Jovan G. Brankov

Digital watermarking robust to geometric distortions

In this paper, we present two watermarking approaches that are robust to geometric distortions. The first approach is based on image normalization, in which both watermark embedding and extraction are carried out with respect to an image normalized to meet a set of predefined moment criteria. We propose a new normalization procedure, which is invariant to affine transform attacks. The resulting watermarking scheme is suitable for public watermarking applications, where the original image is not available for watermark extraction. The second approach is based on a watermark resynchronization scheme aimed to alleviate the effects of random bending attacks. In this scheme, a deformable mesh is used to correct the distortion caused by the attack. The watermark is then extracted from the corrected image. In contrast to the first scheme, the latter is suitable for private watermarking applications, where the original image is necessary for watermark detection. In both schemes, we employ a direct-sequence code division multiple access approach to embed a multibit watermark in the discrete cosine transform domain of the image. Numerical experiments demonstrate that the proposed watermarking schemes are robust to a wide range of geometric attacks.

Multiple-image radiography

Conventional radiography produces a single image of an object by measuring the attenuation of an x-ray beam passing through it. When imaging weakly absorbing tissues, x-ray attenuation may be a suboptimal signature of disease-related information. In this paper we describe a new phase-sensitive imaging method, called multiple-image radiography (MIR), which is an improvement on a prior technique called diffraction-enhanced imaging (DEI). This paper elaborates on our initial presentation of the idea in Wernick et al (2002 Proc. Int. Symp. Biomed. Imaging pp 129-32). MIR simultaneously produces several images from a set of measurements made with a single x-ray beam. Specifically, MIR yields three images depicting separately the effects of refraction, ultra-small-angle scatter and attenuation by the object. All three images have good contrast, in part because they are virtually immune from degradation due to scatter at higher angles. MIR also yields a very comprehensive object description, consisting of the angular intensity spectrum of a transmitted x-ray beam at every image pixel, within a narrow angular range. Our experiments are based on data acquired using a synchrotron light source; however, in preparation for more practical implementations using conventional x-ray sources, we develop and evaluate algorithms designed for Poisson noise, which is characteristic of photon-limited imaging. The results suggest that MIR is capable of operating at low photon count levels, therefore the method shows promise for use with conventional x-ray sources. The results also show that, in addition to producing new types of object descriptions, MIR produces substantially more accurate images than its predecessor, DEI. MIR results are shown in the form of planar images of a phantom and a biological specimen. A preliminary demonstration of the use of MIR for computed tomography is also presented.

Machine Learning in Medical Imaging

This article will discuss very different ways of using machine learning that may be less familiar, and we will demonstrate through examples the role of these concepts in medical imaging. Although the term machine learning is relatively recent, the ideas of machine learning have been applied to medical imaging for decades, perhaps most notably in the areas of computer-aided diagnosis (CAD) and functional brain mapping. We will not attempt in this brief article to survey the rich literature of this field. Instead our goals will be 1) to acquaint the reader with some modern techniques that are now staples of the machine-learning field and 2) to illustrate how these techniques can be employed in various ways in medical imaging.

Tomographic image reconstruction based on a content-adaptive mesh model

In this paper, we explore the use of a content-adaptive mesh model (CAMM) for tomographic image reconstruction. In the proposed framework, the image to be reconstructed is first represented by a mesh model, an efficient image description based on nonuniform sampling. In the CAMM, image samples (represented as mesh nodes) are placed most densely in image regions having fine detail. Tomographic image reconstruction in the mesh domain is performed by maximum-likelihood (ML) or maximum a posteriori (MAP) estimation of the nodal values from the measured data. A CAMM greatly reduces the number of unknown parameters to be determined, leading to improved image quality and reduced computation time. We demonstrated the method in our experiments using simulated gated single photon emission computed tomography (SPECT) cardiac-perfusion images. A channelized Hotelling observer (CHO) was used to evaluate the detectability of perfusion defects in the reconstructed images, a task-based measure of image quality. A minimum description length (MDL) criterion was also used to evaluate the effect of the representation size. In our application, both MDL and CHO suggested that the optimal number of mesh nodes is roughly five to seven times smaller than the number of projection bins. When compared to several commonly used methods for image reconstruction, the proposed approach achieved the best performance, in terms of defect detection and computation time. The research described in this paper establishes a foundation for future development of a (four-dimensional) space-time reconstruction framework for image sequences in which a built-in deformable mesh model is used to track the image motion.

