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Traitement du Signal

0765-0019
Signal, Image, Parole
Nouvel éditeur en 2019
 

 ARTICLE VOL 34/HS - 2017  - pp.89-117  - doi:10.3166/ts.2018.00005
TITRE
Utilisation de la photométrie et d’un patron pour la reconstruction de surfaces pliées et la calibration photométrique

RÉSUMÉ

Le Shape-from-Template consiste à recaler et reconstruire la forme 3D d’un objet en déformation observé sur des images 2D en utilisant un patron. La plupart des méthodes existantes nécessitent des surfaces texturées qui se déforment de manière lisse car elles utilisent l’information de mouvement et des régularisations imposant un fort lissage. Nous proposons de dépasser ces limites à l’aide de deux idées. La première est de combiner l’information de mouvement avec celle de photométrie et de bord, qui contraignent densément la déformation au niveau des régions texturées et peu texturées. Des méthodes précédentes utilisent déjà la photométrie, mais elles simplifient le problème en connaissant a priori les paramètres photométriques ou en contrôlant l’objet et l’illumination. Nous ne faisons pas de telles hypothèses et résolvons le problème d’estimation conjointe des paramètres photométriques et de déformation. La seconde idée est d’utiliser un régulariseur robuste qui préserve automatiquement les plis de la surface sans en connaître a priori la position.



ABSTRACT

Motivations
The goal of Shape-from-Template (SfT) is to reconstruct the 3D shape of a deforming surface from a single image by fitting a known 3D object template. Most SfT methods use only image motion information and thus require well-textured surfaces which deform smoothly. They are unsuccessful for poorly-textured surfaces with complex deformations such as creases. We overcome these two shortcomings with two main ideas. First, we use the shading information, without any a priori photometric calibration, to reconstruct poorly-textured surfaces and creases. Shading uses all image pixels and a photometric model. Second, we use a robust smoothing term to allow the formation of creases without knowing their location a priori.

Template, illumination and camera modeling
We define the object template as a texture-mapped thin shell 3D mesh in a known reference pose with M vertices. At each time t, each vertex is deformed to its unknown 3D camera coordinates xt ∈ R3 x M . We upgrade the template with a photometric texture map which defines how each point of the template’s surface reflects light. We use the Lambertian model and compute the map using an intensity-based segmentation of the texture-map. It gives constant albedo regions with α = {α1 ,..., αK }, the K unknown albedo values. The scene illumination l is unknown, constant over time, fixed the camera coordinates and modeled by spherical harmonics (4 and 9 coefficients). The camera has a linear response, βt ∈ R+ , which is unknown and time-varying.

Integrated cost function
The deformation xt is constrained by image data and deformation priors (isometry and smoothing constraints), and l, βt and α are constrained by the shading term and the batch of images. We use the shading relationship to enforce similarity between the modeled and the measured pixel intensities. As it uses all image pixels, mis-alignement may induce errors. Thus, we use motion and boundary constraints to align the projected 3D surface with its input image and we remove significantly false surface edges on the image with color-based statistical models. We also use a robust smoothing based on an M-estimator, which permits crease modeling.

Solution strategy
The integrated cost function is large scale and highly non-linear, but all constraints are sparse with respect to xt. We use a cascaded initialization for the four types of unknowns: first xt, then using the shading constraint and a batch of input images l, βt and finally α. Using the Gauss-Newton algorithm, a refinement process minimizes the whole integrated cost function for the batch of images. We found that a dense mesh with about O (104) vertices is sufficient to capture the creases.

Experimental results
While studying the smoothing term penalization with different M-estimators, we found that the redescending penalizations of (l1 - l2) and Huber can similarly model creases, contrarily to the non-redescending penalization of Tukey. We compare our approach with four SfT methods on two sets of real datasets. This first set shows that our method, without shading, can capture non-smooth deformations without knowing the crease location a priori. The second set shows that our method using shading and without any a priori photometric calibration provides better reconstructions. This was not possible with previous methods in SfT or SfS.



AUTEUR(S)
Mathias GALLARDO, Toby COLLINS, Adrien BARTOLI

MOTS-CLÉS
Shape-from-Template, Shape-from-Shading, surfaces faiblement texturées, surfaces pliées, calibration photométrique, M-estimateurs, isométrie, bords.

KEYWORDS
Shape-from-Template, Shape-from-Shading, weakly-textured surfaces, creased surfaces, photometric calibration, M-estimators, isometry, boundaries.

LANGUE DE L'ARTICLE
Français

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