Geometric Biomedical Computing


Current Research Projects

Completed Research Projects


Shape and Image Analysis for Computer-Aided Diagnosis of Breast Tumors

The GBC Group is investigating computational methods that may be used to assist in the diagnosis of breast cancer tumors. We have used our techniques to predict two aspects of a cancerous tumor. In the first we utilized our shape and image analysis techniques to assess the histologic grade of a tumor.

Breast cancers can be histologically categorized (graded) based upon their architectural patterns and cellular types. Inaccurate histologic grading can result in inappropriate treatment for a given patient. Computational analysis of breast cancers offers an operator-independent method for histologic grading that should enhance grading reliability. Our approach for automatically and objectively estimating histologic grade is based on image processing and shape analysis of imaged histologic sections. Our work is based on the hypothesis that cellular structures found in breast cancer tumors can be transformed into distinct high-resolution shape distributions using geometric measures from stochastic geometry. The resulting shape distributions define well-populated regions of the associated high-dimensional space. Mapping an unknown breast cancer sample into this high-D space and determining to which region it belongs will allow for the automatic estimation of its histologic grade. See Zhang et al. 2008, Petushi et al. 2011.

In our second project our analysis techniques were used to predict if a breast tumor has metastasized to nearby lymph nodes.

Axillary lymph node metastasis status is still one of the most critical prognostic variables for the breast cancer management decision-making process and patient survival. Metastasis status is determined via examination of a dissected sentinel axillary lymph node. Questions have been raised about the need for routine lymph node dissection. Recently, it has been reported that complete axillary lymph node dissection did not improve survival for patients with small metastatic foci in sentinel lymph nodes. If sentinel lymph node status could be accurately predicted prior to the surgical procedure (lymph node removal), a considerable number of patients with low probability of sentinel lymph node metastases might avoid the procedure altogether, and its associated critical side effects (e.g. swelling, numbness, pain, infection and compromised immunity) and morbidity.

Our approach to predicting breast tumor metastasis is based on image processing and shape analysis of imaged histologic sections at multiple physical scales. We assume that the structure of the nuclear pleomorphisms found in breast cancer tumors can be transformed into distinct high-dimensional shape distributions using geometric measures from stochastic geometry. This geometric space is augmented with information derived from the color variations of the hyperchromatism found in the cancer cell nuclei. We show that shape/color distributions can uniquely capture and characterize the spatial/spectral distribution of neoplastic cells in breast cancer tumors. Once the structure of the cells has been transformed, the dimensionality of the computed distributions is reduced and the resulting feature vectors map into separable regions of the distribution space. Imaging a primary breast carcinoma of unknown status, processing and mapping the image's shapes and colors into feature vectors allow us, via the application of an ensemble-of-classifiers-based approach, to automatically predict a sample's axillary lymph node status, i.e. determine if the cancer has metastasized to nearby lymph nodes by only examining the cellular structures of the primary breast tumor. See Zarella et al. 2015b.

Digital imaging of hematoxylin and eosin (H & E) stained slides has enabled the application of image processing to support pathology workflows. However, the intrinsic variability of biological tissue and the vast differences in tissue preparation protocols lead to significant image variability that can hamper the effectiveness of these computational tools. To address this issue we have explored alternative color metrics for image representation, and transformations to normalize pathology images for improved standardization and calibration in the anatomic pathology laboratory.
The color normalization software tools developed during our work (See Zarella et al. 2015a, Zarella et al. 2017a) may be accessed here.

In our latest work we developed a deep-learning-based technique for classification map generation for prostate cancer specimens. See Tan et al. 2021.

Additionally, we have applied an agent-based approach (See Grimes and Breen 2023) to predict metastasis status in breast cancer tissue. See Grimes et al. 2021.

Related Publications

Zhang et al. 2008, Petushi et al. 2011, Zarella et al. 2015a, Zarella et al. 2015b, Zarella et al. 2017a, Zarella et al. 2017b, Zarella et al. 2018, Tan et al. 2021, Grimes et al. 2021

J. Zhang's Research Day 2008 Poster

J. Zhang's EMBC 2008 Poster

M.A. Reza's Research Day 2010 Poster

SPIE 2011 Poster

Pathology Informatics 2011 E-Poster

M. Zarella's Discovery Day 2012 Poster

This research is performed in collaboration with the Johns Hopkins University's Department of Pathology and Cancer Treatment Centers of America.


