Manifolds of Natural Stochastic Textures

Supplementary material for: Ido Zachevsky and Yehoshua Y. Zeevi, Manifold-based analysis of natural stochastic textures with application in texture synthesis, submitted (2017).

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Texture synthesis

Synthesis of a new texture (middle) by two source textures (left and right columns)

Synthesis of textures with reduced descriptor dimensions

Original synthesis (Gatys et al., 2015) (columns 1,2), and synthesis with order of magnitude less parameters (columns 3,4)

Synthesis of textures with reduced descriptor dimensions

The fundamental features Hurst, Kurtosis (indicates Gaussianity) and coherence (related to local phase) emerge naturally by the manifold.

Traveling between two images in the manifold

Intrinsic path (red) travels more gradually, within the manifold. Euclidean path shown in blue.

Top row: intrinsic path, bottom row: Euclidean path. Neighboring images are semantically closer in the intrinsic path.

First PCA coefficient (63% explained variance) of images in intrinsic path (red) vs. Euclidean path (blue). A more gradual path, corresponding to the images in the path.

Smoothness of parameters in the manifold

Synthesized images exhibit continuous texture features within the manifold.
Images are synthesized for all values of 0 < α < 1 from two images: α=0 and α=1.

Intrinsic clustering: Metric K-means

K-means with manifold-based distances yields better clustering.

Cluster entropy (lower is better)