What are the main issues that need to be considered when using the iterative method?

A number of issues needs to be considered when using the iterative method since the lack of smoothness and the irregularity of the triangle mesh might compromise the robustness of the method.

What is the construction of a graph?

The authors will describe the construction of a graph G = (N,A) containing weighted node set N and directed arc set A. Graph nodes represent the volume voxels, so the authors write N = {n(x, y, z)} for the nodes and w(x, y, z) for the corresponding node weights.

What is the graph column for a layered surface detection problem?

In this case the graph columns correspond to the rays of radial samples in a volumetric data where each radial ray has four neighbours, two axial and two tangential.

What is the method for detecting a surface?

Each surface detection step is solved by an efficient graph cut based algorithm which guarantees theoptimal solution within the search lines.

What is the result of the rough surface refinement?

As a result, to detect an elongated surface, quite a few iterations might be required – in each iteration a surface approaches the data in the graph cut surface refinement step, but is immediately after pulled back by smoothing.

Why is it difficult to choose the right inter column shift constraints?

choosing suitable inter column shift constraints would be problematic, due to the big distortion of the gridin polar regions.

What is the process of defining the transformation of the data into on-surface and/or?

This involves defining the transformation of the data into on-surface and/or in-region costs, e.g. by computing the spatial gradients or the probabilities of the voxels belonging to a region.

What is the cost function for a layered surface detection problem?

The cost function, originally pertaining only to where the data supports the surface, has been extended to incorporate in-region cost, i.e. knowledge about the region above, under or between the surfaces to be detected [15], [16].

Open AccessProceedings Article10.1109/3DV.2014.60

Surface Detection Using Round Cut

Q: What have the authors stated for future works in "Surface detection using round cut" ?

9 ) Future work: To alleviate the convergence problem, the authors plan to incorporate mesh optimization in each iterative step of Round Cut. The authors also plan to extend the Round Cut algorithm with an adaptive mesh subdivision, only in areas where the resolution is small and/or where curvature is high. Having a mesh of a higher quality, with well shaped triangles, will make a calculations of normals less sensitive to noise.

Vedrana Andersen Dahl, +2 more

- 08 Dec 2014

- Vol. 2, pp 82-89

TL;DR: This work proposes an iterative method for detecting closed surfaces in a volumetric data, where an optimal search is performed in a graph build upon a triangular mesh, capable of capturing complex geometries by iteratively refining the surface.

Abstract: We propose an iterative method for detecting closed surfaces in a volumetric data, where an optimal search is performed in a graph build upon a triangular mesh. Our approach is based on previous techniques for detecting an optimal terrain-like or tubular surface employing a regular grid. Unlike similar adaptations for triangle meshes, our method is capable of capturing complex geometries by iteratively refining the surface, where we obtain a high level of robustness by applying explicit mesh processing to intermediate results. Our method uses on-surface data support, but it also exploits data information about the region inside and outside the surface. This provides additional robustness to the algorithm. We demonstrate the capabilities of the approach by detecting surfaces of CT scanned objects.

AI Agents for this Paper

Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps

Most frequently asked questions

1. What are the contributions mentioned in the paper "Surface detection using round cut" ?

The authors propose an iterative method for detecting closed surfaces in a volumetric data, where an optimal search is performed in a graph build upon a triangular mesh.. Their approach is based on previous techniques for detecting an optimal terrain-like or tubular surface employing a regular grid.. This provides additional robustness to the algorithm.. The authors demonstrate the capabilities of the approach by detecting surfaces of CT scanned objects.

2. What have the authors stated for future works in "Surface detection using round cut" ?

9 ) Future work:. To alleviate the convergence problem, the authors plan to incorporate mesh optimization in each iterative step of Round Cut.. The authors also plan to extend the Round Cut algorithm with an adaptive mesh subdivision, only in areas where the resolution is small and/or where curvature is high.. Having a mesh of a higher quality, with well shaped triangles, will make a calculations of normals less sensitive to noise.

3. How many vertices are added to the mesh?

Initially the inter-column shift is set to 20 and is reduced to 10, 5 and 2 after each subdivision to reflect the reduction in vertex distances when new vertices are added.

4. What is the input to a layered surface detection problem?

The input to a layered surface detection problem is a 4D cost con(x, y, z, k), takingsmall values where a volume data I(x, y, z) supports the surface k.

Figure 1. Example of the iterative surface detection. (a) the mesh is initialized as a polyhedron and in (b-d) the boundary iteratively adapts to the data.

Figure 2. A photograph of hamster objects used for testing the Round Cut algorithm.

Figure 5. Comparing Round Cut (a) with a single step approach (b) by detecting a surface of a hamster object from a noise-free scan.

Figure 6. Another comparison of the Round Cut (a) and a single-step approach (b).

Figure 4. Detecting a surface of another hamster object, with the same five steps as in Fig. 3. Only the outer object boundary is detected and a sagittal plane is shown.

Figure 3. Detecting a surface of a hollow hamster object consisting of four parts fitted together. The top row shows surfaces, while the bottom row shows a slice of the volumetric CT data displaying coronal plane together with the segmentation contours. The blue dot is the initialization point, (a) shows initial rough surfaces defining outer and inner object boundary, (b-d) are three iterations of subdivision and surface refinement followed by smoothing, and (e) shows the result after the final graph cut surface refinement.

Citations

•Journal Article•10.1016/j.nima.2023.168011

A flexible event reconstruction based on machine learning and likelihood principles

Philipp Eller, +5 more

- 22 Aug 2022

- Nuclear instruments and methods in physi...