Computational pipeline for automated lymph node metastasis prediction based on image analysis of primary breast tumor histology.


Completed Research Projects


Optical Coherence Tomography (OCT) for the Detection and Characterization of Prostate Cancer

Recent advances have opened the door for high-resolution imaging modalities to flourish in the area of prostate imaging. One particularly promising example includes optical coherence tomography (OCT), a high-resolution optical imaging technique that offers deep tissue penetration, fast acquisition for real-time imaging, nearly cellular resolution, and exceptional contrast in tissue. With the continued development of OCT technology, the ability to visualize architecture for improved detection has the potential to serve an integral role in prostate cancer diagnostics. We are now exploring the use of Optical Coherence Tomography (OCT) to perform imaging of prostates for the purposes of detecting cancer cells.

Our initial investigations developed image processing techniques that extend the effective penetration depth of OCT imaging into tissue.

Related Publications

Nandakumar et al. 2018,

This research was performed in collaboration with the Johns Hopkins University's Department of Pathology and Cancer Treatment Centers of America.


(A) Single unprocessed OCT frame. (B) Single frame after applying wavelet denoising. (C) Coregistered average of 100 sequential frames.


Self-Organizing Primitives for Automated Shape Composition

Motivated by the ability of living cells to form into specific shapes and structures, the GBC Group is developing a new approach to shape modeling based on self-organizing primitives whose behaviors are derived via genetic programming. The key concept of our approach is that local interactions between the primitives direct them to come together into a macroscopic shape. The interactions of the primitives, called Morphogenic Primitives (MP), are based on the chemotaxis-driven aggregation behaviors exhibited by actual living cells. Here, cells emit a chemical into their environment. Each cell responds to the stimulus by moving in the direction of the gradient of the cumulative chemical field detected at its surface. MPs, though, do not attempt to completely mimic the behavior of real cells. The chemical fields are explicitly defined as mathematical functions and are not necessarily physically accurate. The explicit mathematical form of the chemical field functions are derived via genetic programming (GP), an evolutionary computing process that evolves a population of functions. A fitness measure, based on the shape that emerges from the chemical-field-driven aggregation, determines which functions will be passed along to later generations. We have shown that MPs may be used to define field functions that produce a number of simple shapes. The GP-based process has also generated field functions that produce a number of unexpected, but interesting, patterns and shapes.

The GP process is visualized in the following figure.

MPs have also been extended to contain individual coordinate systems. They now detect the orientations of their neighbors and rotate in the direction of the average orientation of nearby MPs while self-assembling.

Related Publications

Bai et al. 2008a, Bai et al. 2008b, Bai et al. 2008c, Bai and Breen 2008, Bai and Breen 2012, Bai et al. 2014, Grimes et al. 2019

L. Bai's Research Day 2008 Poster

L. Bai's Research Day 2009 Poster

IWBDA 2010 Poster

Related Animations

MPs forming into a elllipse shape

MPs forming into a diamond shape

MPs forming into a gear shape

MPs forming into an ellipse shape while self-aligning

MPs forming into a diamond shape while self-aligning

MPs forming into a gear shape while self-aligning




Morphogenic Primitives self-organizing into ellipse, diamond, hourglass and gear-like shapes.


Unexpected and interesting shapes and patterns produced during MP evolution.


MPs self-organizing into an ellipse, diamond, hourglass and cross shape, while aligning their orientations.


3D Reconstruction of the Developing Drosophila Wing Disc

Quantifying and visualizing the shape of developing biological tissues provide information about the morphogenetic processes in multicellular organisms. The size and shape of biological tissues depend on the number, size, shape, and arrangement of the constituting cells. To better understand the mechanisms that guide tissues into their final shape, it is important to investigate the cellular arrangement within tissues. We have developed a set of techniques that generates 3D volumetric surface models of epithelial tissues, as well as geometric descriptions of the tissues' individual cells. The input to the reconstruction process is a stack of confocal microscopy images. The techniques include image acquisition, editing, processing and analysis, 2D cell mesh generation, 3D contour-based surface reconstruction, multiple cell mesh projections and cell geometry construction. Once these steps are completed, geometric calculations are performed to compute the apical cross-sectional areas, heights and volumes of the individual cells. Using these quantities color-based visualization of a tissue's morphological parameters is performed. In their first utilization we have applied these techniques to construct 3D volumetric models at cellular resolution of the wing imaginal disc of larval Drosophila melanogaster. The calculation and visualization of morphological parameters show position-dependent patterns of cell shape in the wing imaginal disc.

