Surface Reconstruction Using Power Watershed

Abstract

Abstract. Surface reconstruction from a set of noisy point measurements has been a well studied problem for several decades. Recently, variational and discrete optimization approaches have been applied to solve it, demonstrating good robustness to outliers thanks to a global energy minimization scheme. In this work, we use a recent approach embedding several optimization algorithms into a common framework named power watershed. We derive a specific watershed algorithm for surface reconstruction which is fast, robust to markers placement, and produces smooth surfaces. Experiments also show that our proposed algorithm compares favorably in terms of speed, memory requirement and accuracy with existing algorithms.

A tutorial on applications of power watershed optimization to image processing

“…Essentially, domain knowledge of the physical characteristics of astronomical images can be incorporated into the weights of edges. PW has also been used for other interesting applications such as surface reconstruction [16] and estimation of separating planes between touching 3D objects [34]. Anisotropic diffusion for L0 [17] is another interesting direction of research.…”

A graph-based mathematical morphology reader

“…From a noisy set of point measurements (left), a dedicated watershed algorithm with global optimality properties computes a smooth surface (right). The algorithm is fast, robust to seed placements, and compares favorably with existing algorithms (Couprie et al, 2011a) them. The authors would also like to thank Hugues Talbot and Christian Ronse for their careful reading of the paper.…”

“…Although energy minimization approaches seem hardly related to the morphological approach based on lattice theory (Serra, 2006), there exists a framework (called the powerwatershed framework (Couprie et al, 2011b)) in which graphcuts (Boykov et al, 2001), shortest paths , random walks (Grady, 2006) and watershed cuts (Cousty et al, 2009a), can all be unified together, and in which we can study their links and differences. Many applications can be designed thanks to this framework, including some that are surprising for morphology: for example the (power) watershed can now be used to perform the anisotropic diffusion process or to produce a surface reconstruction from unstructured cloud points (Couprie et al, 2011a) (see Fig. 10).…”

Gems - Geometric Median Shapes

“…Others have applied the watershed method to solve optimization problems on either a graph or a discrete grid. For example, Cuprie et al [24] used the Power Watershed [25] in their formulation of the surface reconstruction from point cloud problem to minimize a weighted total variation functional where weights are proportional to Euclidean distances between points.…”