The structure of locally orderless images

We propose a representation of images in which a global, but not a local to pology is defined. The topology is restricted to resolutions up to the exte nt of the local region of interest (ROI). Although the ROI's may contain ma ny pixels, there is no spatial order on the pixels within the ROI, the only information preserved is the histogram of pixel values within the ROI's. T his can be considered as an extreme case of a textel (texture element) imag e: The histogram is the limit of texture where the spatial order has been c ompletely disregarded. We argue that locally orderless images are ubiquitou s in perception and the visual arts. Formally, the orderless images are mos t aptly described by three mutually intertwined scale spaces. The scale par ameters correspond to the pixellation ("inner scale"), the extent of the RO I's ("outer scale") and the resolution in the histogram ("tonal scale"). We describe how to construct locally orderless images, how to render them, an d how to use them in a variety of local and global image processing operati ons.