Using Partial Derivatives of 3D Images to Extract Typical Surface Features

Monga, Olivier; Benayoun, Serge

doi:10.1006/cviu.1995.1014

Cited by 161 publications

(75 citation statements)

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“…More precisely, we define them as the loci of the surface where the largest curvature, k 1 , is locally maximal (in absolute value) in the associated principal direction t 1 . In [26], it is shown that these points can be defined as the zero-crossing of an extremality function e, which is the directional derivative of k 1 in the direction t 1 .…”

Section: Extremal Linesmentioning

confidence: 99%

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Landmark-Based Registration Using Features Identified through Differential Geometry

Pennec

Ayache

Thirion

2009

Handbook of Medical Image Processing and Analysis

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Registration of 3D medical images consists in computing the "best" transformation between two acquisitions, or equivalently, determines the point to point correspondence between the images. Registration algorithms are usually based either on features extracted from the image (feature-based approaches) or on the optimization of a similarity measure of the images intensities (intensitybased or iconic approaches). Another classification criterion is the type of transformation sought (e.g. rigid or non-rigid).In this chapter, we concentrate on feature-based approaches for rigid registration, similar approaches for non-rigid registration being reported in another set of publication [35,36]. We show how to reduce the dimension of the registration problem by first extracting a surface from the 3D image, then landmark curves on this surface and possibly landmark points on these curves. This concept proved its efficiency through many applications in medical image analysis as we will see in the sequel. This work has been for a long time a central investigation topic of the Epidaure team [2] and we can only reflect here on a small part of the research done in this area.We present in the first section the notions of crest lines and extremal points and how these differential geometry features can be extracted from 3D images. In Section 2, we focus on the different rigid registration algorithms that we used to register such features. The last section analyzes the possible errors in this registration scheme and demonstrates that a very accurate registration could be achieved.

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Section: Extremal Linesmentioning

confidence: 99%

“…The normalization of these filters is not straightforward; we use the responses to simple polynomials, as proposed in [26]. We choose the Gaussian function because it is isotropic, a prerequisite if we are looking for geometric invariants for rigid transformations.…”

Section: The Automatic Extraction Of the Extremal Pointsmentioning

confidence: 99%

Landmark-Based Registration Using Features Identified through Differential Geometry

Pennec

Ayache

Thirion

2009

Handbook of Medical Image Processing and Analysis

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“…To do so, let us define the iso-intensity surface of a 3D image, which will be called simply the iso-surface in the rest of this paper. For any continuous function C(x, y, z) of IR 3 , any value I of IR (called the iso-value) defines a continuous, not selfintersecting surface, without hole, which is called the iso-intensity surface of C (Monga, Benayoun, and Faugeras, 1992). A non ambiguous way to define the iso-surface is to consider it as being the surface which separates regions of the space where the intensity of C is greater or equal to I from those regions whose intensity is strictly lower than I .…”

Section: Shape Derived Heuristic Information For 3d Image Registrationmentioning

confidence: 99%

Image registration with iterated local search

Cordón

Damas

2006

J Heuristics

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This contribution is devoted to the application of iterated local search to image registration, a very complex, real-world problem in the field of image processing. To do so, we first re-define this parameter estimation problem as a combinatorial optimization problem, then analyze the use of image-specific information to guide the search in the form of an heuristic function, and finally propose its solution by iterated local search.Our algorithm is tested by comparing its performance to that of two different baseline algorithms: iterative closest point, a well-known, image registration technique, a hybrid algorithm including the latter technique within a simulated annealing approach, a multi-start local search procedure, that allows us to check the influence of the search scheme considered in the problem solving, and a real coded genetic algorithm. Four different problem instances are tackled in the experimental study, resulting from two images and two transformations applied on them. Three parameter settings are analyzed in our approach in order to check three heuristic information scenarios where the heuristic is not used at all, is partially used or almost completely guides the search process, as well as two different number of iterations in the algorithms outer-inner loops.

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“…More precisely, we define them as the loci of the surface where the largest curvature, kl, is locally maximal (in absolute value), in the associated principal direction }'l. In Monga et al (1992), it is shown that these points can be defined as the zero-crossing of an extremality function e, which is the directional derivative of kl in the direction t'l, and have proposed a way to characterize them, directly from the voxel values of the 3D image. We have proposed another method to compute them in , for the case of isointensity surfaces.…”

Section: Extremal Linesmentioning

confidence: 99%

“…The normalization of those filters is however not straightforward, we use the responses to simple polynomials, as proposed by Monga et al (1992). We choose the Gaussian function because it is isotropic, a pre-requisite if we are looking for geometric invariants.…”

Section: The Automatic Extraction Of the Extremal Pointsmentioning

confidence: 99%

New feature points based on geometric invariants for 3D image registration

Thirion

1996

Int J Comput Vision

171

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We introduce in this paper a new type of feature points of 3D surfaces, based on geometric invariants.We call this new type of feature points the extremalpoints of the 3D surfaces, and we show that the relative positions of those 3D points are invariant according to 3D rigid transforms (rotation and translation). We show also how to extract those points from 3D images, such as Magnetic Resonance images (MRI) or Cat-Scan images, and also how to use them to perform precise 3D registration. Previously, we described a method, called the Marching Lines algorithm, which allow us to extract the extremal lines, which are geometric invariant 3D curves, as the intersection of two implicit surfaces: the extremal points are the intersection of the extremal lines with a third implicit surface. We present an ~pplication of the extremal points extraction to the fully automatic registration of two 3D images of the same patient, taken in two different positions, to show the accuracy and robustness of the extracted extremal points.

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Using Partial Derivatives of 3D Images to Extract Typical Surface Features

Cited by 161 publications

References 0 publications

Landmark-Based Registration Using Features Identified through Differential Geometry

Landmark-Based Registration Using Features Identified through Differential Geometry

Image registration with iterated local search

New feature points based on geometric invariants for 3D image registration

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