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Texture Analysis
After segmentation, we need to extract colorful texture features from
segmented visible human dataset. We apply Gaussian filter and subsampling
to decompose a dataset in a multiresolution pyramid. The Laplacian filter
and steerable filters ([9]) are also
applied to obtain non-oriented and oriented features of each RGB channel.
This multi-filter scheme is efficient to capture the texture features,
but it costs a lot memory for storage and computational speed. The alternative
solution is to utilize wavelet transform.
Although it is computationally efficient and in-place representation
(without extra memory), this standard wavelet transform only captures features
with orientations parallel to axes. We are interested in extracting features
of the textures selected by segmentation. The wavelet transform is not
helpful in this case because it can not applied directly to a region of
interest. One of the solutions is to apply non-separable filters. Kovacevic,
et el. has been working on non-separable filter design for wavelet transform.
Recently, a lifting scheme to build filter banks for wavelets transform
in any dimension has been proposed ([10]).
The approach involves two lifting steps: prediction and updating. The prediction/updating
aims to design a filter bank, which is created by the Boor-Ron algorithm
for multidimensional polynomial interpolation ([11]).
This filter bank can detect the texture feature on the regions of a segmented
visible human dataset with small modifications.
Texture Modeling
After obtaining the texture features, we create models to describe
the features. We utilize a non-parametric multi-scale statistical model
as opposed to the traditional approach based on the Markov Random Field
[3]. The basis for using this model is based on effectively estimating
and manipulating the entropy of non-Gaussian distributions (natural textures).
We adopt Parzen window density estimation for the following advantages:
(1)Parzen estimate is computed directly from the sample: there is no search
for parameters; (2) The derivative of the entropy of the Parzen estimate
is simple to compute. In addition, this model can estimate cross-scale
distributions which allow us to detect a parent-child relationship by co-occurence
of wavelets at many scales. For these reasons, well defined structure in
natural textures can be modeled and reproduced in texture synthesis. We
also take advantage of flexible histogram introduced by Bonet et al ([12])
to improve computational performance.
Texture Matching
Texture matching in the pure material regions is straightforward after
segmentation of the CT and Visible Human in classes. The corresponding
classes are easily matched. As we discussed earlier, texture is not well
defined in the material-mixture regions since they closer to the boundary
in CT dataset are fuzzy . Intuitively, if texture is fuzzy the texture
matching is not trivial, but, the probabilistic segmentation provides a
percentage of texture for each material or tissue. We utilize this percentage
to set the importance of matching. This matching can be relaxed in accordance
to the weight based on the value of the percentage. This way, we can solve
texture matching in a fuzzy boundary nicely.
The texture matching for the non-parametric multi-scale statistical
model is more complicated . We can apply the cross entropy or Kullback-Leibler
divergence ([13]) from
information theory to measure the difference between two distributions.
Texture Synthesis
After matching, we will fuse the textures from the visible human/optical
colonoscopy dataset into the patient CT dataset. We sample texture directly
from the visible human dataset in the segmented CT dataset if the texture
is un isoptropic pattern such as bone. However, the multiresolution sampling
procedure is required for unisotropic textures such as colon mucosa. Bonet
[6] showed the power of this procedure by keeping track of relationships
between parent and children in the multiresolution model. The selective
resampling for homogeneous and heterogeneous regions is the secret of this
method. Nevertheless, the Bonet method is only applied to reproduce larger
texture (rectangle size). We are developing a new method where texture
is resampled from different source datasets. This approach does not only
reproduce the original texture, but can also be used to perform resampling
in the target region. We also consider fuzzy texture on the contrast region
where textures are resampled by composition task, Fusing different pure
textures in a mixture texture.
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