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In this paper we present the concept and associated methodological framework for a novel locally adaptive scale
notion called local morphological scale (LMS). Broadly speaking, the LMS at every spatial location is defined
as the set of spatial locations, with associated morphological descriptors, which characterize the local structure
or heterogeneity for the location under consideration. More specifically, the LMS is obtained as the union of
all pixels in the polygon obtained by linking the final location of trajectories of particles emanating from the
location under consideration, where the path traveled by originating particles is a function of the local gradients
and heterogeneity that they encounter along the way. As these particles proceed on their trajectory away from
the location under consideration, the velocity of each particle (i.e. do the particles stop, slow down, or simply
continue around the object) is modeled using a physics based system. At some time point the particle velocity
goes to zero (potentially on account of encountering (a) repeated obstructions, (b) an insurmountable image
gradient, or (c) timing out) and comes to a halt. By using a Monte-Carlo sampling technique, LMS is efficiently
determined through parallelized computations. LMS is different from previous local scale related formulations
in that it is (a) not a locally connected sets of pixels satisfying some pre-defined intensity homogeneity criterion
(generalized-scale), nor is it (b) constrained by any prior shape criterion (ball-scale, tensor-scale). Shape descriptors
quantifying the morphology of the particle paths are used to define a tensor LMS signature associated with
every spatial image location. These features include the number of object collisions per particle, average velocity
of a particle, and the length of the individual particle paths. These features can be used in conjunction with
a supervised classifier to correctly differentiate between two different object classes based on local structural
properties. In this paper, we apply LMS to the specific problem of classifying regions of interest in Ovarian
Cancer (OCa) histology images as either tumor or stroma. This approach is used to classify lymphocytes as
either tumor infiltrating lymphocytes (TILs) or non-TILs; the presence of TILs having been identified as an
important prognostic indicator for disease outcome in patients with OCa. We present preliminary results on the
tumor/stroma classification of 11,000 randomly selected locations of interest, across 11 images obtained from
6 patient studies. Using a Probabilistic Boosting Tree (PBT), our supervised classifier yielded an area under
the receiver operation characteristic curve (AUC) of 0.8341 ±0.0059 over 5 runs of randomized cross validation.
The average LMS computation time at every spatial location for an image patch comprising 2000 pixels with 24
particles at every location was only 18s.
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