Although the proposed algorithm for uneven lighting image segmentation has some advantages, there are still two problems requiring further study.
The edge information has an important impact on the wave transformation of pixels in an uneven lighting image.
A wave transformation model, which is introduced by Wei et al., is a prospective idea for uneven lighting image segmentation [36].
Local thresholding methods for uneven lighting image segmentation always have the limitations that they are very sensitive to noise injection and that the performance relies largely upon the choice of the initial window size.
Theorem 1. Suppose the gray level of a pixel (x, y) in the uneven lighting image f δ is constituted by f δ (x, y) = f x, y) + δ x, y), where f x, y) is the original intensity of (x, y) in the image with even light and δ x, y) is the intensity of the uneven light in (x, y).
That is to say that, the weight matrix for the pixel Q(x k, y k ) in the uneven lighting image f δ is approximately equal to the weight matrix for the pixel Q(x k, y k ) in the original image f, namely, v δ (k, j) ≈ v k, j).
Given a pixel (x k, y k ) in an uneven lighting image f δ, where (x k, y k ) represents the original coordinate of the kth pixel, the square neighborhood N δ, k and N δ, j centered at two pixels (x k, y k ) and (x j, y j ) respectively are: {N}_{delta, k}={N}_k+{delta}_k,kern0.5em {N}_{delta, j}={N}_j+{delta}_j.
Given an pixel (x k, y k ) in an uneven lighting image f δ, where (x k, y k ) represents the original coordinate of the kth pixel, v δ (k, j) is the weight matrix for the pixel (x k, y k ).
The gray level of the trough T s, the peak P s, and an arbitrary pixel k in the sub-region ϕ s in the uneven lighting image f δ are respectively: {g}_{delta}left {T}_sright)=gleft {T}_sright)+delta left({T}_sright),kern0.5em {g}_{delta}left {P}_sright)=gleft {P}_sright)+delta left({P}_sright),kern0.5em {g}_{delta } k)=g k)+delta (k).
To prove the effectiveness of our method for uneven lighting images with strong noise injection, experimental tests are implemented on six uneven illumination images corrupted by the Gaussian noise.
