Models and measurements of 3d texture (1999)

This work is an investigation of the visual appearance of real-world surfaces and the dependence of appearance on the geometry of imaging conditions. Image texture can arise not only from surface albedo variations (2D texture) but also from surface height variations (3D texture). Many natural textures fall into the category of 3D texture and yet prior texture research has largely ignored this property. Since the appearance of 3D texture depends on the illumination and viewing direction in a complicated manner, such image texture can be called a bidirectional texture function. 
Measurements of BTF (bidirectional texture function) are presented in a database with image textures from over 60 different samples, each observed with over 200 different combinations of viewing and illumination directions. A related quantity to the BTF is the familiar BRDF (bidirectional reflectance distribution function). The measurement methods involved in the BTF database are conducive to a simultaneous measurement of the BRDF. Accordingly, a BRDF database is constructed with reflectance measurements for over 60 different samples, each observed with over 200 different combinations of viewing and illumination directions. The methods involved in collecting each database are described. The reflectance measurement data is fit to recent BRDF models and the resulting parameters are also available in the BRDF database. Both the BRDF and BTF databases are publicly available and have important implications for computer vision and graphics. 
Modeling the BTF is key to achieve robust texture recognition, segmentation and photorealistic texture rendering. A fundamental representation of image texture is the histogram of pixel intensities. For 3D texture, there is a bidirectional histogram which is a function of illumination and viewing directions. This work describes a concise analytical model for the bidirectional histogram of Lambertian, isotropic, randomly rough surfaces, which are common in real-world scenes. The accuracy of the histogram model is demonstrated by fitting to several samples from the Columbia-Utrecht texture database. The parameters obtained from the model fits are roughness measures which can be used for texture recognition and characterization. 
To extend the histogram model, this work develops a model for correlation length for the same class of 3D textures. Because of local foreshortening and masking, oblique views of 3D texture are not simple transformations of the frontal view. Consequently, texture representations such as the correlation function or power spectrum are also affected by local foreshortening and masking. This model characterizes the spatial relationship among neighboring pixels in an image of 3D texture and the change of this spatial relationship with viewing direction. 
An appearance-based model is presented in which each image texture is represented using multiscale image histograms and the resulting set of histograms is compressed using principal components analysis. This technique is referred to as PCAMH (principal components analysis of multiscale histograms). While this representation requires an input set of texture measurements, it has the advantage of making no assumptions about the surface properties. 
Two applications for BTF modeling are described. A novel 3D texture synthesis procedure is discussed which creates oblique views of 3D texture from frontal views using the histogram model and a resampling procedure. This procedure is applied in simple renderings which show marked improvement over standard texture mapping. The second application is texture recognition using the CUReT database and the PCAMH model for 3D texture. The recognition results indicate that PCAMH accurately and conveniently describes the salient and distinguishing features of 3D texture.