error using Lab color space

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When i change the object from one position to another, considering that their are two pixels at distance d1 and color (1,a1,b1) and (1,a2,b2), why cant i find this two pixels at given previous distance d1 with their color in lab format? eg. let color of p1 be(1,a1,b1) and p2 be (1,a2,b2) and distance between them be d1. than at next image when the rigid object containing this two pixels changes without change in its oriantation, why is the distance between them not same as privious, and why is their a,b value not same? In Lab space if a pixel is change from one light intensity to another than still their a b value should remain same, isn't it? given two points are voxels.