MichaelAlissa

Methods

Accuracy and Temporal Noise Characterization

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To establish a baseline of the error present in the point cloud construction from multi-camera setup, we first characterized the accuracy and temporal noise for a single camera. To accomplish this, we designed an experimental rig—depicted in Figures # and #—which allowed the imaging plane of the camera and the surfaced of the wall to oriented parallel to each other. The camera could then be adjusted to different distances from the wall while maintaining this orientation. We performed recordings ranging from 0.2 – 2 meters at increments of 0.2 meters. Five, 1-minute recording with a sampling rate of 90 frames per second were taken at each measurement distance, analysis for all recordings was confined to the same section of wall, which possessed a matte, textured finish.

Results

Accuracy and Temporal Noise Characterization

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With the recordings described in the Methods section, two metrics were calculated: (1) depth error and (2) temporal noise. Depth error, which relates the camera’s ability to accurately determine an object’s distance, can be described as

$formula$

which is simply average of differences between the wall depths reported by the camera and true distance to the wall. Temporal noise, which characterizes the spread of depth values on an object over the duration of a recording, is calculated as

$formula$

where is the standard deviation of the

$i^{(}th)$

pixel over a recording. Plots of these calculations at different distances can be viewed in Figure #. As seen in these figures, both depth error and temporal noise increase as the square of the distance between the wall and the camera, which—as described below—impacts the ability of these cameras to accurately reconstruct 3D point clouds from this data.

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While performing these calculations, we also analyzed the effect that different surfaces had on camera error. Examining a painted section of wall, shown in Figure #, the temporal noise at 2 meters was evaluated. A heat map of the pixel standard deviations over the minute-long recording can be viewed in Figure #. From this heat map, glossier areas (such as the brown trees in Figure #) create significantly more temporal noise than areas with matte finish. This highlights the d435’s susceptibility to increased error in highly reflective environments, a fact which must be considered whenever recordings are performed.

3D Point Cloud Construction

$\text{Mean}(x)=\frac{1}{N}\sum _{i=1}^{N}depthpixe{l}_i-truevalue$

Appendix

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