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EDT: Team Training Mathematical Scientists
Through Industrial Collaborations

EDT Projects for AY 2017-2018

I. Automatic Extraction of Cell Nuclei from Pathological Images

Pathological examination has been done manually by visual inspection of hematoxylin and eosin (H&E)-stained images. However, this process is labor intensive, prone to large variations, and lacking reproducibility in the diagnosis of a tumor. We aim to develop an automatic workflow to classify different cells found in cancerous tumors portrayed in digital renderings of the H&E-stained images. We first get a rough binary segmentation of object and background pixels via a series of operations. In particular, we apply the SLIC-superpixel algorithm to partition the image, enabling the adaptive thresholding method to be more effective. Morphological dilation follows, connecting appropriate regions over the entire image. Then, the watershed transform is utilized to identify cell walls. To classify cell nuclei, the discrete cosine transform is applied to small windows centered at each pixel, and the respective coefficients act as feature vectors in the K-means clustering model and Gaussian mixture model. We plan to further improve our method by a learning based approach, in particular, using a deep convolutional neural network (CNN) model. The classification results can be used to analyze the morphological properties of the tumor cells, predict further progress of the cancer, and provide support for early detection of cancer.

II. Multisensor tracking of multiple moving targets for defense applications: Modeling Sensor Bias

The Multi-Sensor Integration Group in the Air and Missile Defense Sector at The Johns Hopkins University Applied Physics Laboratory (JHU-APL) develops algorithms to track a moving target using data collected by several different sensors, including Doppler radar systems and sensors onboard the missile that will intercept the target. Because Doppler radar measures partial position and velocity information at a sequence of discrete times, the tracking problem is usually posed in the six-dimensional phase space of positions and velocities. Because of uncertainties in the recorded data, tracking involves computation of the probability density function (pdf) of the 6-D state vector. Assuming the pdf is a multivariate normal distribution, it suffices to compute the time evolution of the mean state vector and the covariance matrix, which can be computed in real time using Kalman filtering to assimilate uncertain measured data into a physics-based system of ODEs that models the motion of the target.

The specific goal of this year's project is to assess different methods for compensating for the effects that bias in the sensors has on the accuracy of tracking algorithms.

The project will provide EDT student trainees with opportunities to work on a problems that combine applied probability, statistical models, Bayesian analysis, combinatorial optimization, scientific computation, and uncertainty quantification, and to learn about applications of the mathematical sciences in the defense sector.

III. Machine Learning for Enhanced Seismic Attributes Constrained by Well Data

In exploration seismology, data is commonly collected in boreholes (wells) and by shooting seismic surveys. Well log data provide high resolution measurements of the subsurface of the Earth in depth but are only available at very sparse well locations. Seismic surveys give structural and material property information over large regions of the subsurface but with lower resolution. Inversion attempts to estimate some of the same parameters measured in wells by minimizing a misfit between data predicted by a mathematical model (the wave equation) and data collected at the surface of the Earth in a seismic experiment. Unfortunately the parameters estimated by inversion may not match the well log data due to a variety of factors. One important problem in exploration seismology is to use the well log data to refine these inversion estimates, which give critical information away from the wells. Machine learning can be used to update our model of the subsurface by determining which mechanical Earth parameters should be used to iteratively improve the match between the seismically derived data predicted by our model and the well data. In this project we are examining a variety of optimization schemes to use in this process, which eliminate or include selected parameters to best improve our match between the well data and seismic attributes.

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