Call me crazy, but shouldn't a line of symmetry be, in fact, a line? As in one straight line? Your "line of symmetry" is a hodgepodge zigzag through the features on the rock. That in itself is a very strong indication there is no intentional symmetry to the rock, but it is an artifact of your imagination, picking and choosing what you want to be.

A look at your marked "symmetrical points" shows they don't look very symmetrical at all. The top of your image, the left side has a smooth curve, the right has a step function - it zigzags. That's not symmetry by any definition I'm familiar with. Your second points down from the top, one is a smooth edge and the other is a corner. Symmetry? How?

The two points at the top of the face region, first they are dramatically offset from the features above. Second, they don't correspond well in size - the right corner is longer and higher than the left.

There's only an eye socket on the left, the right has filled in texture. Maybe he's a Borg, but otherwise I can't see symmetry of two eyes.

There's no nose, which you point out, but where the nose should be you shift the "symmetry line" over to the right. On faces, the symmetry line bisects the nose (or nose region). ???

The mouth is nowhere near where the mouth should be. There is a crevice that sticks from the centerline up to the left at a diagonal. It's like Sammy Davis Jr. to the max. The mouth runs up to the left cheekbone. That face looks like something by Picasso. Picasso's faces are not known for symmetry.

There's very little symmetry in the image. The points you mark as corresponding don't match each other. The line of symmetry you define is a zigzag through random features. The features that resemble facial features are misshapen, non-symmetrical, and out of place. Or missing.

In short, this is a game of "Fill in the Features" to make a face.

Beads? Twists and curls? I can't locate them.

I see the half-goblet shape. Now why should there be a half-goblet shape in the middle of the face? In fact, the half-goblet shape is not very good. It consists of a curve (the bell of the cup) and a straight line (the stem) with an edge for the bottom of the goblet. That's a pretty simple shape, not very complex. However, note that the curve for the side of the goblet extends up to the left, without a break, just a corner. This goblet has a protrusion on the lip. Hmm, not very goblet-like.

Instead of looking at that face, I point out just above the corner of the goblet. Three dark holes in the rock. OHMYGOD, it's a human skull! See, eyesockets and the nasal cavity.

When I look at the colorized version, it takes on the appearance of The Joker (from Batman). See his pointy nose to the right, the crooked smirk, the slashed brow and sharp chin? It's the Joker.