The Heeger & Bergen Pyramid Based Texture Synthesis Algorithm

Abstract

International audienceThis contribution deals with the Heeger-Bergen pyramid-based texture analysis/synthesis algorithm. It brings a detailed explanation of the original algorithm tested on many characteristic examples. Our analysis reproduces the original results, but also brings a minor improvement concerning non-periodic textures. Inspired by visual perception theories, Heeger and Bergen proposed to characterize a texture by its first-order statistics of both its color and its responses to multiscale and multi-orientation filters, namely the steerable pyramid. The Heeger-Bergen algorithm consists in the following procedure: starting from a white noise image, histogram matchings are performed to the noise alternatively in both the image domain and steerable pyramid domain, so that the corresponding histograms match the ones of the input texture.https://doi.org/10.5201/ipol.2014.7

How to Apply a Filter Defined in the Frequency Domain by a Continuous Function

“…Color images can be filtered by applying the algorithms independently to each color channel. The filtering in complex convention (method 1) corresponds to the classical DFT based computations that can be found in the literature [2]. Note that the three methods can be naturally extended to complex-valued images.…”

“…the input image can be recovered from its decomposition. For instance, this property is essential in the Heeger & Bergen texture synthesis algorithm [2,5]. The three building block types (low-pass, high-pass and steered filters) are defined by continuous functions on the Nyquist domain.…”

“…In general none method should be preferred to the others and the choice depends on the desired properties of the filtering. For instance, in our implementation of the Heeger-Bergen pyramid-based texture synthesis algorithm provided in [2], we use method 1 in order to guarantee the exact reconstruction property.…”

“…In practice, the filtering is usually applied by performing discrete Fourier transform (DFT) computations [2,4,8] but, to the best of our knowledge, no clear theoretical justification can be found in the literature. In particular, the interpretations generally involve a trigonometric polynomial interpolation, which is ambiguous for even-sized images, and rely on a convention whose influence on the boundary DFT coefficients should be taken into account.…”

Efros and Freeman Image Quilting Algorithm for Texture Synthesis

“…The synthesis step computes an image that satisfies the statistical constraints estimated during the analysis step. Following the seminal paper of Heeger and Bergen [7,2], several methods are based on statistics of wavelet coefficients or more involved multiscale image representations [12,11,14]. Another approach initially proposed by van Wijk [16], which consists in randomizing the Fourier phase of an image, has been extended to an exemplar-based synthesis method in [6,5].…”