Shortcomings and Flaws in the Mathematical Derivation of the Fundamental Matrix Equation
Bibliographic record
Abstract
In stereo vision, the epipolar geometry is the intrinsic projective geometry between the two views. The essential and fundamental matrices relate corresponding points in stereo images. The essential matrix describes the geometry when the used cameras are calibrated, and the fundamental matrix expresses the geometry when the cameras are uncalibrated. Since the nineties, researchers devoted a lot of effort to estimate the fundamental matrix. Although it is a landmark of computer vision, in the current work, three derivations of the essential and fundamental matrices have been revised. The Longuet-Higgins' derivation of the essential matrix where he draws a mapping between the position vectors of a 3D point; however, the one-to-one feature of that mapping is lost when he changed it to a relation between the image points. In the two other derivations, we demonstrate that the authors established a mapping between the image points through the misuse of mathematics.
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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 | 0.013 | 0.045 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.008 |
| Scholarly communication | 0.003 | 0.010 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.003 | 0.010 |
| Insufficient payload (model declined to judge) | 0.004 | 0.005 |
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".