Aha, ok, use of segmentations to extract the object point cloud seems good and I have used similar approach for face reconstruction l.

Have you tried 3D approachs (ridgid and non rigid alignment)? How similar are the objects? you could use the dense alignment error to determine if the object is the same as a streight one.

But if we go back to image based methods, if your segmentation model is good, it may provide good embeddings already in the encoder. You could take those embeddings and compute thier distance to the embeddings of templates (straight, bent, etc). Kmeans may not cluster as you expect if there is a high variance in samples (shape, size, color, etc), which is why supervised methods could be preferred. Templates provide a prototype for your class to compute distance/similarity to (Euclidean, cosine similarity) . It is crude, but could work in constrained settings.