You can superpose the black and white pixelated photos of your shapes assigning a grayscale value of $1/n * (1/255) ,$ per shape. you will get an image with a black core and shading to gray and feathering to white.

Many photo editing softwares allow you to define a border based on the gray intensity. In your case, it is 127-128.

If some parts of your objects are essential and need to be preserved you can set them to 0.

Edit

I remembered my airplane mechanic talking about ultrasound testing equipment to check for fatigue cracks.

here is a do it yourself ultrasound 3d scanner.

3d ultrasound scanner

hmm. here's a shot in the dark. might require relatively simple surface. this is crude, the are much more sophisticated ways. research metric or distance for 3D shapes.

(1) In a 3D modeling tool, fit a simplified (curvature never too small) convex dummy surface to a typical data surface. Shrink it maybe 50% in a 3D tool, so it is always "inside" the data surfaces. Adjust so it's still convex. Call this shrunken preliminary reference surface R.

(2) Generate list of n evenly spaced points on R, call them vectors A_n. Also generate corresponding vectors N_n normal to R at A_n, and pointing outward. So you have a list of reference "rays" in space originating at A_n, direction N_n. Call these B_n. (note: May be helpful to have more densely spaced points A_n where R has smaller radius of curvature.)

(3) For each of m data set items, call them surfaces S_m: generate vectors C_m,n , defined by the intersection of S_m and B_n. Depending on surfaces you may have to do something to make sure there is only one intersection (eg use the one nearest to A_n looking outward). This is where concave could be an issue. Anyway, you can then use the C_m,n to construct the metric, loosely speaking. The average (or trimmed mean or minimum or whatever) surface, consisting of points D_n can then be constructed from the list C_m,n by simply applying the statistic to the list of |C_m,n| indexed by each n ... you could likewise hopefully use it as a metric.