Modeling Respiratory Signals by Deformable Image Registration on 4DCT Lung Images

Algorithm 4

Local binary pattern error rate.

1. Input the source slice: SrcSliceIM (contains only the left and right lungs) and the target slice: TarSliceIM (contains only the left and right lungs)

2. Extract the LBP features of the source and target slices

   SrcLBPFeatures = ExtractLBPFeatures(SrcSliceIM)

   TarLBPFeatures = ExtractLBPFeatures(TarSliceIM)

3. Gauge the similarity between the LBP features by computing the squared error between them

   Similarity = square(TarLBPFeatures – SrcLBPFeatures)

4. Local Binary Pattern Error Rate

   LBPErrorRate = sum(Similarity)

5. End

6. Result in LBPErrorRate

Appendix

ExtractLBPFeatures method

1. The texture T as the joint distribution of the gray levels of P +1 image pixel

where is the gray level value of the center pixel, surrounded by P equally spaces pixels of gray levels , located on a circle of radius R.

2. Define the Local Binary Pattern (LBP), a grayscale invariant and rotation invariant operator:

Where

and is the sign function. The uniformity function corresponds to the number of spatial transitions in the neighborhood: the larger it is, the more likely a spatial transition occurs in the local pattern.