2.3 Generating Material Attributes

This protocol is extracted from research article:

Learning Medical Materials From Radiography Images

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Front Artif Intell**,
Jun 18, 2021;
DOI:
10.3389/frai.2021.638299

Learning Medical Materials From Radiography Images

Procedure

The distance matrix $\mathbf{D}$ introduced in Section 2.2 maps distances from material categories to other material categories. However, we are also interested in discovering a set of *M* novel material attributes that provide new, useful information that can improve the categorization and separation of image patches.

We reintroduce the method in Schwartz and Nishino (2020) for mapping material categories to material attributes. This procedure preserves the distances discovered in $\mathbf{D}$ while introducing values for the mapping that reflect how humans generally perceive materials. This mapping is encoded in the *material category-attribute matrix*
$\mathbf{A}$.

$\mathbf{A}$ is a $K\times M$ matrix, where *K* is the number of material categories encoded by $\mathbf{D}$ and *M* is a freely selected value that defines the number of material attributes that are generated. The entries of $\mathbf{A}$ are bound to the range $\left[\mathrm{0,1}\right]$ so that each entry represents a conditional probability. The minimization objective for $\mathbf{A}$ is presented in Eq. 4.^{
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The first term of the objective captures the distances between material categories in $\mathbf{D}$ and material attributes in $\mathbf{A}$ with a distance measure that iterates over the L2-distance of columns ${\mathbf{a}}_{k}$ in $\mathbf{A}$ and compares them against individual entries in $\mathbf{D}$.

The second term of the objective captures an important feature of the $\mathbf{A}$ matrix—that its entries should conform to a reasonable distribution that mirrors human perception. Like Schwartz and Nishino (2020), we use a beta distribution with parameters $a,b=0.5$. The beta distribution is ideal because, for human perception, material attributes usually either strongly exhibit a certain material category or not exhibit it at all. We assume that this observation, like with natural categories, holds with expert categories.

Since the Beta distribution is continuous, it still permits intermediate cases where materials may be similar (as is the case for “tumor” and “brain”). The γ-weighted term accomplishes this by embedding the $\mathbf{A}$ matrix in a Gaussian kernel density estimate $q\left(p;\mathbf{A}\right)$ and comparing it to the target beta distribution. This comparison is accomplished by evaluating the Kullback–Leibler (KL) divergence between those two terms. The Gaussian kernel density estimate of $\mathbf{A}$ at point *p* is presented in Eq. 5.

The optimized matrix ${\mathbf{A}}^{\ast}$ from Eq. 4 is held constant and used as the $\mathbf{A}$ matrix in further portions of the system.

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