Research Areas

Geometric Deep Learning

Convolutional neural networks (CNN) have demonstrated an unprecedented success in a variety of visual cognition tasks. Such a success, however, has been concentrated in mostly computer vision and image/signal processing applications, where one can enjoy a nice, grid-like structure of the data set (signal=1D grid of amplitudes, image=2D grid of pixel values, and such). Meanwhile, there is a large number of problems that could not benefit much from such powerful CNNs due to the non-Euclidean nature of the data set. For instance, graphical models, such as computer graphics objects or computer-aided design (CAD) parts, often exist as a boundary representation (B-rep) model in which the geometry of the model is represented by a thin, arbitrary-shaped boundary surface (2D manifold), rather than a grid-like representation. Hence, there is no canonical way of representing such data in a tensor format as expected by CNNs and, thus, the standard CNNs cannot analyze such data. Point clouds from 3D scanners or LiDAR systems, graphs from social network data, molecular structures of pharmaceutical compounds, protein foldings, and many other non-image type geometric data fall into this category. At the Visual Intelligence Laboratory, we aim to develop mathematical foundations and scalable algorithms to expand CNNs to a variety of different geometric domains. Many scientific studies may benefit from such new capability, including computer-aided design and manufacturing (CAD/CAM), computer graphics, 3D sensing systems on autonomous vehicles, the brain mapping problem in neuroscience, and computational mechanics, just to list a few.

Research Projects



 

Digital Human Modeling & Analysis

Each human body can be described through a set of numerical parameters which act similarly to one’s fingerprint. These body shape parameters can be used in a multitude of different scenarios. They can be used in movies, video games, virtual reality, and more to easily create highly realistic avatars and 3D models. These sets can also be analyzed to learn more about how people’s body type is related to their socioeconomic status. We use computational geometry and machine learning techniques to extract such numerical parameters from 3D scans, photographs, etc.

Research Projects



 

Autonomous Human-centered Vehicle Systems

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Medical Image Analysis

By studying shapes and textures of medical images, it is possible to detect disease and predict clinical outcomes more accurately. To this end, we are interested in characterizing shapes and textures of diseases in medical images (X-rays, CT, PET, MRI, etc.) and correlate them with other clinical parameters.


 

Data-driven Design & Simulation

It is hardly a stretch of logic to say many problems in science and engineering begin with reasoning of shapes. We are interested in teaching a computer such “geometric reasoning,” like what human designers and engineers would do when they solve a real-world problem. With an advanced machine cognition, designers and engineers will be able to focus more of their time and power on innovation and better design solutions. Furthermore, we could also learn complex patterns around geometric data that are beyond our cognitive capacity.