Non-parametric synthesis of laminar volumetric textures from a 2D sample

Abstract

The goal of this paper is to evaluate non-parametric algorithms that achieve 3D texture synthesis from a single 2D sample. The algorithms under study are variants of the algorithm proposed by Wei and Levoy [1]. Several authors have proposed different algorithms that intend to better reproduce, in the output texture, the diversity learned in the input sample. Hence, we turn our attention to the improved algorithm proposed by Kopf et al. [2] and the particular histogram matching approach of Chen and Wang [3]. In addition, we propose to visit the voxels during synthesis according to the 3D extension of space filling curves. We investigate the algorithms capability to reproduce anisotropic textures. In particular we are interested in laminar textures, i.e. textures made of anisotropic sheets stacked along a given direction. Examples of such textures are snapshots of dense carbons observed by high resolution transmission electronic microscopy (HRTEM). Beyond the traditional subjective evaluation of the synthesized textures, we propose a genuine quantitative benchmark for the analysis of the synthesized textures which consists in comparing input and output gray level statistics and patterns morphology.

Adaptation of Symmetric Positive Semi-Definite Matrices for the Analysis of Textured Images

“…Table 3. PSNR and CoC values between the coherence images of SIPI textures [49] and noisy versions of these textures, obtained using the proposed approach, the methods in [14,44,48 [42] textures and noisy versions of these textures, obtained using the proposed approach, the methods in [14,44,48] This outperformance does not come at the expense of high frequency components loss, which is verified by the obtained high CoC metric values. In fact, the proposed approach leads to higher CoC values than those obtained with the other algorithms in approximately 94% of the results.…”

“…Finally, the whole set of orientations ranged between -π/2 and π/2, and present in texture I20, is well detected by the positive semi-definite matrix. Table 3 presents a comparison between the PSNR and CoC values obtained by the proposed approach and by the methods proposed in [14,44,48] using 44 textures (I21 to I64) taken from SIPI database [49]. PSNR and CoC metrics are calculated between the coherence images of the original texture and that of a noisy version of this texture.…”

“…This shows that the proposed algorithm succeeds in adaptively estimating the extent of gradient fields smoothing while retaining edges and shape features of the texture, which is verified by the obtained high CoC values. A comparison between PSNR and CoC mertics obtained by the proposed approach and by the methods proposed in [14,44,48] is summarized in the graphs of Fig. 8.…”

“…A non-structured sinusoid-like texture is an image composed of sinusoid waveforms that appear like elongated traces, as it is the case for seismic [46,47] and laminar [48] textures for example.…”

Two-stage Color Texture Synthesis using the Structure Tensor Field

“…Among such extensions, the non-parametric approach of (Kopf et al, 2007), which integrates histogram matching to help the global statistics of the synthesized solid converge towards those of the exemplar. Other parametric (Da Costa & Germain, 2010) and non-parametric (Urs, 2013) 2D/3D extensions have also shown their efficiency in many cases including simulation of atomic structure of materials (Leyssale et al, 2009(Leyssale et al, , 2012.…”