levels
of the same image of different resolutions [11]. An image
with the highest resolution is at the bottom level of a pyramid
while an image with the coarser resolution is at a higher pyramid
level.
There are two basic pyramid operations, namely, reduce and expand. The reduce operation involves filtering and downsampling an image to obtain a new image at the coarser resolution. The expand operation involves upsampling and interpolating an image to obtain an image at the finer resolution. The process of constructing a pyramid from an image is called decompose, which involves continuous reduce operations. While the process of obtaining an image from a pyramid is called collapse, which involves continuous expand operations. The Gaussian, Laplacian, and steerable pyramids are among the most popular ones used for image processing. Gaussian and Laplacian pyramids involve Gaussian and Laplacian-of-Gaussian base functions respectively [11], while steerable pyramid uses wavelet transforms [46], for decomposing an image.
In the pyramid-based texture synthesis, the Laplacian and the steerable pyramids decompose a texture into multiple bands of spatial frequencies and orientations respectively. Each pyramid level represents certain texture features at a particular frequency or orientation. The histogram of each pyramid level is chosen as a descriptor of the related features. The synthesis is based on the idea that a new texture could be generated by matching all the available features (histograms) with the training texture.