Two-step triangular phase-shifting method for 3-D object-shape measurement
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Bibliographic record
Abstract
Traditional sinusoidal phase-shifting algorithms involve the calculation of an arctangent function to obtain the phase, which results in slow measurement speed. This paper presents a novel high-speed two-step triangular phase-shifting approach for 3-D object measurement. In the proposed method, a triangular gray-level-coded pattern is used for the projection. Only two triangular patterns, which are phase-shifted by 180 degrees or half of the pitch, are needed to reconstruct the 3-D object. A triangular-shape intensity-ratio distribution is obtained by calculation of the two captured triangular patterns. Removing the triangular shape of the intensity ratio over each pattern pitch generates a wrapped intensity-ratio distribution. The unwrapped intensity-ratio distribution is obtained by removing the discontinuity of the wrapped image with a modified unwrapping method commonly used in the sinusoidal phase-shifting method. An intensity ratio-to-height conversion algorithm, which is based on the traditional phase-to-height conversion algorithm in the sinusoidal phase-shifting method, is used to reconstruct the 3-D surface coordinates of the object. Compared with the sinusoidal and trapezoidal phase shifting methods, the processing speed is faster with similar resolution. This method therefore has the potential for real-time 3-D object measurement. This has applications in inspection tasks, mobile-robot navigation and 3-D surface modeling.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it