Modern medicine and biology have been enormously benefited from the advancement of imaging. New devices and acquisition methods enabled the first images of viruses. Resolution levels for diagnostic imaging are now at the order of a few hundred microns and in 3D; e.g. MRI or CT scans. Despite of all these advances some information in medical images is latent and extracting it is often a tedious task. Achieving finer resolution levels does not automatically make every tissue visible to the eye of the practitioner. The expansion of the imaging frontiers not only increases grossly the volume of the available data but also makes to want to extract more information from an image. Thus, there is an ever growing demand for the development of reliable, automated or semi-automated image analysis tools. With this goal in mind the interdisciplinary group of investigators in this project aims in making theoretical and algorithmic contributions that can lead to the development of such tools.
The problem motivating this project is how to identify or segment soft-tissues that are of interest to medical practitioners or biologists with high spatial accuracy in 3D-images. To our detriment, most of the time tissues of diagnostic interest have great variability, small volume, low contrast and are corrupted by non-standard noise. Based on the premise that soft-tissues are associated with 3D-textures, the investigators approach soft-tissue discrimination/identification as segmentation/identification of the 3D-textures resulting from the tissues of interest. Notable efforts have been made to solve this problem in 2D but in 3D it is practically untouched. To achieve high spatial accuracy in the segmentation/identification of 3D-textures the investigators will build novel probabilistic models for 3D-rigid motion invariant texture signatures. This will reduce or may even eliminate classification errors due to the positioning of a tissue in the 3D-space. To extract such signatures we will characterize and thoroughly study multiscale data representations that are covariant (steerable) with respect to 3D-rigid motions. A major challenge of this project is to extract 3D-rigid motion invariant texture signatures with reasonable length and adopt probabilistic models governing the classification of these signatures in a computationally manageable manner. The envisioned tools will be tested in (3D) CT-angiography scans and 3D-confocal microscopy images of pyramidal neurons. In the first case we wish to segment various soft tissues such as cardiac muscle, epicardial fat, lumen and calcium while in the second we wish to identify dendrites in a noisy background. The investigators aim in developing an algorithmic platform for soft-tissue segmentation based on novel 3D-data representations rather than a customized application. This research program requires the development of novel mathematical ideas both in mathematical analysis and in probability theory. These new mathematical concepts and methods will endow the envisioned algorithms with a unique ability native to human vision but not yet achieved in computer and robotic vision: the identification of structures and patterns independently of their position in the 3D-space. Indeed, tissues must be correctly identifiable by any automated image analysis system regardless of their position in the 3D-space or in the human body. A system with this ability will be able to circumscribe tissue boundaries with the same high accuracy in every direction in the 3D-space. This algorithmic platform can be adopted for a wide variety of imaging applications in medicine and biology, such as CT-angiography used to diagnose stenosis in coronary arteries or contrast CT for the detection of liver cancer. Detecting abnormalities in the walls of coronary arteries especially of their regions proximal to the ascending aorta will help prevent the most life-threatening infarctions and possibly monitor the treatment of the atherosclerotic plaque without the frequent use of the grossly invasive intravascular ultrasound probes. Identifying cancerous lesions in the liver at their early stages of development can significantly increase the chances of survival in this type of cancer. Capturing accurately the structure of dendrites and of their protruding attachments called spines in images acquired with 3D-confocal microscopes is a prime time goal as spines seem to hold the key of understanding the biological basis of depression and bipolar disorder.
The ever growing availability of high resolution, high volume data in biomedical applications imposes an equally growing demand for the extraction of information with high sensitivity and specificity. However, this task is, still, to a great extend manual or minimally automatized for many applications. The fully automatization of these processes is a difficult problem especially due to the increase in the number of domains of research and by the growing number of data acquisition modalities. Within this general framework our project focused on large multidimensional datasets and addressed a fundamental mathematical problem applicable to this type of data: The preparation of the analysis, and the analysis of the data itself, in a way that the extraction of information is carried out in the native dimensionality of imaged objects. In plain English, a CT-scan analysis software should examine the data not slice-by-slice but from any different 3D angle of observation, in a way similar to which a surgeon inspects the internal organs of our body. The main goal of our project was to develop mathematical tools and algorithms enabling the inspection of the data equally accurately from very different angle of observation, capable of identifying or segmenting different types of tissue or cells of interest in 3D-imaging data sets. Obviously, this problem becomes more complex in 3D images, such as CT and MRI scans or stacks of neuronal images acquired with laser scanning microscopes. Our vision is to design algorithms be implementable on ordinary computers available in any clinical or laboratory environment and for data acquired without exotic equipment and expensive procedures and capable of high-throughput analysis of the data. The mathematical tools and algorithmic suites developed with this project enable the extraction of discriminant metrics which can distinguish two types of soft tissue from the 3D-texture each creates in a 3D CT scan or MRI. We developed digital image filters with 3D-omnidirectional sensitivity to detect the boundary of a neural cell automatically from the background in confocal or multiphoton microscopy image stacks. Our mathematical contributions predict the consistent high accuracy of our algorithms. Using new computational tools we extract morphological characteristics of neuronal cells with no need for extensive system training or manual edits of the end results. Last, we are able to delineate accurately and with minimal need for operator intervention the main body of neural cells, the soma, from the background and from the dendritic arbor and the axon in of confocal microscopy images of neuronal cultures by using a novel mathematical metric of tubular appearance. Our algorithms can become the core software for a number of applications in medical and neuroscience imaging. The soft-tissue discrimination algorithm can evolve into a computer-aided analysis tool of the arterial phase hepatic CT useful for the staging and detection of hepatic metastasis. Multiphase CT of the liver improves the sensitivity and specificity of hepatic metastasis identification but results in a large number of images to be analyzed by the radiologist. The detection of this type of metastasis with x-ray CT is particularly challenging because of the heterogeneous appearance of metastatic lesions and the variation in appearance due to the phase of contrast administration. The use of our algorithms can potentially eliminate the need of additional imaging phases which add to the total radiation dose of the procedure, which is undesirable for patients found to have curable disease. Our work on the detection of hepatic metastasis motivated the fusion of ideas to a totally different application, the elimination of the effects of shadows in images. This is a tremendously interesting problem with applications to image enhancement for face recognition in video and still images obtained under suboptimal illumination conditions. One of the fascinating, likely applications of this work is the enhancement of infrared video and images where a canopy or debris degrade the quality of images. Last but not least, we attempt to sketch the domain in which our algorithmic suites for the semi-automatic segmentation of neurons, identification of neuronal compartments and extraction of anatomical information from confocal and multiphoton microscopy images contribute. These novel imaging modalities facilitate the acquisition of high-resolution fluorescent images of neurons both in vitro and in vivo and allow, thus, the monitoring of their dynamic structural changes of a neuron or of small circuits of neurons in real-time. One of the most fascinating anatomical element in a neuron is its spines. Our completed work has laid the foundation for significant improvement in the automation of the monitoring of spines, which is now performed mostly manually and very painstakingly. With the continuing NSF support we will develop custom designed mathematical tools and algorithms for the detection and classification of spines and the monitoring of synaptic activity in small circuits of neurons. All this work will be built on the foundation work which our completed NSF awarded supported.
