Projective tsdf/tsdf/flipped tsdf Three kinds of truncation symbol distance function comparison of personal understanding

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Description: Projective tsdf only find the closest surface point on the camera's line of sight, which accelerates the operation but has a serious perspective dependency. TSDF chooses to calculate the distance from the nearest point in any of the observable surfaces, but has a strong gradient in the white space portion (+dmax) along the boundary of the occlusion (-dmax). Flipped TSDF is transformed to show the strongest gradient on the surface (see color variations in the image below).

In a recent study of a three-dimensional scene in Princeton University, the TSDF data encoding method has emerged. The comparison chart of three methods in this paper is as follows:

I found some information to study.
(main reference 11th International Conference, Iciar 2014 "Image Analysis and recognition" truncated signed Distance function:e Xperiments on Voxel Size, Diana Werner et al.)

The illustration is a two-dimensional tsdf example. Solid object (green), Camera with field of view, optical axis and Ray (blue), and Tsdf grid (unseen voxels is white, for Others see color bar). The signed distance value of Voxel x is determined by the depth of the corresponding surface point P and the Voxel ' s Camer A distance Camz (x).

Pic (x) is the projection of the Voxel Center x onto the depth image. So Depthi (pic (x)) are the measured depth in between the camera and the nearest object surface point P on the viewing ray CR Ossing x Accordingly, Camz (x) is the distance in between the voxel and the camera along the optical axis. Consequently, SDFI (x) is a distance along the optical axis as well.

The SDF has been truncated at±t. This is beneficial, because large distances was not relevant for surface reconstruction and a restriction of the value ran GE can is utilized to memory footprint. The truncated variant of SDFI (x) is denoted by TSDFI (x).

In Fig TSDFI (x) of the voxel grid was encoded by color.

The TSDF representation requires to select several parameters:
①grid volume size determines the dimensions of the Tsdf Grid.
②voxel Size V is a crucial parameter as it influences memory requirements and surface reconstruction accuracy. If dimensions of a 3D grid is fixed, doubling the voxel size means to reduce the number of voxels to one-eighths. This was associated with the same reduction in memory footprint. Further, it reduces computational cost to updating the TSDF and for Ray tracing. The other is around, an increased voxel size facilitates to increase the scene volume without needing more memory or incr Easing computational cost. However, an increase in voxel size comes along with a decrease on the level of representable details resp. with lowered re Construction accuracy. So it's worth thinking about the optimal voxel size for a particular application.
③distance representation and truncation Distance T i. e. The coding of Distance values TSDFI (x) is crucial for the Reconst Ruction accuracy. The selection of T influences reconstruction accuracy. T should be larger than length of voxel diagonal (√D) • V (voxel size) and the level of noise.