CS 175

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CS 175 Week 1Point Cloud BasicsAcquisition
and Data Structures
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Data Sources

• point clouds generated by
• measurements
• 3D scan, meteorology, geology
• experiments
• numerical simulation
• evaluation

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Point Properties

• dimension
• 1.5D function values along a line
• 2D positions in the plane
• 2.5D function values in the plane
• 3D positions in 3D
• nD multi-modal data
• measurement error

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Data Structures

• Requirements
• access point values (coordinates)
• find neighbours
• within a certain radius r
• the k nearest neighbours

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Storing Values

• vector of values
• values per element
• unique index for every point
• convenient access vi.x,y,z
• but hard to find neighbours

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Octrees

• Hierarchical spatial data structure
• divide-and-conquer
• binary subdivision

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Octrees

• each node contains
• dimensions xmin,xmax x ymin,ymax x
  zmin,zmax
• pointers to eight children
• empty for leaf-nodes
• unique label e.g., p-adic number, p2d1

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Octrees

• 1D example

0011
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Points and Octrees

• store points in an octree
• points reference to node (label)
• leaf nodes list of points (indices)
• subdivision criterion
• maximum number of points

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Creating the Octree

• loop over all points
• find leaf that contains it
• O(l), l octree depth
• add point to this leaf-node

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Creating the Octree

• add point to leaf-node
• add point-index to list
• store node-label in point
• if list-size exceeds maximum
• split this node

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Creating the Octree

• split node
• create sub-nodes
• assign points in list to sub-nodes
• update node-references for points

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Algorithms

• finding neighbours of a point
• within certain radius r
• the k nearest
• two-step process
• create queue of candidate nodes
• consider points contained therein

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Neighbours within Radius

• queue q of nodes
• traverse octree, e.g. depth first
• add leaf-node to q if dmin lt r
• for all nodes in q
• for all points in the node
• if d lt r then add as neighbour

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k Nearest Neighbours

• priority queue q1(dmin) of nodes
• priority queue q2(d) of points
• add root-node to q1
• while q1 not empty, get front
• if not leaf-node, add children to q1, continue
• if node close enough ( dmin lt q2k )
• add all points in node to q2
• take first k elements of q2 as neighbours

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Beyond Octrees

• non-standard octrees
• not axis-aligned
• no uniform subdivision
• binary space-partioning (BSP) trees
• recursive subdivision witharbitrary planes

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Whats Next?

• Thursday
• 3D scanning presentation
• field trip scan Tech spots
• Homework
• scout suitable sites
• make (digital) photos