Image simplification using a robust reconstruction filter
View Patent ↗A method simplifies a data structure representing physical measurements of a real-world phenomena, such as an image of a scene of an object. Input data are first acquired, sensed, or measured. If the data are acquired with a camera, then measurement errors for data points in the data structure are not normally distributed. Therefore, an error term for each data point is constructed according to a Lorentzian estimator. The error term can be determined by taking a difference between the value of the data point, and the value at the data point when a model is fitted to the data structure. The error term is then minimized using a downhill simplex minimization process. Finally, each data point is adjusted by the minimized error term to produce a simplified data structure of the real-world phenomena.
1. A method for simplifying a data structure representing physical measurements of a real-world phenomena, comprising:
acquiring a single input image having measurement errors that are not normally distributed for a plurality of pixels;
determining an error term for each pixel in the single input image according to a Lorentzian estimator;
minimizing the error term;
adjusting each pixel in the single input image by the minimized error term to produce a simplified single output image from the single input image of the real-world phenomena.
2. The method of claim 1 wherein the determining, minimizing and adjusting steps are applied separately to each single input image of a video.
3. The method of claim 1 wherein the determining step further comprises:
identifying a local region of pixels for each pixel in the single input image;
fitting a model function to the pixels in the single input image of each local region;
accumulating, for each pixel in the single input image, differences between pixel values according to the model function and the value of each pixel in the single input image to determine the error term for each pixel in the single input image.
4. The method of claim 3 wherein a size of the local region is set according to a simplification control parameter.
5. The method of claim 3 wherein the model function is a polynomial.
6. The method of claim 3 wherein the model function is a piece-wise continuous function.
7. The method of claim 3 wherein the model function is parameterized by a finite number of parameters.
8. The method of claim 3 further comprising:
adapting the model function dynamically to local statistics of the single input image.
9. The method of claim 3 wherein the model function is static.
10. The method of claim 1 further comprising:
subtracting the simplified single output image from the single input image to produce a single residual image.
11. The method of claim 1 wherein the Lorentzian estimator of an error term x with a standard deviation σ is
ρ
(
x
,
σ
)
=
log
(
1
+
1
2
(
x
σ
)
2
)
,
and a derivative of the Lorentzian estimator is
ψ
(
x
,
ρ
)
=
2
x
2
σ
2
+
x
2
.
12. The method of claim 1 wherein the minimizing uses a downhill simplex method.
13. The method of claim 1 further comprising:
assigning the simplified single output image to the single input image and iteratively determining, minimizing, and adjusting according to a simplification control parameter.
14. The method of claim 1 wherein each color band of the single input image is simplified separately.
15. The method of claim 1 further comprising:
reconstructing output data from the simplified single output image.