# Robert Spann

I am intrigued by the analogs between the compositional rules and color theory principles that artists use and the statistical properties of images. For example, the compositional principle that an image be balanced horizontally and vertically is equivalent to stating that the first horizontal and vertical geometric moments are zero. I start with a given set of desirable statistical properties for an image. These composition constraints can be written as equations which the pixel values of the image must satisfy. I use optimization techniques to produce images that simultaneously satisfy several pre-specified compositional constraints.

This image illustrates the use of equations as a compositional tool plus digital manipulation based on my own aesthetic judgments to produce images. I begin this process by requiring the image to satisfy a series of constraints. These constraints include specific values for the first four moments of the distribution of pixel values for the three color channels; specific values for the image's geometric moments up to order three; a positive horizontal and diagonal correlation; as well as other constraints. The conjugate gradient method is used to produce candidate images that satisfy these constraints. I then choose one of these images for further digital manipulation to produce the final image.

The process for producing this image begins by solving an optimization problem. I specify 39 constraints the pixel values of the image must satisfy. These constraints include specific values for the first four moments of the distribution of pixel values of the three color channels; a correlation between the left and right hand sides of the image (as well as the upper and lower diagonal elements) equal .8; greater variability plus warmer hues at the center; centered geometric means. The conjugate gradient method is used to produce an image that minimize the sum of squared deviations between the image and the constraints. I refine the image using thresholding techniques, plus digital manipulation based on my own aesthetic judgments.