Suppose we are going to extract lesion areas from images. I want to know if the location of lesion is different in test image from the one which is used as training image. Does Local Binary Patterns work properly?
Local binary patterns are extracted from the image, when you train to detect and extract the lesion from the image you are teaching the program how to recognize a pattern, I'm not work in this area specifically but I think that the main idea are the same so in my opinion I think that can work fine.
It depends on how you train your classifier. In principle, if you apply the LBP in subregions and different scales, it should be possible to detect a pattern/texture/object (lesion) wherever it is in the image and whatever the scale.
Check for papers that explain object detection (or even face detection) using local binary patterns.
Basic Local binary patterns (LBP) and some of it's new versions such as NrCLBP, MLBP, MBP, HCLBP are gray-scale invariant, shift invariant and rotation invariant, if we consider them on whole of the train image.
Of course, image shifting may cause some transformation between pixels, But, it can not disturb the relation between center pixels and its neighbors.( Except border pixels). Extracted feature values may not change after shifting significantly. ( In this case, I suggest uniform feature extraction method).
For example, if the value of right neighbors(56) of a considered pixel (48) is higher than center pixel(48). It is higher than center pixel after shifting.