Is there any mathematical relationship between intensity of object and depth of the object ? if a video is shot while varying the distance of object from camera in each frame will it follow some specific relation .Like disparity is inversely proportional to depth does intensity also follow any such relation.
yes it is in some cases but the main dependency is not about camera but light/shadow sources.
I assume you want this for image recognition/reconstruction
you have to know the light model
directional (Sun) or point light (Lamp)?
fully diffused directional light
no matter the distance if you know the source position relative to camera then you can detect surface normals from intensity. For that you either have to know the albedo of surface or you see max or min intensity in some gradient on this surface. max,min is the max/min reflection of light so you can easily compute the vector coordinates ...
point light
here the position and orientation matters so add the distance intensity dependency to bullet #2. Select homogenous surface take few points from it and match computed intensity of 3 points on plane according to your light model until direction and position of the plane matches ... It is similar to CORDIC algorithms
combined
this is tricky but doable in some cases but the complexity growth is exponential
shadows
casted shadows can reveal direct geometry properties just use reverse ray from shadow edge to light source until it hits obstacle edge ... or if shadow is casted by straight edge and it is curved that also tels a lot ...
[Notes]
all bullets are so complex that can fill entire books. I am no expert in this area so take that in mind