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Image morphing with conformal welding

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Abstract

We address the issue of deforming an image of a source object to that of a target. Previous works including barycentric coordinates and functional maps can hardly enforce shape consistency, especially for the objects with complex nested shape components. We leverage the conformal welding theory that maps 2D shapes (planar contours) to the automorphisms of the unit circle, named shape signatures. Conformal welding enables us to apply the Laplacian constraint to deformations in the signature space (or unit circle domain), which renders efficiency and flexibility. Additionally, we are able to fully reconstruct complex shape contours from deformed signatures, and hence generate the morphed images for target shapes. The experiments on complex shape contours and facial images, where multiple components exist, validate the effectiveness of the proposed approach.

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Notes

  1. See [26] for a brief review on the techniques before 2000.

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Acknowledgments

This work is partially supported by the Natural Science Foundation of China (NSFC) under Grant Nos. 61272371 and 61328206, and also by the Civil Aviation Administration of China and NSFC jointly funded project (U1233110).

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Authors and Affiliations

  1. Key Laboratory for Ubiquitous Network and Service Software of Liaoning Province, School of Software, Dalian University of Technology, Dalian, China

    Xin Fan, Yuyao Feng & Zhongxuan Luo

  2. Computer Science Department, Stony Brook University, Stony Brook, USA

    Zhi Chai & Xianfeng David Gu

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  1. Xin Fan
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  2. Yuyao Feng
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  3. Zhi Chai
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  4. Xianfeng David Gu
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  5. Zhongxuan Luo
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Correspondence to Xin Fan.

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Fan, X., Feng, Y., Chai, Z. et al. Image morphing with conformal welding. Vis Comput 32, 1191–1203 (2016). https://doi.org/10.1007/s00371-015-1188-6

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