27 research outputs found
Level Set Segmentation with Shape and Appearance Models Using Affine Moment Descriptors
We propose a level set based variational approach that incorporates shape priors into edge-based and region-based models. The evolution of the active contour depends on local and global information. It has been implemented using an efficient narrow band technique. For each boundary pixel we calculate its dynamic according to its gray level, the neighborhood and geometric properties established by training shapes. We also propose a criterion for shape aligning based on affine transformation using an image normalization procedure. Finally, we illustrate the benefits of the our approach on the liver segmentation from CT images
A level set method with Sobolev Gradient and Haralick Edge Detection
Variational level set methods, which have been proposed with various energy functionals, mostly use the ordinary L type gradient in gradient descent algorithm to minimize the energy functional. The gradient flow is influenced by both the energy to be minimized and the norms, which are induced from inner products, used to measure the cost of perturbation of the curve. However, there are many undesired properties related to the gradient flows due to the 2 L type inner products. For example, there is not any regularity term in the definition of this inner product that causes non-smooth flows and inaccurate results. Therefore, in this work, Sobolev gradient has been used that is more efficient than the 2 L type gradient for image segmentation and has powerful properties such as regular gradient flows, independency to parameterization of curves, less sensitive to local features and noise in the image and also faster convergence rate than the standard gradient. In addition, Haralick edge detector has been used instead of the edge indicator function in this study. Because, the traditional edge indicator function, which is the absolute of the gradient of the convolved image with the aussian function, is sensitive to noise in level set methods. Experimental results on real images , which are abdominal magnetic resonance images, have been obtained for spleen and kidney segmentation. Quantitative analyses have been performed by using different measurements to evaluate the performance of the proposed approach, which can ignore topological noises and detect boundaries successfully
Mathematical morphology on tensor data using the Loewner ordering
The notions of maximum and minimum are the key to the powerful tools of greyscale morphology. Unfortunately these notions do not carry over directly to tensor-valued data. Based upon the Loewner ordering for symmetric matrices this paper extends the maximum and minimum operation to the tensor-valued setting. This provides the ground to establish matrix-valued analogues of the basic morphological operations ranging from erosion/dilation to top hats. In contrast to former attempts to develop a morphological machinery for matrices, the novel definitions of maximal/minimal matrices depend continuously on the input data, a property crucial for the construction of morphological derivatives such as the Beucher gradient or a morphological Laplacian. These definitions are rotationally invariant and preserve positive semidefiniteness of matrix fields as they are encountered in DT-MRI data. The morphological operations resulting from a component-wise maximum/minimum of the matrix channels disregarding their strong correlation fail to be rotational invariant. Experiments on DT-MRI images as well as on indefinite matrix data illustrate the properties and performance of our morphological operators
Mathematical Morphology on Tensor Data Using the Loewner Ordering
The notions of maximum and minimum are the key to the powerful tools of greyscale morphology. Unfortunately these notions do not carry over directly to tensor-valued data. Based upon the Loewner ordering for symmetric matrices this paper extends the maximum and minimum operation to the tensor-valued setting. This provides the ground to establish matrix-valued analogues of the basic morphological operations ranging from erosion/dilation to top hats. In contrast to former attempts to develop a morphological machinery for matrices, the novel definitions of maximal/minimal matrices depend continuously on the input data, a property crucial for the construction of morphological derivatives such as the Beucher gradient or a morphological Laplacian. These definitions are rotationally invariant and preserve positive semidefiniteness of matrix fields as they are encountered in DT-MRI data. The morphological operations resulting from a component-wise maximum/minimum of the matrix channel
Mathematical morphology for tensor data induced by the Loewner orderingin higher dimensions
Positive semidefinite matrix fields are becoming increasingly important in digital imaging. One reason for this tendency consists of the introduction of diffusion tensor magnetic resonance imaging (DTMRI). In order to perform shape analysis, enhancement or segmentation of such tensor fields, appropriate image processing tools must be developed. This paper extends fundamental morphological operations to the matrix-valued setting. We start by presenting novel definitions for the maximum and minimum of a set of matrices since these notions lie at the heart of the morphological operations. In contrast to naive approaches like the component-wise maximum or minimum of the matrix channels, our approach is based on the Loewner ordering for symmetric matrices. The notions of maximum and minimum deduced from this partial ordering satisfy desirable properties such as rotation invariance, preservation of positive semidefiniteness, and continuous dependence on the input data. We introduce erosion, dilation, opening, closing, top hats, morphological derivatives, shock filters, and mid-range filters for positive semidefinite matrix-valued images. These morphological operations incorporate information simultaneously from all matrix channels rather than treating them independently. Experiments on DT-MRI images with ball- and rod-shaped structuring elements illustrate the properties and performance of our morphological operators for matrix-valued data
An extension of min/max flow framework
In this paper, the min/max flow scheme for image restoration is revised. The novelty consists of the fol-
24 lowing three parts. The first is to analyze the reason of the speckle generation and then to modify the
25 original scheme. The second is to point out that the continued application of this scheme cannot result
26 in an adaptive stopping of the curvature flow. This is followed by modifications of the original scheme
27 through the introduction of the Gradient Vector Flow (GVF) field and the zero-crossing detector, so as
28 to control the smoothing effect. Our experimental results with image restoration show that the proposed
29 schemes can reach a steady state solution while preserving the essential structures of objects. The third is
30 to extend the min/max flow scheme to deal with the boundary leaking problem, which is indeed an
31 intrinsic shortcoming of the familiar geodesic active contour model. The min/max flow framework pro-
32 vides us with an effective way to approximate the optimal solution. From an implementation point of
33 view, this extended scheme makes the speed function simpler and more flexible. The experimental
34 results of segmentation and region tracking show that the boundary leaking problem can be effectively
35 suppressed
Shape Calculus for Shape Energies in Image Processing
Many image processing problems are naturally expressed as energy minimization
or shape optimization problems, in which the free variable is a shape, such as
a curve in 2d or a surface in 3d. Examples are image segmentation, multiview
stereo reconstruction, geometric interpolation from data point clouds. To
obtain the solution of such a problem, one usually resorts to an iterative
approach, a gradient descent algorithm, which updates a candidate shape
gradually deforming it into the optimal shape. Computing the gradient descent
updates requires the knowledge of the first variation of the shape energy, or
rather the first shape derivative. In addition to the first shape derivative,
one can also utilize the second shape derivative and develop a Newton-type
method with faster convergence. Unfortunately, the knowledge of shape
derivatives for shape energies in image processing is patchy. The second shape
derivatives are known for only two of the energies in the image processing
literature and many results for the first shape derivative are limiting, in the
sense that they are either for curves on planes, or developed for a specific
representation of the shape or for a very specific functional form in the shape
energy. In this work, these limitations are overcome and the first and second
shape derivatives are computed for large classes of shape energies that are
representative of the energies found in image processing. Many of the formulas
we obtain are new and some generalize previous existing results. These results
are valid for general surfaces in any number of dimensions. This work is
intended to serve as a cookbook for researchers who deal with shape energies
for various applications in image processing and need to develop algorithms to
compute the shapes minimizing these energies