Texture Synthesis with Grouplets

Gabriel Peyré (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

This paper proposes a new method to synthesize and inpaint geometric textures. The texture model is composed of a geometric layer that drives the computation of a new grouplet transform. The geometry is an orientation flow that follows the patterns of the texture to analyze or synthesize. The grouplet transform extends the original construction of Mallat and is adapted to the modeling of natural textures. Each grouplet atoms is an elongated stroke located along the geometric flow. These atoms exhibit a wide range of lengths and widths, which is important to match the variety of structures present in natural images. Statistical modeling and sparsity optimization over these grouplet coefficients enable the synthesis of texture patterns along the flow. This article explores texture inpainting and texture synthesis, which both require the joint optimization of the geometric flow and the grouplet coefficients.

Mots clés: Texture; grouplets; texture synthesis; inpainting.; inpainting

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Gabriel Peyré. Texture Synthesis with Grouplets. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2009, 32 (4), pp.733-746. ⟨10.1109/TPAMI.2009.54⟩. ⟨hal-00360795⟩