3DMA-Rock

Three Dimensional Image Analysis

W. B. Lindquist

Three dimensional, non-invasive imaging technology is hot! It has vital applications in medical diagnosis, scientific inquiry, industry, and "homeland" security. In medical diagnosis, computer-aided X-ray tomography (CT) and magnetic resonance imaging (MRI) are the dominant 3D imaging techniques, while serious efforts are undergoing to improve acoustic tomography. In biological fields, especially neroscience, three dimensional laser-scanning microscopy, either through confocal or multi-photon means, is the dominant 3D imaging tool. In biomedical engineering CT imaging (bone, circulatory system, lungs) and MRI (heart) are the dominant imaging paradigms. Whole animal MRI and CT systems have recently come on-line for small animal imaging. Brain activity studies are dominated by PET-scanning techology. In material science, where dosage requirments are less stringent, the penetration capability of CT scanning is important. At molecular length scales, in physics and chemistry, electron tomography is being rapidly developed. The fiber industry is adopting CT imaging as a primary means of examining woven and non-woven fiber products. Global terrorism has spawned a security industry that relies heavily on X-ray technology. Here, limited angle CT scanning holds great promise for improved error detection capability over that provided by classical, single view, 2D X-ray imaging.

Of necessity, primary 3D imaging research has focused on production and improvement of imaging hardware and on development of the algorithms necessary to produce the 3D image from the recorded data. One example of this is the historical development from first generation CT (pencil beam, single pixel recording) through to current "n-th generation" medical CT scanners (cone-shaped X-ray beam and areal CCD cameras mounted on a frame that performs a helical trace around the patient). However, mature two dimensional imaging technology (including stereoscopic imaging) such as satellite photography has demonstrated that automation of the analysis of the contents of images, especially feature recognition, is vital for large scale usage of imaging technology. (In mature imaging technologies, a great quantitiy of images can be produced cheaply, overwhelming manual-based efforts to analyze the images.) In addition, automated image analysis reduces user-bias and fatique-related errors associated with human analysis. Character recognition, biometric recognition of faces, fingerprints - even voices (as acoustic signals are indeed ``images'') are all recognized as important automated feature recognition problems.

Three dimensional feature recognition is harder than 2D recognition, but it has at least the "shoulders" of the work in 2D to "stand upon". The 3DMA algorithmic suite has focussed on four areas of application for the development of feature recognition ability in three dimensional imaging technologies. These are (in historical order), two phase geologic media (rock), neurons, fiber products and trabecular bone. Feature detection and automated quantification of parameters of interest in geologic media is very similar to that in bone and also includes analysis of concrete, soil, and industrial composite materials.

In general, a 3D imaging problem can be reduced to the following sequence of steps.

  • Segmentation: identification the separate material "phases" in the image. Much of the time this can be reduced to a two-phase problem: eg. for rock the phases are grain and air; in images of the central nervous system, the phases are nerve cell and exterior tissue; in fiber imagery the phases are cellulose (or, in the case of synthetics, polymer) and air. The 3DMA suite utilizes a segmentation method based upon indicator kriging (developed by Oh and Lindquist) to perform segmentations. There is a vast field of literature on segmentation methods, each of which performs well for certain segmentation problems; none of which perform well in all cases. One should always endeavor to pick the "best" segmentation algorithm for the task at hand. A recent paper [S. Rajagopalan, M.J. Yaszemski, R. Robb, Evaulation of thresholding techniques for segmenting scaffold images in tissue engineering, Medical Imaging 2004: Physiology, Function and Structure from Medical Images. A.A. Amini and A. Manduca eds. Proc. SPIE, Vol. 5370 (2004) 1456-1465.] has shown our indicator kriging method to be the best in a field of 12 methods studied on biological images.

    It should be noted that, in optical images (e.g. laser scanning confocal microscopy) a correction for the point-spread function effects induced by the optics, should be made before segmentation is applied. This correction is known as deconvolution. In our experience with laser scanned images, we have found the blind deconvolution method utilized in the commercial package Autoquant (www.aqi.com) to be superior.

  • Skeletonization: Each phase forms a three dimensional object, often of convoluted shape. Skeletonization is the process of embedding a lower dimensional backbone within each phase of interest to provide a searchable network "in order to find one's way around". A digitized medial axis (MA), which preserves the topology of the object and retains a strict geometrical relationship relative to the surface of the object is a valuable way to provide the skeleton. 3DMA uses the digital medial axis algorithm of Lee, Kashyap and Chu, although other algorithms are available. One desirable feature of the MA is that each point on the MA provides a unique "location" within the object. While the MA can be used to extract some limited information concerning the object, its most desirable feature is that of a searchable network.

    It should be noted that, as the surface of the imaged object (the phase) contains noise, and the MA is defined relative to the object surface, surface noise translates to MA noise. Thus practical use of the MA requires either trimming to eliminate noise-induced branching or careful use of the MA to avoid susceptibility to noise.

  • Feature recognition algorithms: Using a trimmed version of the medial axis, we have developed the following feature recognition algorithms in the 3DMA suite of software:

    3DMA-rock: throat finding. Identification of local minima in cross sectional area of the object as one travels along the MA. We have developed two major algorithms (slow and accurate [Venkatarangan and Lindquist], faster but slightly less accurate [Shin and Lindquist])

    3DMA-neuron: identification of dendritic spines (post synaptic terminals) identification of separate dendritic branches We are currently working on the problems of separate identification of dendrites and axons, and on identifying axonal boutons (pre-synatic swellings). These should appear May or August as part of the thesis of my student Firas Daabouhl.

    3DMA-fiber: identification of individual fibers in a matte. (Fibers touch as they cross.) We have also recently added code to identify and analyze individual plys in a two-ply tissue.

  • Statistical quantification of measured parameters: We take the viewpoint that returning only mean values of measured quantities is inadequate information. We always summarize the full distribution of any measured parameter, as data printout of all measured values found and as graphical display of (a histogram of) the measured distribution.