Video sequences contain rich dynamic patterns, such as dynamic texture patterns that exhibit stationarity in the temporal domain, and action patterns that are non-stationary in either spatial or temporal domain. We show that an energy-based spatial-temporal generative ConvNet can be used to model and synthesize dynamic patterns. The model defines a probability distribution on the video sequence, and the log probability is defined by a spatial-temporal ConvNet that consists of multiple layers of spatial-temporal filters to capture spatial-temporal patterns of different scales. The model can be learned from the training video sequences by an “analysis by synthesis” learning algorithm that iterates the following two steps. Step 1 synthesizes video sequences from the currently learned model. Step 2 then updates the model parameters based on the difference between the synthesized video sequences and the observed training sequences. We show that the learning algorithm can synthesize realistic dynamic patterns. We also show that it is possible to learn the model from incomplete training sequences with either occluded pixels or missing frames, so that model learning and pattern completion can be accomplished simultaneously.
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This content will become publicly available on December 15, 2026
Decomposition of Beatty and Complementary Sequences
In this paper, we express the difference of two complementary Beatty sequences as the sum of two other closely related Beatty sequences. In the process, we introduce a new algorithm that generalizes the well-known Minimum Excluded algorithm and provides a method to combinatorially generate any pair of complementary Beatty sequences in a natural way.
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- Award ID(s):
- 2316986
- PAR ID:
- 10649935
- Publisher / Repository:
- Journal of Integer Sequences Colgate University
- Date Published:
- Journal Name:
- Integers: Electronic Journal of Combinatorial Number Theory
- ISSN:
- ###############
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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