How are human eyes able to detect the different curvatures of surface ? Basically how are the human eyes able to differentiate between a plane surface and a convex or a concave surface?
This is possible because we have two eyes. They furnish depth perception, which lets us perceive curvatures.
Even with only one eye, we can be fooled into believing a perfectly flat 2-D surface is curved in 3 dimensions by processing cues of color, shading and perspective based on experience. This is the reason that we can "understand" a painting or a printed picture as representing 3-dimensional objects when the rendering itself is strictly 2-dimensional.
So, curvatures can be perceived because we have stereoscopic vision and because we have image-processing programs running in our brains that help identify curvature.
Although stereoscopic vision can be useful for perceiving curvature of surfaces, in my experience shading (in the case of diffusive surfaces) is more important. Curvature in a specular surface is also easy to perceive using only one eye, because concave and convex mirrors impose different distortions on reflected scenes. Also, a person with vision in only one eye can easily learn to perceive curvature almost as well as a person with normal vision. Consider what you perceive when looking at a photograph of a curved surface. You perceive the curvature correctly most of the time, despite the fact that the photo was shot from a single point perspective. All that said, it's a bit easier to fool a single eye than a pair of eyes, into misinterpreting a scene. Bottom line: it is not so much a property of the eye or eyes that allows us to see curvature. Rather, it is our brain that makes it possible.