Page 210 - Computational Retinal Image Analysis

206 CHAPTER 11 Structure-preserving guided retinal image filtering

the deep learning-based optic disc segmentation and sparse learning-based CDR
computation.

The remaining sections of this chapter are organized as follows. Section 2
introduces the method to remove the clouding effect, which includes a step of global
structure transferring and a step of global edge-preserving smoothing. Section 3
shows the effectiveness of the method to improve the contrast of the retinal images as
well as its application in optic cup segmentation and CDR computation. Conclusions
are drawn in the last section.

2 Structure-preserving guided retinal image filtering
In GIF [53], a guidance image G is used to guide the process. G could be identical to
the input image I. The output image O is computed by a linear transformation of G
in a window W p centered at the pixel p, that is,
O = a G + b , ∀∈ p (3)
iW ,
p
i
p
i
where i indicates pixel index.
The linear transform coefficients a p , b p are determined by minimizing the
following objective function:
2
I
E = ( O − ) 2 + a , (4)
p
i
i
where ϵ is a regularization parameter.
The solution is given as:
1 ∑ GI − µ − (5)
∈
| W | iW p ii p I p
a = p ,
σ p 2 +
p
−
b p = I p− a µ , (6)
p
p
−
where I p denotes the mean of I in W p ; |W p | denotes the cardinality of W p ; and μ P and
σ denote the mean and variance of G in W p , respectively.
2
p
Each pixel i is included in many overlapping window W p , and the outputs of Eq.
(5) from different windows are not identical. GIF [53] adopts an averaging strategy,
that is,
O = a G + b ,
p
i
i
p
(7)
where a p and b denote the mean values of a p′ and b p′ in W p :
p
1 (8)
a = ∑ a ,
p′
p
| W | pW p
′∈
p
1
b = ∑ b . (9)
p′
p
| W | pW p
′∈
p
It has been pointed out that a pixel from a high-variance area will retain its value
while the intensity of a pixel from a flat-contrast area will be smoothed by its nearby