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Marching Cubes
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Marching Cubes


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Computer Graphics and Animation course
TU Delft

Published in: Technology, Health & Medicine

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  • - Objective paper - Introduction to 3D medical algorithms - Related work
  • Octree: BUT each of these techniques throw away useful information in the original data. The marching cubes approach uses information from the original 3D data to derive inter-slice connectivity, surface location and surface gradient.
  • Explain algorithm Divide and conquer Slices and cubes Intersection cubes and surface 14 patterns Normalized vector and density
  • Implementation Overview Errors
  • Transcript

    • 1. 1Challenge the futureMarching CubesA High Resolution 3D Surface ConstructionAlgorithm
    • 2. 2Challenge the futureIntroduction• Algorithm developed by William E. Lorensen and Harvey E.Cline and published in the 1987 SIGGRAPH proceedings.• Aims to create 3D models from Medical data:• X-ray computed tomography (CT)• Magnetic resonance (MR)• Single-photon emission computedtomography (SPECT)
    • 3. 3Challenge the future3D Medical Algorithms & Related WorkWorkflow:1. Data acquisition: multiple 2D slices2. Image processing to find structures or filter data3. Surface construction4. DisplayApproaches:• Contours of the surface on consecutive slicesconnected with triangles• Creates surfaces from cuberilles• Octree, etc.
    • 4. 4Challenge the futureMarching Cubes Algorithm• Locate surface to a user-specified value• Create triangles• Calculate normals to ensure the quality of the imageIdea
    • 5. 5Challenge the futureMarching Cubes Algorithm• Divide-and-conquer to locate surface in cube• 2 adjacent slices• 4 pixels used on both slices tocreate vertices of cubeLocate surface
    • 6. 6Challenge the futureMarching Cubes Algorithm• Cube vertices are assigned with binary values• One for inside (or on) the surface• Zero for outside the surface• In 2D:Create triangles
    • 7. 7Challenge the futureMarching Cubes Algorithm• In 3D:• 28= 256 casesCreate triangles
    • 8. 8Challenge the futureMarching Cubes Algorithm• Use symmetry and rotation toreduce 256 cases to 14 patterns• Index of 8 bits to numberthe cases• With linear interpolation the surfaceintersection is foundCreate triangles
    • 9. 9Challenge the futureMarching Cubes Algorithm• Final step to increase the quality of the image• With central differences an unit normal can be calculated forevery cube vertex using 4 slices• Interpolation of these normalsCalculate normals
    • 10. 10Challenge the futureImprovements• Efficiency increased by using pixel-to-pixel and line-to-linecoherence.• 3 new edges are needed to interpolate• Other 9 edges are obtained from previous slices, lines or pixels• Reducing slice resolution by averaging four pixels into one• Solid modeling using the three notions “inside”, “outside”,and “on”
    • 11. 11Challenge the futureImplementation and ResultsImplementation• Number of triangles is proportional to the area of the surface = A lot!• Filtering is applied to reduce the resolution and number of trianglesResults• CT• MR• SPECT
    • 12. 12Challenge the futureConclusions• Realism is achieved by the calculation of the normalized gradient• Large number of triangles reduced by surface cutting andconnectivity• The algorithm has some flaws:• high amount of memory needed to store resulting surface• Sign change in the 14 original patterns can lead to mistakes