Texel-based Texture Segmentation

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Introduction
Images generally consist of distinct parts representing
different surfaces in the scene. Surfaces made of an optically
homogeneous material and under smoothly varying
illumination give rise to image parts with a smooth variation
of image brightness, referred to as non-texture subimage. In
contrast, surfaces with discontinuities in depth, material, illumination,
etc., give rise to texture subimages. The spatial
variation of intensity in each image part contains different
information about the scene, often requiring different types
of algorithms to be invoked on these parts. Depending on
its purpose, an algorithmmay apply to either texture or nontexture
subimages, or both. For example, if a surface in the
scene gives rise to the texture subimage it may be better
to estimate the surface’s shape by shape-from-texture algorithms
than by shape-from-shading methods.


Relationships to PriorWork
This section reviews prior work in texture modeling and
segmentation. Methods that explicitly encode texel properties
in their models of texture typically use the following
texel representations: (a) salient blobs [28, 5]; (b) interest
points within texels [18, 12, 21]; © combination of interest
points and Canny edges [25]; or (d) user-specified templates
and filter functions [17, 30, 27, 19]. In contrast, we use segments
that facilitate delineating the exact texel boundaries,
and thus accurate identification of texel regions. Julesz and
his colleagues [15] have argued the use of special features
called textons (e.g., closure, line endpoints, corners) for texture
modeling. There have been several attempts to mathematically
define the notions of textons and texels. In [30],
for example, texture is modeled as a superposition of Gabor
base functions which are generated by a user-specified
vocabulary of texton templates. The region-based, hierarchical
texel model of [3] encodes only the intrinsic properties
of texels. In contrast to this approach, we additionally
consider the modeling of texel placement properties.


The Feature Space of Region Properties
This section presents our Step 1. Since, in general, texels
are not homogenous-intensity regions, but contain hierarchically
embedded structure, their representation should be
hierarchical [3]. Access to such image structure is provided
by a strictly hierarchical,multiscale segmentation algorithm
that partitions the image over a range of photometric scales
(i.e., contrasts) [1, 4]. At each scale, the pixel-intensity
variations within each region are smaller than those across
the region boundary at each scale. The algorithm guaranties
that regions obtained at lower contrasts will strictly
merge into larger regions as the photometric scale increases.


Voronoi-based Binned Meanshift
This section presents our Step 2 that introduces twomodifications
to the meanshift: (i) Variable-bandwidthGaussian
kernel, and (ii) New hierarchical kernel that uses (i). These
modifications will allow us to explicitly account for structural
properties of texels, which is beyond the scope of the
original meanshift formulation [8, 7]. We begin by reviewing
the meanshift algorithm.

4.1. Technical Rationale
The meanshift procedure starts from a random point in
the feature space, y1, and then visits a sequence of points
{yt}, t=1, 2, . . ., where yt+1 = yt + m(yt), and m(yt)
is the meanshift vector pointing along the density gradient.