Defining an action of SO(d)-rotations on images generated by projections of d-dimensional objects: Applications to pose inference with Geometric VAEs.

Recent advances in variational autoencoders (VAEs) have enabled learning latent manifolds as compact Lie groups, such as SO(d). Since this approach assumes that data lies on a subspace that is homeomorphic to the Lie group itself, we here investigate how this assumption holds in the context of images that are generated by projecting a d-dimensional volume with unknown pose in SO(d). Upon examining different theoretical candidates for the group and image space, we show that the attempt to define a group action on the data space generally fails, as it requires more specific geometric constraints on the volume. Using geometric VAEs, our experiments confirm that this constraint is key to proper pose inference, and we discuss the potential of these results for applications and future work.

Les récents progrès dans le domaine des autoencodeurs variationnels (VAEs) ont permis l'apprentissage de variétés latentes sur des groupes de Lie compacts, tels que SO(d). Une telle approche supposant l'espace des données homéomorphe au groupe de Lie, nous étudions ici la validité de cette hypothèse dans le contexte d'images générées par projection d'un volume de dimension d, dont la pose dans SO(d) est inconnue. Après examen de différents candidats définissant l'espace des images et groupe, on montre que l'on ne peut de manière générale obtenir une action de groupe, sans une contrainte supplémentaire sur le volume. En appliquant des VAEs géométriques, nos expériences confirment que ces contraintes géométriques sont essentielles pour l'inférence de la pose associée au volume projeté, et nous discutons pour conclure des applications potentielles de ces résultats.

Emergency department diagnosis and management of skin diseases with real-time teledermatologic expertise.

IMPORTANCE: Skin conditions are a common reason for patients to consult emergency department (ED) physicians. OBJECTIVE: To evaluate real-time teledermatologic expertise with the use of mobile telephones for the diagnosis and management of skin conditions in patients seen in the ED. DESIGN, SETTING, AND PARTICIPANTS: This observational study of adults who consecutively consulted in the ED for a dermatologic condition was conducted under routine conditions in the ED from May 1, 2008, through June 30, 2010. MAIN OUTCOMES AND MEASURES: Diagnosis agreement and management concordance. RESULTS: One hundred eleven patients were enrolled in the study. Eighty-three patients (74.8%) were evaluated using videoconferencing. Dermatologic remote expertise invalidated, enlarged, or clarified ED physicians' diagnosis and management in 75 of 110 cases (68.2%). Videoconferencing improved the diagnostic performance in 57 of 83 cases (68.7%) (P < 10(-4)). Management concordance was moderate between ED physicians and dermatologists for specialist consultation within 24 hours (κ, 0.49; 95% CI, 0.14-0.84) and immediate hospitalization (κ, 0.49; 95% CI, 0.41-0.57). Patients were significantly more often discharged by dermatologists (46.8% vs 39.1%) (P < 10(-4)). CONCLUSIONS AND RELEVANCE: Compared with standard hardware, new-generation mobile devices reduce the cost of videoconferencing, increase the versatility of teledermatology, and decrease general practitioner investment time.