
8. The method of claim 1 , further comprising:
generating an output video based on a plurality of digital output images generated by performing the method of claim 1 separately on a series of frames independently.
9. The method of claim 1 , wherein generating the digital output image further includes limiting the warping of the digital input image to at least one of (a) a user defined region, (b) a color change in the image, (c) a geometric change in the image, or (d) a region attenuated by distance from the model.
10. A system comprising:
a processor; and
a memory with computer code instructions stored therein, the memory operatively coupled to said processor such that the computer code instructions configure the processor to implement:
fit a model of a geometry to digital input image;
matte a region of the digital input image according to the model based on a sampling function;
generate a deviation function based on the matted region, the deviation function representing a deviation of the matted region of the digital input image from the model;
extrapolate the deviation function to an image wide warping field; and
generate a digital output image by warping the digital input image according to the image wide warping field.
11. The system of claim 10 , wherein:
generating the deviation function includes generating a function ƒ(x),
x representing coordinates of one of the axes,
the value ƒ(x) is based on a value of
∑
y
(
I
(
x
,
y
)
-
S
(
y
)
)
S
′
(
y
)
∑
y
S
′
(
y
)
2
,
I(x,y) represents an intensity profile of the matted region for given co-ordinates x and y, and
S(y) represents an average of edge profiles for all values of x in relation to the matted region.
12. The system of claim 10 , wherein fitting the model further includes:
receiving an approximate model of a geometry from user input; and
fitting the model of the geometry based on a best match of the approximate model to the digital input image.
13. The system of claim 10 , wherein fitting the model further automatically detects at least one model of the digital input image.
14. The system of claim 10 , wherein the model can be expressed by a parametric equation.
15. The system of claim 10 , wherein the sampling function further transforms the region of the digital input image to a canonical image stripe.
16. The system of claim 10 , wherein:
fitting the model of the geometry to the digital input image includes fitting a plurality of models of at least one geometry to the input image;
matting the region of the digital input image further includes matting each region corresponding to each plurality of the models;
generating the deviation function further includes generating a plurality of deviation functions each based on a corresponding matted region;
extrapolating the deviation function to an image wide warping field further includes extrapolating each deviation function to a plurality of image wide warping fields; and
generating the digital output image by warping the digital input image according to each image wide warping field.
17. The system of claim 10 , wherein the processor is further configured to:
generate an output video based on a plurality of digital output images generated by employing the system of claim 10 separately on a series of frames independently.
18. The system of claim 10 , wherein the processor is further configured to limit the warping of the digital input image to at least one of (a) a user defined region, (b) a color change in the image, (c) a geometric change in the image, or (d) a region attenuated by distance from the model.
19. A non-transitory computer-readable medium configured to store instructions for analyzing an image, the instructions, when loaded and executed by a processor, causes the processor to:
fit a model of a geometry to a digital input image;
matte a region of the digital input image according to the model based on a sampling function;
generate a deviation function based on the matted region, the deviation function representing a deviation of the matted region of the digital input image from the model;
extrapolate the deviation function to an image wide warping field; and
generate a digital output image by warping the digital input image according to the image wide warping field.
20. The non-transitory computer-readable medium of claim 19 , the instructions further cause the processor to:
generate the deviation function further includes generating a function ƒ(x),
x represents coordinates of one of the axes,
the value ƒ(x) is based on a value of
∑
y
(
I
(
x
,
y
)
-
S
(
y
)
)
S
′
(
y
)
∑
y
S
′
(
y
)
2
,
I(x,y) represents an intensity profile of the matted region for given co-ordinates x and y, and
S(y) represents an average of edge profiles for all values of x in relation to the matted region.