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Mathematics Colloquium


Date:  Tuesday, January 22, 2008

Title:  Multiscale Analysis of Vincent Van Gogh's paintings

Abstract:  This talk discusses an analysis of 101 high definition gray value scans of paintings by Vincent Van Gogh and other artists, in the framework of a workshop for Art Historians and Image Processors, held in May 2007 at the Van Gogh Museum in Amsterdam. All the work was done in collaboration with Eugene Brevdo and Shannon Hughes, two graduate students in Electrical Engineering at Princeton University. The analysis was based on wavelet transforms of the high resolution gray-level images; the distribution of wavelet coefficients in every orientation and at every scale was modeled as a mixture of two zero-mean gaussian distributions (one wide, one narrow), associated with a hidden Markov tree, with two hidden states (one for each of the distributions). This model is based upon the intuition that locations in the picture where sharp edges are present correspond to wavelet coefficients that are of type W (for wide), i.e. distributed according to the wide distribution at every scale (and thus admitting quite large values); locations where the content depicted in the picture varies smoothly correspond to wavelet coefficients of type N, i.e. distributed according to the narrow distribution (so that all values are small). Less sharp edges can correspond to a hidden state of type N for fine scale coefficients, switching to W for coarser scales. The parameters of the hidden Markov tree model were optimized; these optimal values were then combined into a feature vector that characterized the paintings. Machine learning algorithms showed that the features that dominated the classification between paintings by Van Gogh and other artists were mostly transition probabilities from type N to type W (going from coarser to finer scales), linked to orientation-dependent scale values; these features mostly identified the scales at which detail information "emerges", as one gradually zooms in, in Van Gogh paintings more so than in non-Van Gogh paintings. These characteristic scales turn out to be different for features in different directions; the relative strength of details in each scale and orientation seems characteristic for Van Gogh's style. To pinpoint paintings, such as copies or forgeries of true Van Goghs, that are stylistically similar to Van Goghs but are by another artist's hand, much finer scales in the wavelet transform turned out to be useful; the relative abundance of extremely fine detail led us indeed separate copies and forgeries from most of the authentic, original Van Goghs.

Speaker:  Ingrid Daubechies
Institution:  Princeton University


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