Statistical models for irregularly sized objects

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The primary objective of this project is prediction of a continuous output Y from images acting as covariates Xthrough a nonlinear regression function f() in the equation: Y = f(X) + residual. In order for the regressionmodel to be valid all of the X covariates must have the same dimension. Unlike in most image processingapplications images in this project are of differing sizes. In standard applications irregularly sized rectangularimages can be transformed via compression, stretching, cropping, and padding to bring the images to acommon size. However in our application a transformed image with a high value of Y will be equivalent to anun-transformed image of the same dimension with a low value of Y. In other words, the size normalizingtransformation process induces artifacts that will destroy the regression relationship. This project expands themethods used for image processing to account for this type of problem. Ultimately the insights of theregression model will be used to predict optimal ways in which image X can be modified so as to produce anincreased/decreased value of Y. In this project we try to predict year Y images X from an art database whereart pieces are arbitrarily sized rectangles with any aspect ratio. Compressing an image will distort the imagecontents in ways that could be inconsistent with its time period. Cropping an image removes importantfeatures for prediction. Padding images with extrapolated coloured space makes the image equivalent to adifferent art piece. In such cases an early renaissance piece may become dominated by the transformationfeatures making it equivalent to a recent modern art piece. The secondary goal of this work is to examine howto modify an art work so as to make it equivalent to an earlier or later form of that style. These methods areapplicable to the partner company, Unbounce, in that they will assist them in advising their client customers inhow to modify artwork optimally while maintaining it's overall style.