Equivalence of Julesz Ensembles and FRAME Models

By Ying Nian Wu, Song-Chun Zhu, Xiuwen Liu. 2000

86 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Atmospheric Science, Computer Vision and Pattern Recognition, Probabilistic & Bayesian Methods

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Citations in the corpus

Learning Energy-Based Spatial-Temporal Generative ConvNets for Dynamic Patterns (2019, methodology): “The FRAME (Filters, Random fields, And Maximum Entropy) model [31], [32], [33] is a Markov”
Learning Non-Convergent Non-Persistent Short-Run MCMC Toward Energy-Based Model (2019, methodology): “An early version of EBM is the FRAME (Filters, Random field, And Maximum Entropy) model [51, 45, 50], which is an exponential family model, where the features are the responses from a bank of filters.”
On the Anatomy of MCMC-based Maximum Likelihood Learning of Energy-Based Models (2019, background): “The RBM [15] and FRAME (Filters, Random field, And Maximum Entropy) [43, 35] model introduce energy functions with greater representational capacity.”
Divergence Triangle for Joint Training of Generator Model, Energy-Based Model, and Inferential Model (2018, methodology): “An early version of the energy-based model is the FRAME (Filters, Random field, And Maximum Entropy) model [6], [7].”
Video Primal Sketch: A Unified Middle-Level Representation for Video (2015, methodology): “According to the theorem of ensemble equivalence (Wu et al (2000)), the Gibbs distribution converges to the uniform distribution over the set ΩK(hj) in (7), when Λim,j is large enough.”
On Learning Non-Convergent Short-Run MCMC Toward Energy-Based Model (2019, methodology): “An early version of EBM is the FRAME (Filters, Random field, And Maximum Entropy) model [56, 47, 55], which is an exponential family model, where the features are the responses from a bank of filters.”
From BoW to CNN: Two Decades of Texture Representation for Texture Classification (2018, background): “At the end of the last century there was a renaissance of texton-based approaches, including Zhu et al. [248, 249, 270, 271, 269, 272] on the mathematical modelling of textures and textons.”
Natural Image Statistics for Natural Image Segmentation (2003, unknown): “Recently, the statistics of £lter outputs turned out to provide powerful and general models for image statistics and texture [29, 30, 17, 16, 27].”
Learning Generative Models via Discriminative Approaches (2007, background): “The existing generative model learning frameworks [11, 3, 21, 23] have difﬁculty in capturing patterns of high complexity.”
Introspective Classification with Convolutional Nets (2017, background): “Our progressively learned discriminative classifier can be viewed as carving out the feature space on φ(x), which essentially becomes an equivalent class for the positives; the volume of the equivalent class that satisfies the condition is exponentially large, as analyzed in [46].”
From Information Scaling of Natural Images to Regimes of Statistical Models (2007, background): “Borrowing this insight, Wu, Zhu, and Liu (2000) considered the following ensemble, which is called micro-canonical ensemble in statistical physics (Chandler, 1987): Π = {I : Hk(I) = Ĥk,∀k}, (18) where Ĥk can be estimated from observed image.”