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3D gradient enhancement

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Abstract

Enhancement can exaggerate visual details in both image processing and 3D rendering. In this paper, we adapt the gradient enhancement technique from image processing to 3D rendering through differentiating the rendering result with respect to the image space coordinates under point lighting. In this way, we can achieve 3D enhancement taking into account the gradient of geometry, projection transform, visibility and highlight. We also propose a tunable shape descriptor for users to achieve rendering results in different enhancement extent. Moreover, we extend this method to the environment lighting with some simplifications. Finally, we demonstrate that our method can handle the grazing angle area and the edges of sharp slope better than the previous method due to the gradient of the projection transform.

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Acknowledgements

Many thanks to Romain Vergne et al. for sharing their OpenGL Shader source code, the anonymous reviewers for their valuable comments and Ming Zeng and Bo Jiang for proof reading. The testing scenes are courtesy of Stanford 3D Scanning Repository (Armadillo and Dragon). This work was partially supported by NSFC (No. 60970074), Fok Ying-Tong Education Foundation and the Fundamental Research Funds for the Central Universities.

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  1. State Key Lab of CAD&CG, Zhejiang University, Zhejiang, China

    Fukai Zhao & Xinguo Liu

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  1. Fukai Zhao
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  2. Xinguo Liu
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Correspondence to Fukai Zhao.

Appendix:  The derivation of ∇n(x), ∇G Ph(x) and ∇ω i (x)

Appendix:  The derivation of ∇n(x), ∇G Ph(x) and ∇ω i (x)

We take triangle meshes as the input data. Let T be the triangle that contains the point x. Denote the vertices of triangle T by x 0, x 1 and x 2. The barycentric coordinates, b v (x)=[b 0(x),b 1(x),b 2(x)]T, can be evaluated by

where |T| represents the area of the triangle, and n T is the normal of the triangle. Thus, we can interpolate the normal at point x by vertex normals N v of the triangle using the barycentric coordinates b v (x), and then normalize it as

$$\mathbf{n}(\mathbf{x}) = \frac{\mathbf{h}(\mathbf{x})}{\|\mathbf {h}(\mathbf{x})\|},\qquad \mathbf{h}(\mathbf{x}) = N_v \mathbf{b}_v(\mathbf{x}), $$

where N v =[n 0,n 1,n 2] is the matrix of vertex normals.

Therefore, the gradient of the normal can be approximated by

The gradient of barycentric coordinates, ∇b v (x), can be evaluated by

As we have defined G Ph(x)=〈r(x),ω o (x)〉a, we can evaluate its gradient as

According to the definition of r(x) in Sect. 3.2, its gradient can be evaluated by

The derivation of ∇n(x) is given in Sect. 3.2. The gradient of ω i (x) and ω o (x) can be evaluated by

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Zhao, F., Liu, X. 3D gradient enhancement. Vis Comput 30, 113–126 (2014). https://doi.org/10.1007/s00371-013-0787-3

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