A shape signature based on surface Ricci flow and optimal mass transportation is introduced for the purpose of surface comparison. First, the surface is conformally mapped onto plane by Ricci flow, which induces a measure on the planar domain. Second, the unique optimal mass transport map is computed that transports the new measure to the canonical measure on the plane. The map is obtained by a convex optimization process. This optimal transport map encodes all the information of the Riemannian metric on the surface. The shape signature consists of the optimal transport map, together with the mean curvature, which can fully recover the original surface. The discrete theories of surface Ricci flow and optimal mass transportation are explained thoroughly. The algorithms are given in detail. The signature is tested on human facial surfaces with different expressions accquired by structured light 3-D scanner based on phase-shifting method. The experimental results demonstrate the efficiency and efficacy of the method.
Cone-beam computed tomography (CBCT) has attracted growing interest of researchers in image reconstruction. The
mAs level of the X-ray tube current, in practical application of CBCT, is mitigated in order to reduce the CBCT dose.
The lowering of the X-ray tube current, however, results in the degradation of image quality. Thus, low-dose CBCT
image reconstruction is in effect a noise problem. To acquire clinically acceptable quality of image, and keep the X-ray
tube current as low as achievable in the meanwhile, some penalized weighted least-squares (PWLS)-based image
reconstruction algorithms have been developed. One representative strategy in previous work is to model the prior
information for solution regularization using an anisotropic penalty term. To enhance the edge preserving and noise
suppressing in a finer scale, a novel algorithm combining the local binary pattern (LBP) with penalized weighted leastsquares
(PWLS), called LBP-PWLS-based image reconstruction algorithm, is proposed in this work. The proposed
LBP-PWLS-based algorithm adaptively encourages strong diffusion on the local spot/flat region around a voxel and less
diffusion on edge/corner ones by adjusting the penalty for cost function, after the LBP is utilized to detect the region
around the voxel as spot, flat and edge ones. The LBP-PWLS-based reconstruction algorithm was evaluated using the
sinogram data acquired by a clinical CT scanner from the CatPhan® 600 phantom. Experimental results on the noiseresolution
tradeoff measurement and other quantitative measurements demonstrated its feasibility and effectiveness in
edge preserving and noise suppressing in comparison with a previous PWLS reconstruction algorithm.
KEYWORDS: Facial recognition systems, Nose, 3D image processing, Databases, 3D modeling, Detection and tracking algorithms, Mouth, Principal component analysis, Eye, 3D acquisition
In this paper, we propose a 3D face recognition approach based on the conformal representation of facial surfaces. Firstly, facial surfaces are mapped onto the 2D unit disk by Riemann mapping. Their conformal representation (i.e. the pair of mean curvature (MC) and conformal factor (CF) ) are then computed and encoded to Mean Curvature Images (MCIs) and Conformal Factor Images (CFIs). Considering that different regions of face deform unequally due to expression variation, MCIs and CFIs are divided into five parts. LDA is applied to each part to obtain the feature vector. At last, five parts are fused on the distance level for recognition. Extensive experiments carried out on the BU-3DFE database demonstrate the effectiveness of the proposed approach.
Human colon has complex structures since it turns, twists, and even mobiles when the position of patient changes. The
awareness of the locations and orientations is very important for improving the experience of virtual navigation,
registration of supine/prone images and polyp matching. Teniae coli (TCs) are three longitudinal muscles along the
human colon. They are parts of the colon wall, and they have the potential to serve as reliable landmarks to provide the
above mentioned awareness. Morphologically, TCs are three smooth narrow bands, approximately perpendicular to the
haustral folds, and extending between the fold pairs in a parallel manner. Such characteristics make the TCs detectable
if the folds have been extracted already. In this study, based on the previous work of the segmentation of haustral folds,
we introduce a new method of automatically detecting the three TCs. The experiments will be conducted on real patient
studies to demonstrate the feasibility of the method, and solid evaluation will be conducted based on a flattened two-dimensional
(2D) colon representation.
Bladder cancer is reported to be the fifth leading cause of cancer deaths in the United States. Recent advances in medical
imaging technologies, such as magnetic resonance (MR) imaging, make virtual cystoscopy a potential alternative with
advantages as being a safe and non-invasive method for evaluation of the entire bladder and detection of abnormalities.