In the second study, a more detailed investigation was conducted on early stage Drosophila wing discs in order to quantify the change of the geometric parameters of the disc's individual cells during development. Our results showed that the cells' areas constrict, the heights increase and the volumes stay constant during the beginning of the wing disc's formation.

Related Publications

Breen et al. 2012, Bai et al. 2013, Breen et al. 2019,

L. Bai's BioVis 2011 Poster

D. Breen's MORPH 2012 Poster

This research was performed in collaboration with the Dr. Frank Jülicher's Biological Physics Department at the Max Planck Institute for the Physics of Complex Systems and Dr. Christian Dahmann's Group at the Dresden University of Technology


3D reconstruction of a Drosophila wing imaginal disc. Individual cells have been color-coded as a function of their apical cross-sectional area. Key units are in microns2.


3D reconstruction of a Drosophila wing imaginal disc. Individual cells have been color-coded as a function of their height. Key units are in microns.


3D reconstruction of a Drosophila wing imaginal disc. Individual cells have been color-coded as a function of their volume. Key units are in microns3.


3D reconstruction of a Drosophila wing imaginal disc at an earlier developmental stage. Individual cells have been color-coded as a function of their apical cross-sectional area.


3D reconstruction of a Drosophila wing imaginal disc at an earlier developmental stage. Individual cells have been color-coded as a function of their height.


3D reconstruction of a Drosophila wing imaginal disc at an earlier developmental stage. Individual cells have been color-coded as a function of their volume.


Plots showing the relationship between wing imaginal disc cell number (developmental stage) and apical face area (in microns2), cell height (in microns) and cell volume (in microns3) for 20 specimens. A line computed with a least squares fit to the data is drawn in each plot. The results show that the cells' areas constrict, the heights increase and the volumes stay constant during the beginning of the wing disc's formation.



Video Analysis for the Characterization of Fly Behavior

The fruit fly, Drosophila melanogaster, is a well-established model organism used to study the mechanisms of both learning and memory. The ability to study learning and memory behavior in Drosophila has significantly increased our understanding of the underlying molecular mechanisms of this behavior, and allows for the rational design of therapeutics in diseases that affect cognition. The existing human-observer-based techniques used to assess this behavior in flies are powerful. However, they are time-consuming, tedious, and can be subjective. An automated method based on video analysis of fly movements can replace and improve a labor-intensive, possibly inconsistent evaluation process. Automating the process will provide a reliable and reproducible analysis of fruit fly courtship behavior. Additionally, it also enables quantification of many aspects of the behaviors that are not easily perceived by a human observer. Moreover, the automation promises the possibility of robust, high-throughput analysis of substantial quantities of video data, which would be useful for large-scale genetic and drug screens, and disease modeling.

One fly behavior that is well established in the field is courtship conditioning. Courting behavior by male flies in Drosophila follows a linear, stereotyped, and well documented set of behaviors, and this behavior is modified by previous sexual experience. After 1 hour of courting a mated female, males suppress their courtship behavior even towards subsequent receptive virgin females for 1-3 hours. This courtship suppression is measured by the Courtship Index (CI), which is calculated by dividing the total amount of time each male fly spends courting by the total duration of a testing period. CI is the standard metric used to assess learning and memory in courtship suppression analysis.

