computing 3d geometry directly from range images
DESCRIPTION
Computing 3D Geometry Directly From Range Images. Sarah F. Frisken and Ronald N. Perry Mitsubishi Electric Research Laboratories. Geometry from Range Data A Classic Approach. Subject. Range images. Range surfaces. Final model. Volumetric Methods. - PowerPoint PPT PresentationTRANSCRIPT
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Computing 3D Geometry DirectlyFrom Range Images
Sarah F. Frisken and Ronald N. PerryMitsubishi Electric Research Laboratories
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Geometry from Range DataA Classic Approach
Subject Range images Range surfaces Final model
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Volumetric Methods
• Create a volumetric representation of the object from the range surfaces
• Triangulate the volume data
• Advantages• Robust to scanner noise and image alignment errors• Provide good-quality, water-tight models
• Disadvantages• Resolution limited by volume size• Large memory footprint• Long processing times
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Curless and Levoy (SIGGRAPH ‘96)
• Generate range surfaces from range images
• For each range surface• Compute signed distances to nearby volume points along
the line of sight from the sensor• Weight the computed distance based on uncertainty
• Combine distances using a weighted average
• Triangulate the zero-valued iso-surface of the volume using Marching Cubes
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Wheeler (Ph.D. thesis, CMU ‘96)
True distance
Distance along line-of-sight
• Similar to Curless and Levoy except:• Compute true distances from range surfaces • Compute and store distances in a 3-color octree• Triangulate the octree using a modified Marching Cubes
algorithm
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Our Approach
• Use Adaptively Sampled Distance Fields (ADFs) as the volumetric representation• Reduces computation and memory footprint
• Compute the ADF directly from range images • Avoids generating range surfaces and computing distances from range
surfaces
• Add detail and edit occluded regions directly• ADFs provide a direct and intuitive sculpting interface
• Use a new triangulation method• Fast (200,000 triangles in 0.37 seconds)• Produces optimal triangle models• Produces LOD triangle models
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Distance Fields
2D shape with sampled distances
to its edge
Regularly sampled distance values
2D distance field
-6520
-90-130 -95 -62 -45 -31 -46 -57 -86 -129
-90 -49 -2 17 25 16 -3 -43 -90
-71 -5 30 -4 -38 -32 -3
-46 12 1 -50 -93 -3
• Specify the (possibly) signed distance to a shape
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Regularly Sampled Distance Fields
• Similar to regularly sampled images, insufficient sampling of distance fields results in aliasing
• Because fine detail requires dense sampling, excessive memory is required with regularly sampled distance fields when any fine detail is present
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Adaptively Sampled Distance Fields (ADFs)
• Detail-directed sampling• High sampling rates only where needed
• Spatial data structure (e.g., an octree)• Fast localization for efficient processing
• Reconstruction method (e.g., trilinear interpolation) • For reconstructing the distance field and its gradient
from the sampled distance values
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Advantages of ADFs
ADFs consolidate the data needed to represent complex objects
ADFs provide• Spatial hierarchy
• Distance field
• Object surface
• Object interior
• Object exterior
• Surface normal (gradient at surface)
• Direction to closest surface point (gradient off surface)
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Comparison of 3-color Quadtrees and ADFs
23,573 cells (3-color) 1713 cells (ADF)
• Fewer distance computations• Smaller memory footprint
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Computing ADFs Directly from Range Images
• Range images measure distances along the line-of-sight rather than true distances
• At each ADF sample point• Compute the projected distance to the object surface from the line-of-
sight distance for each range image• Correct each projected distance by dividing by the local gradient
magnitude of the projected distance field to approximate the true distance
• Choose the true distance with the highest confidence
• The local gradient magnitude is constant in the direction perpendicular to the range image• Can be pre-computed and stored as a 2D image
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Editing Occluded Regions and Adding Detail to Scanned Models
• ADFs are a volumetric representation• Provide an intuitive interface for direct sculpting of 3D
models
• Kizamu (Perry and Frisken, SIGGRAPH 2001)
• System for sculpting digital characters• Can sculpt high resolution ADFs (equivalent to 20483
volumes) at interactive rates• Reasonable memory footprint• Produces LOD triangulations of the sculpted models
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Triangulation Method
• Seed• Each boundary leaf cell of the ADF is assigned a vertex
that is initially placed at the cell’s center
• Join• Vertices of neighboring cells are joined to form triangles
• Relax• Vertices are moved to the surface using the distance field
• Improve• Vertices are moved over the surface towards their average
neighbors' position to improve triangle quality
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Creating LOD Triangle Models
• Adapt triangulation to generate LOD models• Traverse octree from root to leaf cells• Seed vertices in (possibly) non-leaf boundary cells that
satisfy a minimum error criterion• Ignore cells below these in the hierarchy
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Results
ADF generated from an 800x800 elevation image of the Grand Canyon
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Results
Sphere generated from 2 range images (synthetic data)
Sphere generated from 14 range images (synthetic data)
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Results
Two views of a cow model generated from 14 range images (synthetic data)
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Summary
• Use of distance fields provides more robust methods and water-tight surfaces
• ADFs result in significant savings in memory and distance computations
• Distances are computed directly from range images rather than from range surfaces
• Resultant models can be directly sculpted to add detail and to edit occluded regions
• Fast new triangulation method produces optimal triangle meshes from the ADF
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Future Work
• Address noise in scanned data• Incorporate probabilistic methods from prior art for
combining multiple scans• Extend probabilistic methods to exploit the distance
field
• Align scans using the distance field (replacing point-based alignment methods such as Iterative Closest Point)
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The End