A Novel Method for Approximating Object Location Error in Bounding Box Detection Algorithms Using a Monocular Camera
Bibliographic record
Abstract
Many autonomous vehicles and advanced driver-assistance systems are equipped with front-facing cameras that detect and track objects using deep-learning-based algorithms. However, the localization capability of monocular cameras is often overlooked. In this paper, a novel method for estimating the pixel-wise error in a detected objects location versus its ground truth is proposed. As the object moves away from the camera, the pixel errors are shown to be normally distributed with unique spreads along the images vertical axis (y-pixel). The pixel error appears to be smaller as objects get farther away, while at the same distance range, objects have similar error distribution across the cameras horizontal view. The horizontal axis (x-pixel) error appears to be smaller while the distance moves further away. However, the x-pixel location along a constant y-pixel row has no impact on the error distribution. The estimated x and y-pixel error distributions can in turn be used to form a spatial error distribution for finding the location of a detected object within a certain confidence interval. The spatial errors are then projected onto the world coordinate system using a camera transformation matrix to give a more realistic sense of what this error means. The results show that location estimation using monocular cameras generates an elliptical error distribution around the object with a larger error in the y-pixel direction compared to the x-pixel direction. This error distribution can be important to fuse information from multiple range-detecting sensors as well as multi-vehicle and multi-object tracking. The uncertainty characterization for position measurement, as demonstrated in this paper is an essential element of tracking and, is sensor and algorithm dependent.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".