Biography | Research | Teaching | Publications | Talks | Software | Collaborations | Home


Minh N. Do: Research Statement



Imaging was selected by the National Academy of Engineering as one of the 20 greatest engineering achievements of the 20th century. Imaging technologies continue to have significant impacts on many aspects of our lives. Everyday users access multimedia information on the Web. Doctors routinely rely on medical images (such as MRI and CT scans) for diagnostics. Scientists use images from very large scale (astronomical images) to understand the origin of the universe to very small scale (molecular images) to understand how billions of DNA molecules give rise to a human being.

This trend of increasing dependency on imaging technologies has created an unprecedented demand for more powerful and effective image processing algorithms and applications. At the fundamental level, traditional image processing has largely been developed as a simple separable extension from the one-dimensional signal processing. My primary research goal has been developing new "true" multidimensional tools that can capture geometrical structures that typically are the dominant feature in images and multidimensional data.

Geometric image representations and processing. Efficient representation of visual information lies at the heart of many image processing tasks such as reconstruction, compression, denoising, and feature extraction. For example, a 512 by 512 color image can be considered as a point in a 512*512*3 dimensional space (each pixel is represented by a triple of color components). However, as we can see in the figure below, a randomly chosen image from this space is far from being a "real" image. In other words, "real" images live in tiny parts of the huge space of all possible images. Effectively exploring this fact allows us to compress an image or to filter a clean image out from contaminated noise.

A natural image A bioimage A random image

As can be seen from the above figure, the key distinguishing feature of "real" images is that they have intrinsic geometrical structure. In particular, visual information is mainly contained in the geometry of object boundaries. Although geometry has been long considered in mathematics and computer vision for modeling visual information, the challenges in exploring geometry in image processing come from the discrete nature of the data, as well as the issues of robustness and efficiency. I am working on a discrete-space framework for the construction of multiscale geometric image transforms and algorithms that can be applied to sampled images. I plan to use this as a stepping stone to bridge the gap between the low-level image processing algorithms and the high-level geometry models in computer vision. Furthermore, by connecting and unifying ideas from harmonic analysis, visual perception, computer vision, and signal processing, I seek new fruitful interactions between these fields.

Integrating image formation and image processing. On the other side of the image processing world is image formation -- the process of forming an image from acquired data (e.g. generating a computer tomography image from X-ray measurements). Typically, these two fields have been developed independently using digital images as the link. To be more effective, future imaging systems need to integrate all layers from image formation to high level image processing.

Since images are formed and processed in digital form, at the heart of this integration is the intersection between the continuous and discrete domains. Traditionally, this is handled via the Shannon sampling theorem under the bandlimited condition, which is typically violated by the existence of a discontinuity. Consequently, it is of considerable interest to develop new sampling and reconstruction schemes for more general image classes than the usual bandlimited model. I am working toward a new sampling theory for multidimensional signals that can be represented or approximated by a finite number of parameters (e.g. piecewise smooth images with piecewise smooth boundaries). Such sampling theory would lead to powerful image processing algorithms that work directly with the acquired data.

Image processing and reconstruction from multiple sensors. Existing visual recording systems use a single camera, and thus provide viewers with a passive viewing experience. I envision the development of new systems employing multiple cameras and sensors to deliver unprecedented immersive recording and viewing capabilities. Such systems are expected to be feasible thanks to the continuing improvement in digital technology that now offers low-cost sensors and massive computing power.

In this direction, I am investigating new imaging techniques for reconstruction of the visual recording at an arbitrary location in space and time from multiple cameras and sensors. This can be seen as a sampling problem of the high-dimensional plenoptic function that describes the light intensity passing through every viewpoint, in every direction, for all time, and for every wavelength. My main goal here is to search for new high-dimensional representations and processing algorithms that can deal effectively with plenoptic geometrical structures.

In summary, I am interested in developing new multidimensional signal processing tools, and applying these tools to a wide range of imaging applications. This work will require deep ideas in mathematics and information theory, and will also combine notions from the physics of sensor data, computer algorithms, and the psychology of perception. I have found that performing research from pure theoretical investigations to practical applications, especially where there is a cross feeding between theory and practice as well as between different fields, is extremely productive.