# LEARNING NONLINEAR MANIFOLDS OF DYNAMIC TEXTURES

### Ishan Awasthi, Ahmed Elgammal

#### 2006

#### Abstract

Dynamic textures are sequences of images of moving scenes that show stationarity properties in time. Eg: waves, flame, fountain, etc. Recent attempts at generating, potentially, infinitely long sequences model the dynamic texture as a Linear Dynamic System. This assumes a linear correlation in the input sequence. Most real world sequences however, exhibit nonlinear correlation between frames. In this paper, we propose a technique of generating dynamic textures using a low dimension model that preserves the non-linear correlation. We use nonlinear dimensionality reduction to create an embedding of the input sequence. Using this embedding, a nonlinear mapping is learnt from the embedded space into the image input space. Any input is represented by a linear combination of nonlinear bases functions centered along the manifold in the embedded space. A spline is used to move along the input manifold in this embedded space as a similar manifold is created for the output. The nonlinear mapping learnt on the input is used to map this new manifold into a sequence in the image space. Output sequences, thus created, contain images never present in the original sequence and are very realistic.

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#### Paper Citation

#### in Harvard Style

Awasthi I. and Elgammal A. (2006). **LEARNING NONLINEAR MANIFOLDS OF DYNAMIC TEXTURES** . In *Proceedings of the First International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP,* ISBN 972-8865-40-6, pages 243-250. DOI: 10.5220/0001378202430250

#### in Bibtex Style

@conference{visapp06,

author={Ishan Awasthi and Ahmed Elgammal},

title={LEARNING NONLINEAR MANIFOLDS OF DYNAMIC TEXTURES},

booktitle={Proceedings of the First International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP,},

year={2006},

pages={243-250},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001378202430250},

isbn={972-8865-40-6},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the First International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP,

TI - LEARNING NONLINEAR MANIFOLDS OF DYNAMIC TEXTURES

SN - 972-8865-40-6

AU - Awasthi I.

AU - Elgammal A.

PY - 2006

SP - 243

EP - 250

DO - 10.5220/0001378202430250