Signed Distance Function Representation, Tracking, and Mapping - - PowerPoint PPT Presentation

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Signed Distance Function Representation, Tracking, and Mapping - - PowerPoint PPT Presentation

Mar 11, 2024 5.1k likes •6.02k views

Signed Distance Function Representation, Tracking, and Mapping Tanner Schmidt Overview - Explicit and implicit surface representations - SDF fusion - SDF tracking - Related research - KinectFusion - Patch Volumes - DART -

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Signed Distance Function Representation, Tracking, and Mapping

Tanner Schmidt

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Overview

  • Explicit and implicit surface representations
  • SDF fusion
  • SDF tracking
  • Related research
  • KinectFusion
  • Patch Volumes
  • DART
  • DynamicFusion
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Overview

  • Explicit and implicit surface representations
  • SDF fusion
  • SDF tracking
  • Related research
  • KinectFusion
  • Patch Volumes
  • DART
  • DynamicFusion
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Explicit Surface Representations

  • Geometry is stored explicitly as a list of points, triangles, or other geometric fragments
  • e.g. meshes, point clouds

Vertices: [ (x0, y0, z0), (x1, y1, z1), …, (xn, yn, zn) ] Indices: [ (i0, i1), (i2, i3), …, (in-1, in) ]

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  • Geometry is not stored explicitly but rather defined as a level set of a function defined
  • ver the space in which the geometry is embedded
  • There are parametric representations:

Implicit Surface Representation

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  • Geometry is not stored explicitly but rather defined as a level set of a function defined
  • ver the space in which the geometry is embedded
  • And there are nonparametric representations:

Implicit Surface Representation

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  • Geometry is not stored explicitly but rather defined as a level set of a function defined
  • ver the space in which the geometry is embedded
  • And there are nonparametric representations:

Implicit Surface Representation

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Implicit to Explicit Conversion

  • In two dimensions, we can use an algorithm called marching squares
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Implicit to Explicit Conversion in 3D

  • Typically done using marching cubes, a 3D analogue to marching squares
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Implicit to Explicit Conversion in 3D

  • Can also be done by raycasting for a view-dependent partial surface
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  • Can be done by finding the closest point between each discrete location and any part of

the geometry

Explicit to Implicit Conversion

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  • Can also be done with a distance transform

Explicit to Implicit Conversion

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Overview

  • Explicit and implicit surface representations
  • SDF fusion
  • SDF tracking
  • Related research
  • KinectFusion
  • PatchVolumes
  • DART
  • DynamicFusion
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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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Signed Distance Function Fusion

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  • This addition requires the per-frame projected truncated signed distance volumes

to be globally registered

Signed Distance Function Fusion

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Overview

  • Explicit and implicit surface representations
  • SDF fusion
  • SDF tracking
  • Related research
  • KinectFusion
  • PatchVolumes
  • DART
  • DynamicFusion
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Signed Distance Function Tracking

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Signed Distance Function Tracking

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Signed Distance Function Tracking

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Signed Distance Function Tracking

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Signed Distance Function Tracking

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Signed Distance Function Tracking

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Signed Distance Function Tracking

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Signed Distance Function Tracking

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Point-plane Iterative Closest Point (ICP)

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Point-plane Iterative Closest Point (ICP)

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Point-plane Iterative Closest Point (ICP)

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Point-plane Iterative Closest Point (ICP)

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Point-plane Iterative Closest Point (ICP)

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Point-plane Iterative Closest Point (ICP)

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Point-plane Iterative Closest Point (ICP)

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Point-plane Iterative Closest Point (ICP)

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Direct Signed Distance Function Tracking

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Direct Signed Distance Function Tracking

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Direct Signed Distance Function Tracking

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Online fusion

  • Tracking requires the fused SDF volume for all frames up to the current frame
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Online fusion

  • Tracking requires the fused SDF volume for all frames up to the current frame
  • We must maintain a running average SDF value at each cell
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Online fusion

  • Tracking requires the fused SDF volume for all frames up to the current frame
  • We must maintain a running average SDF value at each cell
  • Each cell stores both an SDF value and a weight
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Truncated Signed Distance Function

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Overview

  • Explicit and implicit surface representations
  • SDF fusion
  • SDF tracking
  • Related research
  • KinectFusion
  • PatchVolumes
  • DART
  • DynamicFusion
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Overview

  • Explicit and implicit surface representations
  • SDF fusion
  • SDF tracking
  • Related research
  • KinectFusion
  • PatchVolumes
  • DART
  • DynamicFusion
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Tracking Failure

Color-only Tracking Depth-only Tracking

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Loop Closure

Without Loop Closure With Loop Closure

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Overview

  • Explicit and implicit surface representations
  • SDF fusion
  • SDF tracking
  • Related research
  • KinectFusion
  • PatchVolumes
  • DART
  • DynamicFusion
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Overview

  • Explicit and implicit surface representations
  • SDF fusion
  • SDF tracking
  • Related research
  • KinectFusion
  • PatchVolumes
  • DART
  • DynamicFusion
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