TL;DR: In this paper , the full likelihood for a many-sensor detector can be broken apart into smaller terms, and then neural networks can be trained to approximate all terms solely based on forward simulation, which results in a fast, flexible, and close-to-optimal surrogate model proportional to the likelihood.

...read moreread less

•Proceedings Article•10.1109/CVPR42600.2020.01279

Sparse Layered Graphs for Multi-Object Segmentation

Niels Jeppesen, +3 more

- 14 Jun 2020

TL;DR: This work forms a general method for adding containment and exclusion interaction constraints to layered graphs, and proposes three algorithms for further reducing the spatial complexity of SLGs, by using ordered multi-column graphs.

...read moreread less

Proceedings Article•10.1109/ISBI.2016.7493408

Automatic measurement of orbital volume in unilateral coronal synostosis

Vedrana Andersen Dahl, +7 more

- 13 Apr 2016

TL;DR: This work proposes a method with higher degree of automation based on finding an optimal smooth closed surface for rapid evaluation of orbital volume in UCS, and obtains similar measures, as well as high Dice scores, compared to the experts.

...read moreread less

•Proceedings Article•10.1109/ICPR.2018.8545715

Layered Surface Detection for Virtual Unrolling

Vedrana Andersen Dahl, +3 more

- 01 Aug 2018

TL;DR: The unrolled image is undistorted, and the surface structures may be accurately quantified making the approach a good candidate for an industrial application of virtual unrolling.

...read moreread less

Journal Article•10.48550/arXiv.2305.06341

Non-Euclidean Motion Planning with Graphs of Geodesically-Convex Sets

Thomas Cohn, +3 more

- 10 May 2023

- arXiv.org

TL;DR: In this paper , a reduction procedure for the zero-curvature case to a mixed-integer convex optimization problem is presented, where configuration spaces are modeled as Riemannian manifolds.

...read moreread less

References

•Journal Article•10.1109/TPAMI.2004.60

An experimental comparison of min-cut/max- flow algorithms for energy minimization in vision

Yuri Boykov, +1 more

- 01 Sep 2004

- IEEE Transactions on Pattern Analysis an...

TL;DR: This paper compares the running times of several standard algorithms, as well as a new algorithm that is recently developed that works several times faster than any of the other methods, making near real-time performance possible.

...read moreread less

4.7K

•Book Chapter•10.1007/3-540-44745-8_24

An Experimental Comparison of Min-cut/Max-flow Algorithms for Energy Minimization in Vision

Yuri Boykov, +1 more

- 03 Sep 2001

TL;DR: The goal of this paper is to provide an experimental comparison of the efficiency of min-cut/max flow algorithms for applications in vision, comparing the running times of several standard algorithms, as well as a new algorithm that is recently developed.

...read moreread less

4.4K

Proceedings Article•10.1145/218380.218473

A signal processing approach to fair surface design

Gabriel Taubin

- 15 Sep 1995

TL;DR: A very simple surface signal low-pass filter algorithm that applies to surfaces of arbitrary topology that is a linear time and space complexity algorithm and a very effective fair surface design technique.

...read moreread less

2.1K

Journal Article•10.1145/78956.78958

A butterfly subdivision scheme for surface interpolation with tension control

Nira Dyn, +2 more

- 01 Apr 1990

- ACM Transactions on Graphics

TL;DR: A new interpolatory subdivision scheme for surface design is presented that is designed for a general triangulation of control points and has a tension parameter that provides design flexibility.

...read moreread less

916

•Journal Article•10.1109/TPAMI.2006.19

Optimal Surface Segmentation in Volumetric Images-A Graph-Theoretic Approach

Kang Li, +3 more

- 01 Jan 2006

- IEEE Transactions on Pattern Analysis an...

TL;DR: An optimal surface detection method capable of simultaneously detecting multiple interacting surfaces, in which the optimality is controlled by the cost functions designed for individual surfaces and by several geometric constraints defining the surface smoothness and interrelations is developed.

...read moreread less

778

Surface Detection Using Round Cut

Chat with Paper

AI Agents for this Paper

Most frequently asked questions

1. What are the contributions mentioned in the paper "Surface detection using round cut" ?

2. What have the authors stated for future works in "Surface detection using round cut" ?

3. How many vertices are added to the mesh?

4. What is the input to a layered surface detection problem?

5. What are the main issues that need to be considered when using the iterative method?

6. What is the construction of a graph?

7. What is the graph column for a layered surface detection problem?

8. What is the method for detecting a surface?

9. What is the result of the rough surface refinement?

10. Why is it difficult to choose the right inter column shift constraints?

11. What is the process of defining the transformation of the data into on-surface and/or?

12. What is the cost function for a layered surface detection problem?

Figures

Citations

A flexible event reconstruction based on machine learning and likelihood principles

Sparse Layered Graphs for Multi-Object Segmentation

Automatic measurement of orbital volume in unilateral coronal synostosis

Layered Surface Detection for Virtual Unrolling

Non-Euclidean Motion Planning with Graphs of Geodesically-Convex Sets

References

An experimental comparison of min-cut/max- flow algorithms for energy minimization in vision

An Experimental Comparison of Min-cut/Max-flow Algorithms for Energy Minimization in Vision

A signal processing approach to fair surface design

A butterfly subdivision scheme for surface interpolation with tension control

Optimal Surface Segmentation in Volumetric Images-A Graph-Theoretic Approach

Related Papers (5)

Triangle mesh-based edge detection and its application to surface segmentation and adaptive surface smoothing

3D non-rigid deformable surface estimation without feature correspondence

Image-based multiresolution shape recovery by surface deformation

Regular 3D mesh reconstruction based on cylindrical mapping

Effectivity of spherical object reconstruction using star-shaped simplex meshes