Natural scene statistics predict how humans pool information across space in surface tilt estimation
Fig 4
Constructing local and global models of tilt estimation.
A Image cues and groundtruth tilt in natural scenes. Image cues are derived directly from photographic stereo images (top). Groundtruth tilt at each pixel is computed directly from the range data (cf. Fig 2A). Here, groundtruth tilt is depicted with local surface normals instead of a colormap (cf. Fig 2B). B The local model estimates tilt based on local image cues. Local estimates are obtained via lookup tables that store conditional means (i.e., posterior means) given all possible combinations of three quantized unsigned image cue values (i.e., 643 unique cue combinations), and one quantized signed image cue value (i.e., 64 unique cue values), as computed from the natural image database. We have previously verified that quantizing the cue values is not a primary limiting factor on the performance of the model [16]. C Pooling local estimates in a spatial pooling region centered on a target location. D Each global estimate is obtained by pooling local estimates over a spatial neighborhood. Each local estimate is obtained by combining cues that are computed from multiple pixels in the image. Note that the area of the image that contributes to the global estimate is slightly larger than the purported area of the global pooling region, because each local estimate is computed from image gradients across an image region with non-zero spatial extent.