Geoffrey E. Hinton, Christopher Williams, Michael D. Revow
Hand-printed digits can be modeled as splines that are governed by about 8 control points. For each known digit. the control points have preferred ., home" locations, and deformations of the digit are generated by moving the control points away from their home locations. Images of digits can be produced by placing Gaussian ink generators uniformly along the spline. Real images can be recognized by finding the digit model most likely to have generated the data. For each digit model we use an elastic matching algorithm to minimize an energy function that includes both the defor(cid:173) mation energy of the digit model and the log probability that the model would generate the inked pixels in the image. The model with the lowest total energy wins. If a uniform noise process is included in the model of image generation, some of the inked pixels can be rejected as noise as a digit model is fitting a poorly segmented image. The digit models learn by modifying the home locations of the control points.