Post-Processing in ERC

Outlier Rejection
To smooth the vector field, when a vector is a outlier vector, then filter it. Decision making by value and phase of MV.

Window Weighted Neighboring Pixel
Using a window to weight the wanted pixel. Reducing block artifacts.

Median Filter
To dismiss high isolate noisy point.

VMF(Vector Median Filter)
∑Ni=1||v⃗ M−v⃗ i||r≤∑Ni=1||v⃗ j−v⃗ i||r,j=1,2,⋯,N

SVMF(Selective Vector Median Filter)
Two processes to remove outliers.
1、noise detection:
calculate S¯=1N∑Nj=1Sj , Sj stands for neighboring’s distance sum.
Si=∑Nj=1||xi−xj||,i=1,⋯,N This stands for norm.
If S>kS¯, then it’s noise. And can’t be put into calculating into window.
2、noise removal:
remove noise of state 1 and use VMF vector.

Detail-preservation Adaptive Vector Median Filter
1、noise detection:
NPc={1,0,if L(N+1)/2>T & NOc=1 others
where:
L1=∑Nj=1||f1−fj||2, f1 is the minimal vector.

t1=L1

L(N+1)/2 is the vector distance correspond to f(N+1)/2

Laverage=∑Nj=1||faverage−fj||2

t2=N+deltaNLaverage

T=t1+t22+deltak2
as for NOs:
if Zmin<Zmed<Zmax,toB
otherwise, increasing windows size.
if windowsize<Smax, repeat A
otherwise output B.
B:
if Zmin<Zxy<Zmax, output Zxy
otherwise:Zmed
if the brightness value is inconsistent with original value, set NOc be 1.
2、median filter:
f(n)={f1,f(N+1)/2,if L(N+1)/2 & NOc=1 others

RRVMF(Robust Rank Vector Median Filter)
Firstly, detecting whether this part is noise or not.
if ||yVMF−Xc||>torR(Xc)>r, using vector median filter.
Else no filtering.

yVMF=argmin∑Ni=0||X−Xi||r, here using Euclidean distance(r = 2). N stands for window size.

AWVMF(Adaptively Weighted Vector Median Filter)
To overcome the drawback of VMF’s lacking of tuning parameter.
∑Ni=1wi⋅||v⃗ M−v⃗ i||r≤∑Ni=1wi⋅||v⃗ j−v⃗ i||r,j=1,2,⋯,N
How to get wi, using the MSE of neighboring vector(using vector information).
wi=DFDB(v⃗ c)DFDB(v⃗ i)

Linear Approximation of Vector Median Filter
V(v⃗ )=||v⃗ ||=∑Ni=1v2i−−−−−−−√

approximate as:

V^(v⃗ )=a∑Ni=1b|v|(i)

a=21+∑Ni=1(i√−i−1√)2√

b=i√−i−1−−−−√

From:

OPTIMUM LINEAR APPROXIMATION OF THE EUCLIDEAN NORM TO SPEED UP VECTOR MEDIAN FILTERING

Robustified Vector Median Filter(RVMF)
This method is using the mind of cluster.
The coal of this method is:
xmed=arg min∑nj=1α{x,xj}

α{x,xj}=

{|x−y|,h,if |x−y|≤hotherwise

Kalman Filter
Making the edge information stayed and estimate the initial data.
Do well in post-processing error concealment.
http://myfeeeling.blog.163.com/blog/static/54959910201042991349633/
x(n) = A(n-1)x(n-1) + w(n)
y(n) = C(n)x(n) + r(n)
x(n) is L state variables;A(n-1) is LxL state transition matrix;w(n) is white noise with Lx1;
y(n) is observation Rx1 vector;C(n) is an RXL measurement matrix that relates y(n) to x(n);r(n) is Rx1 observation noise vector.

Adaptive Inter-Mode Estimation
If we don’t use median filter, we can use merge method to estimate MV.

Fast 3X3 Median Filtering
This guy has a good method to find median of 3X3 window median.
http://www.cnblogs.com/BYTEMAN/archive/2012/07/21/2602181.html
maxmum group：
Max0 = max[P0，P3，P6]，Max1 = max[P1，P4，P7]，Max2 = max[P2，P5，P8]
median group：
Med0 = med[P0，P3，P6]，Med1 = med[P1，P4，P7]， Med2 = med[P2，P5，P8]
minimum group：
Min0 = Min[P0，P3，P6]，Min1 = Min[P1，P4，P7]，Min2 = max[P2，P5，P8]
Compare the minimum value in maximum group, median in median group, maximum in least group.

Window Filter
Using a simple matrix to reduce block artifacts.