Pattern Theory: From Representation to Inference

By U. Grenander, M. Miller. 2007

239 citations recorded by the source corpus.

Subfields: 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, background): “In the pattern theory [18], [19] of Grenander, a visual pattern is represented by a probability distribution.”
Learning Non-Convergent Non-Persistent Short-Run MCMC Toward Energy-Based Model (2019, methodology): “The maximum likelihood learning of the energy-based model (EBM) [32, 55, 22, 44, 33, 37, 8, 35, 52, 53, 25, 9, 51] follows what Grenander [17] called “analysis by synthesis” scheme.”
Learning Descriptor Networks for 3D Shape Synthesis and Analysis (2018, methodology): “The training of the proposed model follows an “analysis by synthesis” scheme [7].”
Testing for Homogeneity with Kernel Fisher Discriminant Analysis (2007, background): “This problem arises in many applications, ranging from computational an tomy [10] to process monitoring [7].”
Cooperative Training of Descriptor and Generator Networks (2016, methodology): “˜ Y i In the two diagrams in (15 The learning of both the descriptor and the generator follows the “analysis by synthesis” principle (Grenander & Miller, 2007).”
Diffeomorphic registration using geodesic shooting and Gauss–Newton optimisation (2011, unknown): “, 2008, 2009) or in various textbooks (Younes, 2010; Holm et al., 2009; Grenander and Miller, 2007).”
Consistent estimation of a population barycenter in the Wasserstein space (2013, methodology): “In this setting, a widely used approach is Grenander’s pattern theory [19, 20, 34, 35] that models geometric variability by the action of a Lie group on an infinite dimensional space of curves (or images).”
Facial expressions of emotion are not culturally universal (2012, methodology): “Like a generative grammar (19, 20), we randomly generated all possible three-dimensional facial movements (see Movie S1 for an example).”
Building a Telescope to Look Into High-Dimensional Image Spaces (2018, methodology): “Gibbs distributions defined on a pixel graph have been widely used as an effective family for modeling patterns of real images [13, 17, 18, 52, 53].”
AOGNets: Compositional Grammatical Architectures for Deep Learning (2017, background): “Compositionality, recon-ﬁgurability and lateral connectivity are well-known principles in cognitive science, neuroscience and pattern theory [12, 44, 17, 13, 31, 13].”
Characterization of barycenters in the Wasserstein space by averaging optimal transport maps (2012, methodology): “In the presence of geometric variability in time or space in the data, a widely used approach is Grenander’s pattern theory [25, 26, 40, 41] that models such a variability by the action of a Lie group on an infinite dimensional space of curves or images.”
Brain templates and atlases (2012, unknown): “…and Friston, 2005, 2009, 2011, Ashburner and Klöppel, 2010; Auzias et al., 2011; Beg et al., 2005; Christensen et al., 1997; Chung et al., 2001; Grenander and Miller, 2007; Guo et al., 2005; Lian and Davatzikos, 2011; Miller, 2004; Miller et al., 1993, 2002, 2006; Thompson and Toga, 1996,…”
On Learning Non-Convergent Short-Run MCMC Toward Energy-Based Model (2019, methodology): “The maximum likelihood learning of the energy-based model (EBM) [28, 56, 19, 41, 29, 35, 4, 32, 49, 54, 21, 5, 48], or the Gibbs distribution, follows what Grenander [15] called “analysis by synthesis” scheme.”
AOGNets: Deep AND-OR Grammar Networks for Visual Recognition (2017, background): “e space in Fig.2(a) in a way better than existing networks? Compositionality, reconﬁgurability and lateral connectivity are well-known principles in cognitive science, neuroscience and pattern theory [13,47,19,14,34,14]. They are fundamental for the remarkable capabilities possessed by humans, of le”