11 research outputs found
Local Geometric Transformations in Image Analysis
The characterization of images by geometric features facilitates the precise analysis of the structures found in biological micrographs such as cells, proteins, or tissues. In this thesis, we study image representations that are adapted to local geometric transformations such as rotation, translation, and scaling, with a special emphasis on wavelet representations. In the first part of the thesis, our main interest is in the analysis of directional patterns and the estimation of their location and orientation. We explore steerable representations that correspond to the notion of rotation. Contrarily to classical pattern matching techniques, they have no need for an a priori discretization of the angle and for matching the filter to the image at each discretized direction. Instead, it is sufficient to apply the filtering only once. Then, the rotated filter for any arbitrary angle can be determined by a systematic and linear transformation of the initial filter. We derive the Cramér-Rao bounds for steerable filters. They allow us to select the best harmonics for the design of steerable detectors and to identify their optimal radial profile. We propose several ways to construct optimal representations and to build powerful and effective detector schemes; in particular, junctions of coinciding branches with local orientations. The basic idea of local transformability and the general principles that we utilize to design steerable wavelets can be applied to other geometric transformations. Accordingly, in the second part, we extend our framework to other transformation groups, with a particular interest in scaling. To construct representations in tune with a notion of local scale, we identify the possible solutions for scalable functions and give specific criteria for their applicability to wavelet schemes. Finally, we propose discrete wavelet frames that approximate a continuous wavelet transform. Based on these results, we present a novel wavelet-based image-analysis software that provides a fast and automatic detection of circular patterns, combined with a precise estimation of their size
A Novel Adaptive Level Set Segmentation Method
The adaptive distance preserving level set (ADPLS) method is fast and not dependent on the initial contour for the segmentation of images with intensity inhomogeneity, but it often leads to segmentation with compromised accuracy. And the local binary fitting model (LBF) method can achieve segmentation with higher accuracy but with low speed and sensitivity to initial contour placements. In this paper, a novel and adaptive fusing level set method has been presented to combine the desirable properties of these two methods, respectively. In the proposed method, the weights of the ADPLS and LBF are automatically adjusted according to the spatial information of the image. Experimental results show that the comprehensive performance indicators, such as accuracy, speed, and stability, can be significantly improved by using this improved method
New Region-Scalable Discriminant and Fitting Energy Functional for Driving Geometric Active Contours in Medical Image Segmentation
We propose a novel region-based geometric active contour model
that uses region-scalable discriminant and fitting energy functional for handling the intensity inhomogeneity and weak boundary problems in medical image segmentation. The region-scalable discriminant and fitting energy functional is defined to capture the image intensity characteristics in local and global regions for driving the evolution of active contour. The discriminant term in the model aims at separating background and foreground in scalable regions while the fitting term tends to fit the intensity in these regions. This model is then transformed into a variational level set formulation with a level set regularization term for accurate computation. The new model utilizes intensity information in the local and global regions as much as possible; so it not only handles better intensity inhomogeneity, but also allows more robustness to noise and more flexible initialization in comparison to the original global region and regional-scalable based models. Experimental results for synthetic and real medical image segmentation show the advantages of the proposed method in terms of accuracy and robustness
Automation of Hessian-Based Tubularity Measure Response Function in 3D Biomedical Images
The blood vessels and nerve trees consist of tubular objects interconnected into a complex tree- or web-like structure that has a range of structural scale 5 μm diameter capillaries to 3 cm aorta. This large-scale range presents two major problems; one is just making the measurements, and the other is the exponential increase of component numbers with decreasing scale. With the remarkable increase in the volume imaged by, and resolution of, modern day 3D imagers, it is almost impossible to make manual tracking of the complex multiscale parameters from those large image data sets. In addition, the manual tracking is quite subjective and unreliable. We propose a solution for automation of an adaptive nonsupervised system for tracking tubular objects based on multiscale framework and use of Hessian-based object shape detector incorporating National Library of Medicine Insight Segmentation and Registration Toolkit (ITK) image processing libraries
Scale spaces on Lie groups
In the standard scale space approach one obtains a scale space representation u:R of an image by means of an evolution equation on the additive group (R d ,¿+¿). However, it is common to apply a wavelet transform (constructed via a representation of a Lie-group G and admissible wavelet ¿) to an image which provides a detailed overview of the group structure in an image. The result of such a wavelet transform provides a function on a group G (rather than (R d ,¿+¿)), which we call a score. Since the wavelet transform is unitary we have stable reconstruction by its adjoint. This allows us to link operators on images to operators on scores in a robust way. To ensure -invariance of the corresponding operator on the image the operator on the wavelet transform must be left-invariant. Therefore we focus on left-invariant evolution equations (and their resolvents) on the Lie-group G generated by a quadratic form Q on left invariant vector fields. These evolution equations correspond to stochastic processes on G and their solution is given by a group convolution with the corresponding Green’s function, for which we present an explicit derivation in two particular image analysis applications. In this article we describe a general approach how the concept of scale space can be extended by replacing the additive group R d by a Lie-group with more structure. The Dutch Organization for Scientific Research is gratefully acknowledged for financial support This article provides the theory and general framework we applied in [9],[5],[8]
Nonlinear Diffusion on the 2D Euclidean Motion Group
Linear and nonlinear diffusion equations are usually considered on an image, which is in fact a function on the translation group. In this paper we study diffusion on orientation scores, i.e. on functions on the Euclidean motion group SE(2). An orientation score is obtained from an image by a linear invertible transformation. The goal is to enhance elongated structures by applying nonlinear left-invariant diffusion on the orientation score of the image. For this purpose we describe how we can use Gaussian derivatives to obtain regularized left-invariant derivatives that obey the non-commutative structure of the Lie algebra of SE(2). The Hessian constructed with these derivatives is used to estimate local curvature and orientation strength and the diffusion is made nonlinearly dependent on these measures. We propose an explicit finite difference scheme to apply the nonlinear diffusion on orientation scores. The experiments show that preservation of crossing structures is the main advantage compared to approaches such as coherence enhancing diffusion
Linear image reconstruction by Sobolev norms on the bounded domain
The reconstruction problem is usually formulated as a variational problem in which one searches for that image that minimizes a so called prior (image model) while insisting on certain image features to be preserved. When the prior can be described by a norm induced by some inner product on a Hilbert space the exact solution to the variational problem can be found by orthogonal projection. In previous work we considered the image as compactly supported in and we used Sobolev norms on the unbounded domain including a smoothing parameter ¿>¿0 to tune the smoothness of the reconstruction image. Due to the assumption of compact support of the original image components of the reconstruction image near the image boundary are too much penalized. Therefore we minimize Sobolev norms only on the actual image domain, yielding much better reconstructions (especially for ¿¿»¿0). As an example we apply our method to the reconstruction of singular points that are present in the scale space representation of an image