Representation, Tracking, and Signed Distance …...Signed Distance Function Representation,...

Signed Distance Function Representation, Tracking, and

MappingTanner Schmidt

Overview

- Explicit and implicit surface representations- SDF fusion- SDF tracking- SDF limitations- Related research

- KinectFusion- KinTinuous- BundleFusion- DART- DynamicFusion

Overview

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) ]

- Geometry is not stored explicitly but rather defined as a level set of a function defined over the space in which the geometry is embedded

- There are parametric representations:

Implicit Surface Representation

- And there are nonparametric representations:

Implicit to Explicit Conversion

- In two dimensions, we can use an algorithm called marching squares

Implicit to Explicit Conversion in 3D

- Typically done using marching cubes, a 3D analogue to marching squares

Implicit to Explicit Conversion in 3D

- Can also be done by raycasting for a view-dependent partial surface

- Can be done by finding the closest point between each discrete location and any part of the geometry

Explicit to Implicit Conversion

- Can also be done with a distance transform

Explicit to Implicit Conversion What if we want to build surface representations from raw (noisy) observations?

Overview

Signed Distance Function Fusion

1.356 1.384 1.422 1.511 1.607

- This addition requires the per-frame projected truncated signed distance volumes to be globally registered

Overview

Signed Distance Function Tracking

Point-plane Iterative Closest Point (ICP)

Direct Signed Distance Function Tracking

Online fusion

- Tracking requires the fused SDF volume for all frames up to the current frame

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

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

Truncated Signed Distance Function

Overview

● Size: ○ In general, scales linearly with the volume of the computed distance field, and exponentially in the

resolution● Thin surface representation:

○ If the resolution is insufficient, observations from opposing sides of thin surfaces can “cancel out”

SDF Limitations

● Size: ○ In general, scales linearly with the volume of the computed distance field, and exponentially in the

resolution● Thin surface representation:

○ If the resolution is insufficient, observations from opposing sides of thin surfaces can “cancel out”

SDF Limitations

Overview

KinectFusion [Newcombe et al.]

Overview

- Explicit and implicit surface representations- SDF fusion- SDF tracking- Related research

Overview

Representation, Tracking, and Signed Distance …...Signed Distance Function Representation,...

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