To help reducing the interpretation time and reading fatigue of the readers or radiologists, we introduce a computer-aided
detection scheme based on the thickness mapping of the bladder wall since locally-thickened bladder wall often appears
around tumors. In the thickness mapping method, the path used to measure the thickness can be determined without any
ambiguity by tracing the gradient direction of the potential field between the inner and outer borders of the bladder wall.
The thickness mapping of the three-dimensional inner border surface of the bladder is then flattened to a twodimensional
(2D) gray image with conformal mapping method. In the 2D flattened image, a blob detector is applied to
detect the abnormalities, which are actually the thickened bladder wall indicating bladder lesions. Such scheme was
tested on two MR datasets, one from a healthy volunteer and the other from a patient with a tumor. The result is
preliminary, but very promising with 100% detection sensitivity at 7 FPs per case.
Magnetic resonance visual cystoscopy or MR cystography (MRC) is an emerging tool for bladder tumor detection,
where three-dimensional (3D) endoscopic views on the inner bladder surface are being investigated by researchers. In
this paper, we further investigate an innovative strategy of visualizing the inner surface by flattening the 3D surface into
a 2D display, where conformal mapping, a mathematically-proved algorithm with shape preserving, is used. The
original morphological, textural and even geometric information can be visualized in the flattened 2D image. Therefore,
radiologists do not have to manually control the view point and angle to locate the possible abnormalities like what they
do in the 3D endoscopic views. Once an abnormality is detected on the 2D flattened image, its locations in the original
MR slice images and in the 3D endoscopic views can be retrieved since the conformal mapping is an invertible
transformation. In such a manner, the reading time needed by a radiologist can be expected to be reduced. In addition to
the surface information, the bladder wall thickness can be visualized with encoded colors on the flattened image. Both
normal volunteer and patient studies were performed to test the reconstruction of 3D surface, the conformal flattening,
and the visualization of the color-coded flattened image. A bladder tumor of 3 cm size is so obvious on the 2D flattened
image such that it can be perceived only at the first sight. The patient dataset shows a noticeable difference on the wall
thickness distribution than that of the volunteer's dataset.
KEYWORDS: Shape analysis, 3D modeling, Control systems, Brain, Brain mapping, Image segmentation, Magnetic resonance imaging, Sensors, Data modeling, Visualization
A number of studies have documented that autism has a neurobiological basis, but the anatomical extent of these
neurobiological abnormalities is largely unknown. In this study, we aimed at analyzing highly localized shape
abnormalities of the corpus callosum in a homogeneous group of autism children. Thirty patients with essential autism
and twenty-four controls participated in this study. 2D contours of the corpus callosum were extracted from MR images
by a semiautomatic segmentation method, and the 3D model was constructed by stacking the contours. The resulting 3D
model had two openings at the ends, thus a new conformal parameterization for high genus surfaces was applied in our
shape analysis work, which mapped each surface onto a planar domain. Surface matching among different individual
meshes was achieved by re-triangulating each mesh according to a template surface. Statistical shape analysis was used
to compare the 3D shapes point by point between patients with autism and their controls. The results revealed significant
abnormalities in the anterior most and anterior body in essential autism group.
Recent advances in imaging technologies, such as Magnetic Resonance Imaging (MRI), Positron Emission Tomography (PET) and Diffusion Tensor Imaging (DTI) have accelerated brain research in many aspects. In order to better understand the synergy of the many processes involved in normal brain function, integrated modeling and analysis of MRI, PET, and DTI is highly desirable. Unfortunately, the current state-of-art computational tools fall short in offering a comprehensive computational framework that is accurate and mathematically rigorous. In this paper we present a framework which is based on conformal parameterization of a brain from high-resolution structural MRI data to a canonical spherical domain. This model allows natural integration of information from co-registered PET as well as DTI data and lays the foundation for a quantitative analysis of the relationship between diverse data sets. Consequently, the system can be designed to provide a software environment able to facilitate statistical detection of abnormal functional brain patterns in patients with a large number of neurological disorders.
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