We have developed a computational approach to fly behavior quantification and characterization based on the analysis of videos of courting fruit flies. The approach includes identifying individual flies in the video, quantifying their size (which is correlated with their gender), and tracking their motion, which also involves computing the flies' head directions. Geometric measures are then computed, for example distance between flies, relative orientation, velocities, contact time between the flies, and the time when one fly looks at another. This data is computed for numerous experimental videos and produces high-dimensional feature vectors that represent the behavior of the flies. We formulated a computational equivalent (Computational Courtship Index) of the existing CI, based on the feature vector values, and compared it with CI. Clustering techniques, e.g., k-means clustering, are then applied to the feature vectors in order to computationally group the specimens based on their courtship behavior. Our results show that we are able to reproduce CI values and automatically differentiate between normal and memory/learning defective flies using only the feature vectors derived from our video analysis.

Related Publications

Reza et al. 2012, Reza et al. 2013

M.A. Reza's Research Day 2011 Poster

Related Animations

Fly tracking results

This research was performed in collaboration with the Dr. Dan Marenda's Lab and Dr. Aleister Saunder's Lab in Drexel's Biology Department


Steps in the fly identification and tracking process. Calculating a background image, image subtraction, thresholding and filtering to find the flies. Followed by object tracking, that allows us to calculate the geometric quantities from which we derive feature vectors for each video segment.


Contour-based Surface Reconstruction

A wide variety of objects, animals and specimens are scanned for scientific purposes every day in imaging centers across the globe, producing a steady stream of volumetric datasets. Objects such as developing mouse and frog embryos, rat and monkey brains, nerve cells of all types, bones and even fossils are examined by MRI, CT, ET scanners, as well as physically sliced and imaged to produce 3D samplings of these real objects. Once the objects/specimens have been imaged the resulting volume datasets can be manually segmented. In this process, an experienced anatomist goes over selected slices (i.e. images) of the dataset, identifies relevant structures, and circles them with a stylus, producing a series of parallel contours that outline the object of interest. From these sets of contours it is usually required to produce a high quality, smooth 3D surface model that reconstructs the original object. The reconstructed surface is useful for visualization and further processing.

To date, the GBC Group has investigated three solutions to the contour-based surface reconstruction problem. In the first project, which was led by Dr. Ken Museth of Linköping (Sweden) University, we utilize velocity-adjusted 2D level set contour morphing. With this approach, morphing one contour into the next sweeps out a 3D surface. This is accomplished by equating time in the 2D contour morphing process with the third spatial dimension. A critical aspect of this approach utilizes distance estimates corresponding to the arc lengths of trajectories that connect the adjacent contours in the image plane. These distances, together with a time-of-arrival, are used to estimate the speeds (in contour normal directions) needed to produce a smooth morph when transitioning between sets of contours. Animations of the method in action are here and here.

The second project investigated the effectiveness of Multi-level Partition of Unity (MPU) implicit models to reconstruct surfaces from noisy input contours. Almost all contour-based surface reconstruction techniques exactly interpolate the input contours. MPU implicit surfaces are a type of point set surface that approximates input data within user-specified error bounds. Thus they offer an approach that inherently copes with noisy data in a controllable fashion. The MPU-based reconstruction technique interprets the contour data (pixels in individual images) as points in 3-space. Since MPU implicits also require normal information, it was necessary to develop an algorithm to estimate surface normals from the stacked contours.

A third technique utilizes spline-based 2D distance field interpolation to produce a volumetric representation of the reconstructed surface. Filtering techniques are employed in order to remove the medial axis discontinuities that are found in distance fields. Additionally, monotonicity-constraining natural cubic splines are used to prevent overshoot during interpolation. This third reconstruction approach has proven to be most effective when processing high-complexity, multi-component contours.

Related Publications

Nilsson et al. 2005, Marker et al. 2006, Braude et al. 2007, Petushi et al. 2008

J. Marker's Research Day 2006 Poster

This research was performed in collaboration with the Graphics Group of Linköping (Sweden) University, the DUCoM Laboratory for Bioimaging and Anatomical Informatics and the DUCoM Advanced Pathology Imaging Laboratory.


Contour-based surface reconstruction using 2D level set metamorphosis. Pelvis dataset with 35 input contours.



Contour-based surface reconstruction using MPU implicit surfaces. Mouse embryo skin dataset with 186 input contours (46,204 points). Mouse embryo heart dataset with 34 input contours (4,528 points). Mouse embryo stomach dataset with 34 input contours (4,088 points).


Contour-based surface reconstruction using monotonicity-constrained splines to perform 2D distance field interpolation (48 contours).



