Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2602.12525 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912902259146752 |
|---|---|
| author | Sun, Xueying Li, Zijia Li, Nan |
| author_facet | Sun, Xueying Li, Zijia Li, Nan |
| contents | This paper investigates singular configurations of the P3P problem. Using local dual space, a systematic algebraic-computational framework is proposed to give a complete geometric stratification for the P3P singular configurations with respect to the multiplicity $μ$ of the camera center $O$: for $μ\ge 2$, $O$ lies on the ``danger cylinder'', for $μ\ge 3$, $O$ lies on one of three generatrices of the danger cylinder associated with the first Morley triangle or the circumcircle, and for $μ\ge 4$, $O$ lies on the circumcircle which indeed corresponds to infinite P3P solutions. Furthermore, a geometric stratification for the complementary configuration $O^\prime$ associated with a singular configuration $O$ is studied as well: for $μ\ge 2$, $O^\prime$ lies on a deltoidal surface associated with the danger cylinder, and for $μ\ge 3$, $O^\prime$ lies on one of three cuspidal curves of the deltoidal surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12525 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometric Stratification for Singular Configurations of the P3P Problem via Local Dual Space Sun, Xueying Li, Zijia Li, Nan Computer Vision and Pattern Recognition This paper investigates singular configurations of the P3P problem. Using local dual space, a systematic algebraic-computational framework is proposed to give a complete geometric stratification for the P3P singular configurations with respect to the multiplicity $μ$ of the camera center $O$: for $μ\ge 2$, $O$ lies on the ``danger cylinder'', for $μ\ge 3$, $O$ lies on one of three generatrices of the danger cylinder associated with the first Morley triangle or the circumcircle, and for $μ\ge 4$, $O$ lies on the circumcircle which indeed corresponds to infinite P3P solutions. Furthermore, a geometric stratification for the complementary configuration $O^\prime$ associated with a singular configuration $O$ is studied as well: for $μ\ge 2$, $O^\prime$ lies on a deltoidal surface associated with the danger cylinder, and for $μ\ge 3$, $O^\prime$ lies on one of three cuspidal curves of the deltoidal surface. |
| title | Geometric Stratification for Singular Configurations of the P3P Problem via Local Dual Space |
| topic | Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2602.12525 |