SurfCut: Free-Boundary Surface Extraction
We present SurfCut, an algorithm for extracting a smooth simple surface with unknown boundary from a noisy 3D image and a seed point. In contrast to existing approaches that extract smooth simple surfaces with boundary, our method requires less user input
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Abstract. We present SurfCut, an algorithm for extracting a smooth simple surface with unknown boundary from a noisy 3D image and a seed point. In contrast to existing approaches that extract smooth simple surfaces with boundary, our method requires less user input, i.e., a seed point, rather than a 3D boundary curve. Our method is built on the novel observation that certain ridge curves of a front propagated using the Fast Marching algorithm are likely to lie on the surface. Using the framework of cubical complexes, we design a novel algorithm to robustly extract such ridge curves and form the surface of interest. Our algorithm automatically cuts these ridge curves to form the surface boundary, and then extracts the surface. Experiments show the robustness of our method to errors in the data, and that we achieve higher accuracy with lower computational cost than comparable methods. Keywords: Segmentation · Surface extraction · Fast Marching methods · Minimal path methods · Cubicle complexes
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Introduction
Minimal path methods [2], built on the Fast Marching algorithm [3], have been widely used in computer vision. They provide a framework for extracting continuous curves from possibly noisy images. They have been used for instance in edge detection [4] and object boundary detection [5], mainly in interactive settings as they typically require user defined seed points. Because of their ability to provide continuous curves, robust to clutter and noise in the image, generalizations of these techniques to extract the equivalent of edges in 3D images, which form surfaces, have been attempted [6,7]. These methods apply to extracting a surface with a boundary that forms a curve, possibly in 3D, which we call a free-boundary. Extraction of surfaces with free-boundary is important in various applications, including medical (e.g., the outer wall of ventricles forms a surface with boundary) [8] and scientific imaging (e.g., fault surfaces in seismic images) [9]. In [8] an alternative method to extract such surfaces, based on the theory of Electronic supplementary material The online version of this chapter (doi:10. 1007/978-3-319-46478-7 11) contains supplementary material, which is available to authorized users. c Springer International Publishing AG 2016 B. Leibe et al. (Eds.): ECCV 2016, Part VII, LNCS 9911, pp. 171–186, 2016. DOI: 10.1007/978-3-319-46478-7 11
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M. Algarni and G. Sundaramoorthi
Fig. 1. SurfCut determines a surface whose boundary is a 3D curve from a noisy image. [Left]: The result of a competing method [1] contains holes and inaccurate surface boundary caused by noise. [Right]: SurfCut results in accurate surfaces without holes. (Color figure online)
minimal surfaces, is provided. However, existing approaches to surface extraction for surfaces with free-boundary have a limitation - they require the user to provide the boundary of the surface or other user laborious input. In this paper, we build on Fast Marching algorithms to create an algorithm for extracting the boundary of a surface from a 3D i
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