A fast approach for accurate content-adaptive mesh generation

Mesh modeling is an important problem with many applications in image processing. A key issue in mesh modeling is how to generate a mesh structure that well represents an image by adapting to its content. We propose a new approach to mesh generation, which is based on a theoretical result derived on the error bound of a mesh representation. In the proposed method, the classical Floyd-Steinberg error-diffusion algorithm is employed to place mesh nodes in the image domain so that their spatial density varies according to the local image content. Delaunay triangulation is next applied to connect the mesh nodes. The result of this approach is that fine mesh elements are placed automatically in regions of the image containing high-frequency features while coarse mesh elements are used to represent smooth areas. The proposed algorithm is noniterative, fast, and easy to implement. Numerical results demonstrate that, at very low computational cost, the proposed approach can produce mesh representations that are more accurate than those produced by several existing methods. Moreover, it is demonstrated that the proposed algorithm performs well with images of various kinds, even in the presence of noise.

A physical model of multiple-image radiography

We recently proposed a phase-sensitive x-ray imaging method called multiple-image radiography (MIR), which is an improvement on the diffraction-enhanced imaging technique. MIR simultaneously produces three images, depicting separately the effects of absorption, refraction and ultra-small-angle scattering of x-rays, and all three MIR images are virtually immune to degradation caused by scattering at higher angles. Although good results have been obtained using MIR, no quantitative model of the imaging process has yet been developed. In this paper, we present a theoretical prediction of the MIR image values in terms of fundamental physical properties of the object being imaged. We use radiative transport theory to model the beam propagation, and we model the object as a stratified medium containing discrete scattering particles. An important finding of our analysis is that the image values in all three MIR images are line integrals of various object parameters, which is an essential property for computed tomography to be achieved with conventional reconstruction methods. Our analysis also shows that MIR truly separates the effects of absorption, refraction and ultra-small-angle scattering for the case considered. We validate our analytical model using real and simulated imaging data.

A computed tomography implementation of multiple-image radiography

Conventional x-ray computed tomography (CT) produces a single volumetric image that represents the spatially variant linear x-ray attenuation coefficient of an object. However, in many situations, differences in the x-ray attenuation properties of soft tissues are very small and difficult to measure in conventional x-ray imaging. In this work, we investigate an analyzer-based imaging method, called computed tomography multiple-image radiography (CT-MIR), which is a tomographic implementation of the recently proposed multiple-image radiography method. The CT-MIR method reconstructs concurrently three physical properties of the object. In addition to x-ray attenuation, CT-MIR produces volumetric images that represent the refraction and ultrasmall-angle scattering properties of the object. These three images can provide a rich description of the objects physical properties that are revealed by the probing x-ray beam. An imaging model for CT-MIR that is based on the x-ray transform of the object properties is established. The CT-MIR method is demonstrated by use of experimental data acquired at a synchroton radiation imaging beamline, and is compared to the pre-existing diffraction-enhanced imaging CT method. We also investigate the merit of an iterative reconstruction method for use with future clinical implementations of CT-MIR, which we anticipate would be photon limited.

Spatiotemporal processing of gated cardiac SPECT images using deformable mesh modeling

In this paper we present a spatiotemporal processing approach, based on deformable mesh modeling, for noise reduction in gated cardiac single-photon emission computed tomography images. Because of the partial volume effect (PVE), clinical cardiac-gated perfusion images exhibit a phenomenon known as brightening-the myocardium appears to become brighter as the heart wall thickens. Although brightening is an artifact, it serves as an important diagnostic feature for assessment of wall thickening in clinical practice. Our proposed processing algorithm aims to preserve this important diagnostic feature while reducing the noise level in the images. The proposed algorithm is based on the use of a deformable mesh for modeling the cardiac motion in a gated cardiac sequence, based on which the images are processed by smoothing along space-time trajectories of object points while taking into account the PVE. Our experiments demonstrate that the proposed algorithm can yield significantly more-accurate results than several existing methods.

An extended diffraction-enhanced imaging method for implementing multiple-image radiography

Diffraction-enhanced imaging (DEI) is an analyser-based x-ray imaging method that produces separate images depicting the projected x-ray absorption and refractive properties of an object. Because the imaging model of DEI does not account for ultra-small-angle x-ray scattering (USAXS), the images produced in DEI can contain artefacts and inaccuracies in medical imaging applications. In this work, we investigate an extended DEI method for concurrent reconstruction of three images that depict an objects projected x-ray absorption, refraction and USAXS properties. The extended DEI method can be viewed as an implementation of the recently proposed multiple-image radiography paradigm. Validation studies are conducted by use of computer-simulated and synchrotron measurement data.

Segmentation of dynamic PET or fMRI images based on a similarity metric

In this paper, we present a new approach for segmentation of image sequences by clustering the pixels according to their temporal behavior. The clustering metric we use is the normalized cross-correlation, also known as similarity. The main advantage of this metric is that, unlike the traditional Euclidean distance, it depends on the shape of the time signal rather than its amplitude. We model the intra-class variation among the time signals by a truncated exponential probability density distribution, and apply the expectation-maximization (EM) framework to derive two iterative clustering algorithms. Our numerical experiments using a simulated, dynamic PET brain study demonstrate that the proposed method achieves the best results when compared with several existing clustering methods.