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Motion Blur Estimation at CornersGiacomo Boracchi and Vincenzo Caglioti
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Motion Blurred Image
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Motion Blurred Image
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Motion Blurred Image
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Motion Blurred Image
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Motion Blurred Image
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Motion Blurred Image
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Motion Blurred Image
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Motion Blurred Image
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Motion Blurred Image
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Motion Blurred Image
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Preliminary Remarks
Dealing with blurred images it is complicated (lack of information)
Blur is often assumed uniform, but this is restrictive
We propose to analyze blur on some image regions
We focus on regions containing a corners
We consider only motion blur• Blur is approximated as parametric – direction and length -• Estimation of corner linear displacement
Any other blurring phenomena are neglected (e.g out of focus blur).
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Outline
Image Model Corner Model Problem Solution Robust Solution Experiments Concluding Remarks
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Blurred Image Model
A blurred noisy image given the original image
and the blur operator
( ) ( )( ) ( )I x K y x x (0, ),N x X
K
( )( ) ( , ) ( )X
K y x k x y d
we assume that blur locally is constant
point spread function
0
0 0( )( ) ( ) ( )xU
K y x v x y d v y x
0v
I
00 , xx X U X and
y
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Blur Assumptions
Point spread function has 1D support,
Constant value (Uniform Speed)
Parametric approach, estimate and
we call the corner displacement , the vector having direction and length
These assumptions hold only locally…
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0 ( ) ( )lv R s x 1 21/(2 1) , 0
0l
l l x l xs
else
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v
1x
2x
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Presentation Outline
Image Model Corner Model Problem Solution Robust Solution Experiments Concluding Remarks
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Why Corners?
No Aperture Problem, when blurred.
Easy to Detect (Harris, Hessian)
Easy to Model
Meaningful for scene understanding
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1
2
1
2
The Corner Model
The Corner has to be binary in the considered region D
Not every displacement can be managed.
/ 2, / 2 Exclude “self intersecting” corners
D
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Presentation Outline
Image Model Corner Model Problem Solution Robust Solution Experiments Concluding Remarks
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Vector Relation
Consider an Image Region D containing a blurred corner
in the noise free case,
v
0( ) ,v K y x x D
0 , ( ) 0D x K y x D
the aperture problem holds
However both at corners blurred edges may be used to solve this ambiguity
0 , ( ) , 0D x K y x T D T
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Least Square Solution
A “good” image region should containpixels from both blurred edges
Several pixels have to be considered, for example x
wi ;¡ n < i < n weights
~vx =argminv°°°A(x) v ¡ ¢ [w¡ n ; :::;w0; :::;wn]
T°°°2
A(x) ~vx =
2
66664
w¡ n r I (x¡ n)T
:::w0 r I (x)T
:::wnr I (xn)T
3
77775~vx = ¢ [w¡ n ; :::;w0; :::;wn]
T
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Drawbacks
Solution is not robust in presence of outliers and noise
Whenever image assumptions are not met (e.g. textured or shaded corners, smoothed contours, other image artifacts) solution is seriously corrupted.
Compute the solution on every pixel : method is slow
Requires a filtering procedure as every estimate depends on
Then, better look for a vector that satisfy the basic equation for a significant number of pixels, disregarding how far from the solution is for few pixels
x
v
v
~vx =argminv°°°A(x) v ¡ ¢ [w¡ n ; :::;w0; :::;wn]
T°°°2
x
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Presentation Outline
Image Model Corner Model Problem Solution Robust Solution Experiments Concluding Remarks
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Robust Solution
Considering only two gradient vectors it would be enough if appropriately chosen
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( )aN x
( )bN x( )aN x
( )bN x
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N(x) = r I (x)jjr I (x)jj2 ¢
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The Hough Transform
For each input data determine theset of possible solutions.
The solutions are represented in the parameter space
A vote (1) is assigned to all parameters that are compatible with a given data
being , the parameters,the coordinates of end point (in pixels)
Evaluate all inputs and sum the votes
The most voted pair in the parameter space are taken as solution,as they represent the parameters satisfying most of data
1 2( , )u uuv
( )N x
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The votes in parameter space
Consider also parameters close to the solutions• Assign them a fraction of vote (<1)• Assign a full vote to exact solutions
Being a tuning parameter and noise standard deviation
For every data , votesare assigned by this vote function opportunely rotated and translated
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N (x)
x̀(u1;u2) = R( ¼2 ¡ µ)¡`¢([u1;u2]T ¡ N (x))
x̀(u1;u2)
(̀u1;u2) = exph¡³
u21+kju1 j¾r ´
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Robust Solution- Votes sum
Sum of votes
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Presentation Outline
Image Model Corner Model Problem Solution Robust Solution Experiments Concluding Remarks
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Experiment on Synthetic Images
Synthetic images constructed according to
I (x) = K¡y+»
¢(x) +´(x) ; x = (x1;x2)
»(x) » N (0;¾»)
´(x) » N (0;¾́) where represents electronic noise
represents differences between the binary corner and the synthetic image
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Experiments on Synthetic images
Point Spread Function of 10° degrees and 20 pixels extents
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Experiments on Synthetic images
Point Spread Function of 70° degrees and 30 pixels extents
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Experiment on a Test Image
5 regions containing a corner have been selected on house image
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Results on a Test Image
house image has been artificially blurred by motion blur psf having• direction 30 degrees• length 25 pixels
Error in pixels : 2.07
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Results on a Test Image
house image has been artificially blurred by motion blur psf having• direction 30 degrees• length 25 pixels
house image has been artificially blurred by motion blur psf having• direction 30 degrees• length 25 pixels
Error in pixels : 2.75
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Results on a Test Image
house image has been artificially blurred by motion blur psf having• direction 30 degrees• length 25 pixels
house image has been artificially blurred by motion blur psf having• direction 30 degrees• length 25 pixels
Error in pixels : 3.19
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Results on a Test Image
house image has been artificially blurred by motion blur psf having• direction 30 degrees• length 25 pixels
house image has been artificially blurred by motion blur psf having• direction 30 degrees• length 25 pixels
Error in pixels : 1.87
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Results on a Test Image
house image has been artificially blurred by motion blur psf having• direction 30 degrees• length 25 pixels
house image has been artificially blurred by motion blur psf having• direction 30 degrees• length 25 pixels
Error in pixels : 2.04
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Experiments on camera images
Triplets of images have been taken according to the following scheme• still image (A)• Blurred image moving the camera on a rack (B)• still image (C)
Motion has been estimated in selected image regions in B and compared with the ground truth obtained by matching the feature in the corresponding regions in A and in C.
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A - still image at initial camera position
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B – the Blurred Image
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C – still image at final camera position
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Five selected Image regions
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Five selected Image regions
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Five selected Image regions
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Five selected Image regions
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Five selected Image regions
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Results from camera images
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Presentation Outline
Image Model Corner Model Problem Solution Robust Solution Experiments Ongoing Works
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Conclusions
Fourier based methods usually fail at corners and on small regions
Method to estimate motion blur parameters at corners from a single blurred image
We handle space varying blur as every image region is considered separately
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Ongoing Work
Manage all possible displacement, also the self – intersecting case
Detect Blurred Corners
Adaptively select region for motion estimation
Extend the algorithm to psf having 1D support, and non-uniform density.
Measure the Goodness of our estimate
Fusing estimates coming from different corners