Contour-based surface reconstruction using monotonicity-constrained splines to perform 2D distance field interpolation. Segmented and classified breast cancer histology image. Color-coded 3D reconstruction of the breast cancer tumor from 9 slices.

Breast cancer tumor reconstructions (distance interpolation method)


Simulation of Chemotaxis-based Cell Aggregation and Sorting

The GBC Group is developing a computational model and simulation system that may be used to investigate the fundamental biological processes controlling chemotaxis-based cell aggregation. Chemotaxis is the phenomenon where cells emit chemicals (chemoattractants) into and detect chemical gradients within their environment. They respond to the chemical stimulus by moving in the direction of the chemical gradient and attaching themselves to the other cells upon contact. This process produces cell aggregates that are the building blocks of biological tissue and structure formation. Understanding the influence of the many components of chemotaxis on overall cell aggregation may lead to technologies for tissue engineering based on controlling or directing these underlying biological processes. The key technical challenge in this project is to define a computational model that can be computed efficiently and can effectively capture the biological phenomena of interest, ultimately leading to a predictive simulation capability that supports the discovery of new knowledge in cell biology.

The computational model has been extended to simulate the sorting of heterotypic cell populations. The model for studying cell sorting consists of a subset of features from the chemotaxis-based cell aggregation model. The cells in our sorting experiments do not attach to each other, divide or die, but they do age, and emit and respond to chemoattractant gradients. Additionally new features/parameters have been added to each cell type, namely the excretion of a distinct chemoattractant, a chemotactic response rate and a probability of gradient following for each chemoattractant. Our initial in-silico cell sorting experiments only contained two types of cell populations, T1 and T2. Each cell type emits a unique chemoattractant chemical, C1 and C2 respectively. Both types of cells can sense/respond to both types of chemicals and the strengths of these interactions are defined with parameters L1 and L2. A cell's velocity is proportional to the sum of the sensed, adjusted gradients. Another parameter added in the sorting model is P1 and P2, the probability that a cell will follow the gradient of a specific chemoattractant (C1 and C2) during a simulation time step. If a cell does not respond to a gradient it takes a random step. This computational model produces the sorting results included below.

Related Publications

Eyiyurekli et al. 2007a, Eyiyurekli et al. 2007b, Eyiyurekli et al. 2008, Eyiyurekli et al. 2010, Bai et al. 2013

M. Eyiyurekli's Research Day 2007 Poster

M. Eyiyurekli's Research Day 2008 Poster

This research was performed in collaboration with the Drexel Integrated Laboratory for Cellular Tissue Engineering and Regenerative Medicine,

Cell aggregation simulation results.


Cell sorting simulation results.



Bone Scan Analysis

Drexel's Bone Biology Laboratory studies the microscopic structure of human bones in order to understand the relationship between these structures, aging, health and the large-scale mechanical properties of bone. The Facility acquires high-resolution microscopic optical images of bone under various lighting and filtering conditions, as well as microCT scans.

Cortical bone modeling and drift plays an important role in determining adult bone shape, quantity and quality. With increasing evidence that the bone we grow as children likely affects the health of our bone as we age, it is important to better quantify this process through ontogeny. Moreover, automated means of quantifying these processes can be useful for evaluating the consequences of various health conditions and nutritional deficits on bone growth, important both in modern, orthopedic contexts, and in anthropological contexts to gain insights into the functional adaptations of past populations. In order to investigate this issue the GBC Group is developing a methodology for user-guided segmentation of microCT images of cortical bone cross-sections to (1) discriminate regions of periosteal primary bone apposition that reflect the history of cortical drift in a long bone shaft section and (2) perform measurements that can provide information on bone shape through ontogeny that can then be computationally compared with other the shapes of other bones.

Related Publications

J. DiCristo's STAR 2009 Poster

1) A microCT scan of an adolescent bone. 2) Screenshot of program for specifying segmentation parameters. 3) Results of the segmentation. Pores that fall within a specified size range are highlighted in green. 4) Radial lines are used to calculate the thickness of the periosteal primary bone region (between the circular polyline and the bone boundary) as a function of angle.


Last modified on January 23, 2023.