Defining Point-Set Surfaces Nina Amenta Yong Joo Kil SIGGRAPH 2004 - - PowerPoint PPT Presentation

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May 11, 2023 502 likes •685 views

Defining Point-Set Surfaces Nina Amenta Yong Joo Kil SIGGRAPH 2004 11/2/2005 1 Point-Set Surfaces Surface S implied by the point cloud P No connectivity Surface properties Does x belong to S Project x to S 11/2/2005 2

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Defining Point-Set Surfaces

Nina Amenta Yong Joo Kil SIGGRAPH 2004

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Point-Set Surfaces

Surface S implied by the point cloud P

– No connectivity

Surface properties

– Does x belong to S – Project x to S

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MLS Surface

Given a point cloud P and a point r near P
1. Find (a, t) that minimizes

Weights depend on an unknown plane

r

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MLS Surface

Local minima over occur at discrete

set of inputs (a, t)

2. Define f(r) to be x nearest to r
3. Stationary points of f form the MLS surface

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MLS Surface

Need to solve optimization problem to find

f(r)

– Expensive – Original paper proposed that one iteration is enough

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MLS Projection

Levin’s method, minimizes
Not a projection

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MLS Energy

Rewrite in terms of a point and a direction

– Domain is

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Explicit MLS Definition

Define
MLS surface consists of points x such that

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Extremal Surfaces

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MLS Projection

PointShop method (linear approximation)

– Alternate searching for x and best-fit plane

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New MLS Projection

Search for local minima along lx, n(x)

– If this process converges, it produces a point on S

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Projection Results

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Comparison with Levin’s Method

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MLS for Surfels

Input (pi, ai)

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Varying Normal Weight

Distance function favors the normal component

All weights equal

Only normals

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MLS for Weighted Point Clouds

Separate weight for each point