

UNIVERSITY
OF CALIFORNIA,
SANTA CRUZ 







Kernel
Regression for Image Processing and Reconstruction
Presented
by Hiroyuki Takeda, Dr. Sina Farsiu, and Professor Peyman Milanfar
This
page shows that the applicability of the kernel regression technique
to a wideclass of problems:

Image
denoising
 Image reconstruction
(interpolation + denoising)
The details of the
kernel regression technique are described in here.
The software package is also available here. 







Lena
image

 Added
white Gaussian noise (standard deviation 25)
 The noise
is generated by MATLAB commands "randn" by initialized
the seed with 0.
 RMSE (root
mean square error) is around 25.

Comment
: Although the RMSE of our method is slightly worse than the one of
the wavelet method, the ringing effect and some artifacts, which we
can see in the denoised image by the wavelet method, are invisible in
our result. We cannot tell which one is better than the other, and leave
the judgement to everyone. However, we can say that, with only the assumption
of zero mean noise (unlike the wavelet method assuming noise is Gaussian),
the iterative steering kernel regression method did a good job.






Compression
Artifact Reduction


 Equivalent
to the zeroth order bilateral kernel regression
 Gaussian
kernel for both spatial and radiometric kernels
 Spatial
smoothing parameter is 2.0
 Radiometric
smoothing parameter is 4.1
 Window
size is 7
 RMSE is
8.52

Iterative
steering kernel regression
 The second
order steering kernel regression with iterative filtering algorithm
 Gaussian
kernel
 Global
smoothing parameter is 2.0
 The number
of iterations is 3
 RMSE is
8.49







Film
Grain Reduction


Noisy
John F. Kennedy image
 343 x 367
color image
 Real film
grain noise (the statistics of noise is unknown)




 Equivalent
to the zeroth order bilateral kernel regression
 Gaussian
kernel for both spatial and radiometric kernels
 Spatial
smoothing parameter is 2.0
 Radiometric
smoothing parameter is 3.5
 Window
size is 7

Iterative
steering kernel regression
 The second
order steering kernel regression with iterative filtering algorithm
 Gaussian
kernel
 Global
smoothing parameter is 2.0
 The number
of iterations is 3

Wavelet 
Bilateral filter 
Iterative steering kernel
regression 

Almost no
objects are visible in the residual image of iterative steering
kernel regression, therefore the iterative method removed noise
the most effectively. 
Note: We did this denoising experiment in the YCrCb
channels.












Image
Reconstruction from an Irregularly Sampled Data Set


Irregularly
sampled data set

Delaunayspline
smoother*
 Regularization
parameter is 0.087
 RMSE is
9.05



Classic
kernel regression
 Gaussian
kernel
 The second
order
 Global
smoothing parameter is 2.25
 RMSE is
9.69

Iterative
steering kernel regression
 The second
order steering kernel regression with iterative filtering algorithm
 Gaussian
kernel
 Global
smoothing parameter is 1.6
 The number
of iterations is 1
 RMSE is
8.21

*To
implement the Delaunayspline smoother we used MATLAB's "griddata"
function with "cubic" parameter to transform the irregularly
sampled data set to a dense regularly sampled data set (Delaunay triangulation).
The quality of the resulting image was further enhanced by applying
MATLAB's spline smoother routine "csaps".






Image
Fusion
Tank
Sequence



64
x 64 video sequence
 8 frames
 Taken by
an infrared camera
 Courtesy of B. Yasuda and the FLIR research groupe in the
Sensors Technology Branch, Wright Laboratory, WPAFB, OH

Classic
kernel regression
 Gaussian
kernel
 The zeroth
order
 Global
smoothing parameter is 0.8
 Resolution
enhancement factor is 5 for both vertical and horizontal directions



Classic
kernel regression
 Gaussian
kernel
 The second
order
 Global
smoothing parameter is 0.8
 Resolution
enhancement factor is 5 for both vertical and horizontal directions

 Deblurring
on the image reconstructed by the second order classic kernel
regression
 PSF is
the 5 x 5 Gaussian with standard deviation 1.0
 Used the
bilateral total variation regularization

Emily
Sequence



35
x 54 video sequence
 53 frames
 Taken by
a commercial webcam (3COM, Model No.3718)

Singleframe
Delaunayspline smoother
 Single
frame upscaling
 Resolution
enhancement factor is 5
 Regularization
factor is 0.01



 Multi
frame upscaling
 Resolution
enhancement factor is 5
 Regularization
factor is 0.067

Iterative
steering kernel regression
 The second
order steering kernel regression with iterative filtering algorithm
 Gaussian
kernel
 Global
smoothing parameter is 1.0
 The number
of iterations is 0







Super
Resolution


A
real compressed color video sequence

 Multi
frame upscaling
 Resolution
enhancement factor is 5
 Regularization
parameters for Y, Cr, and
Cb are 0.5, 1.0, and 1.0, respectively
 Deblurring
 PSF
is the 5 x 5 disk kernel
 Bilateral
total variation regularization



Classic
kernel regression
 Resolution
enhancement factor is 5
 Gaussian
kernel
 The second
order
 Global
smoothing parameters for Y, Cr,
and Cb are 2.0, 3.5, and 3.5, respectively
 Deblurring
 PSF
is the 5 x 5 disk kernel
 Bilateral
total variation regularization

Iterative
steering kernel regression
 Resolution
enhancement factor is 5
 Gaussian
kernel
 The second
order steering kernel regression with iterative filtering algorithm
 The number
of iterations is 1
 Global
smoothing parameters for Y, Cr,
and Cb are 4.0, 8.0, and 8.0, respectively
 Deblurring
 PSF
is the 5 x 5 disk kernel
 Bilateral
total variation regularization





