2010/11/17 by Charles F. Cadieu, Cadieu, Charles F., Kilian Koepsell +1 · 2 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Advanced Image Processing Techniques #Algorithm #Amplitude #Artificial intelligence #Boltzmann distribution #Boltzmann machine #Computer Vision and Pattern Recognition (cs.CV) #Computer science #Computer vision #Deep learning #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Biological sciences #FOS: Computer and information sciences #FOS: Physical sciences #Filter (signal processing) #Generative Adversarial Networks and Image Synthesis #Geometry #Image and Signal Denoising Methods #Linear subspace #Machine Learning (stat.ML) #Mathematics #Neurons and Cognition (q-bio.NC) #Optics #Pattern recognition (psychology) #Phase (matter) #Physics #Statistical physics #Subspace topology #cond-mat.dis-nn #cs.CV #q-bio.NC #stat.ML
paper · pdf · doi:10.48550/arxiv.1011.4058
published in arXiv (Cornell University) (Cornell University) · 11 pages, 6 figures
arxiv created 2010/11/17 · openalex publication_date 2010/11/17 · arxiv updated 2010/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We describe a model for capturing the statistical structure of local amplitude and local spatial phase in natural images. The model is based on a recently developed, factorized third-order Boltzmann machine that was shown to be effective at capturing higher-order structure in images by modeling dependencies among squared filter outputs (Ranzato and Hinton, 2010). Here, we extend this model to Lp-spherically symmetric subspaces. In order to model local amplitude and phase structure in images, we focus on the case of two dimensional subspaces, and the L2-norm. When trained on natural images the model learns subspaces resembling quadrature-pair Gabor filters. We then introduce an additional set of hidden units that model the dependencies among subspace phases. These hidden units form a combinatorial mixture of phase coupling distributions, concentrated in the sum and difference of phase pairs. When adapted to natural images, these distributions capture local spatial phase structure in natural images.