Iconic feature based nonrigid registration: the PASHA algorithm

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Abstract

In this paper, we first propose a new subdivision of the image information axis used for the classification of nonrigid registration algorithms. Namely, we introduce the notion of iconic feature based (IFB) algorithms, which lie between geometrical and standard intensity based algorithms for they use both an intensity similarity measure and a geometrical distance. Then we present a new registration energy for IFB registration that generalizes some of the existing techniques. We compare our algorithm with other registration approaches, and show the advantages of this energy. Besides, we also present a fast technique for the computation of local statistics between images, which turns out to be useful on pairs of images having a complex, nonstationary relationship between their intensities, as well as an hybrid regularization scheme mixing elastic and fluid components. The potential of the algorithm is finally demonstrated on a clinical application, namely deep brain stimulation of a Parkinsonian patient. Registration of pre- and immediate postoperative MR images allow to quantify the range of the deformation due to pneumocephalus over the entire brain, thus yielding to measurement of the deformation around the preoperatively computed stereotactic targets.

Introduction

Nonrigid image registration is an important task of image processing. In medical image analysis, it is a fundamental step as soon as we want to quantify the evolution of a patient in a follow-up study, or when comparing two different patients. Consequently, it is a very creative field of research; techniques are numerous and inspired from a wide range of theories or techniques: statistics and information theory, theory of continuum mechanics or viscoelastic fluids, theory of thermodynamics, optical flow, splines, wavelets, block matching, and so on.

To get a better understanding of the different technical choices one faces when designing a registration algorithm, several classifications have been proposed [8], [36], [38], [61]. One major axis shared by all these classifications is the image feature axis, i.e., the kind of information that drives the registration process.

Most, if not all, classifications split this axis into two parts: on the one hand, geometric algorithms, which use a geometric distance between segmented features in the images; on the other hand, intensity based algorithms, which use a similarity measure between the image intensities.

However, we found that the group of intensity based algorithms includes two different registration approaches that behave very differently, independently of the similarity measure or the deformation model. We formalize their difference in Section 2 by introducing the notion of iconic (i.e., image intensity related) feature based registration and show how it changes the standard classification of registration algorithms. In Section 3, we propose a new registration energy for iconic feature based registration. We show that this energy generalizes the “demons” algorithm, as well as Feldmar’s “generalized ICP,” and enables a better insight of the behavior of these algorithms. Based on this energy, we develop the PASHA2 algorithm. This energy is general and may use different similarity or regularization energies: in this respect, we present Gaussian-weighted local similarity measures in Section 4, which are efficiently computed using an original convolution based technique, as well as an original mixed elastic/fluid regularization in Section 5. We compare PASHA to close algorithms in Section 6. Finally, we present in Section 7 a clinical application of PASHA for brain motion recovery during deep brain stimulation of Parkinsonian patients, and show how our algorithm recovers and propagates deformation in the brain with smooth, realistic displacement fields.

Section snippets

A new classification

Despite the large number of techniques used in registration, the main classifications found in the literature all use at least the following two major axes:

  • The deformation model, used to regularize the registration problem. It expresses the prior knowledge we have on the shape of the transformation.

  • The image features used by the algorithm to guide the deformation model towards (hopefully) the desired transformation.

We first briefly detail in Section 2.1 the different kinds of deformation

An energy for iconic feature based registration

Looking at the existing IFB algorithms, one remarks that they generally do not minimize a global energy. IFB algorithms like the “demons” or block matching, proceed in alternating two steps. In a first step, they search for a set of correspondences C, using an intensity similarity measure. In a second step, they search for a transformation T that approximates this set of correspondences, using one of the regularization techniques presented in Section 2.1. However, even if each of these steps

Local statistic based similarity measures

In the previous section, we introduced a registration energy (2) without specifying any similarity or regularization energy. Indeed, registration algorithms seldom have a unique set of tools: most are flexible and propose a panel of energies to better suit any registration problem [49]. This is also the case with PASHA.

In this section, we present similarity measures based on local statistics, as they are implemented in PASHA. We believe that our technique could be interesting for a wide range

Regularization

A registration algorithm can also propose different kind of regularization energies—although this is far less common than for similarity measures. A study of the different regularization energies is far beyond our scope here; one can take a look at [11] for a panel of possibilities. The important feature of PASHA is that when R is quadratic and uniform, the regularization is done using convolutions. This enables particularly simple and fast regularization techniques; we illustrate it here by

Comparison with the “demons” algorithm and its extensions

The “demons” algorithm [60] and its extensions [6], [14], [30] are a limit case of PASHA when the parameter σ of Eq. (2) tends to zero (S being then the SSD, and R the energy yielding Gaussian filtering). Indeed, in that case, the closeness constraint between T and C disappears during the first step, and we end up minimizing the SSD alone: this is exactly how these algorithms work. Following Section 3.2, this means that these algorithms assume that the images are noiseless, or more generally,

A clinical application to neurosurgery

Previous sections presented theoretical aspects of PASHA, as well as some comparisons with other approaches. Despite the excellent results obtained previously, it is important to show that the algorithm works for real studies as well. Actually, our algorithm has been used already in several studies, mainly for brain tracking in ultrasound images [47], and for multipatient MRI registration [12]—not to mention all the studies based on the “demons” algorithm (e.g., [23], [30]), of which PASHA is a

Conclusion

In this paper, we have first highlighted a fundamental difference that exists between intensity based registration algorithms. On the one hand, standard intensity based (SIB) algorithms use an intensity similarity measure to quantify the quality of the registration. On the other hand, iconic feature based (IFB) algorithms use a geometric distance between homologous geometric features, whose pairing is based on intensities. This last category includes the “demons” algorithm, the “generalized

References (68)

  • W.M. Wells et al.

    Multi-modal volume registration by maximization of mutual information

    Med. Image Anal.

    (1996)
  • R.J. Althof et al.

    A rapid and automatic image registration algorithm with subpixel accuracy

    IEEE Trans. Med. Imag.

    (1997)
  • P.R. Andresen et al.

    Surface-bounded growth modeling applied to human mandibles

    IEEE Trans. Med. Imag.

    (2000)
  • J. Ashburner et al.

    Image registration using a symmetric prior—in three dimensions

    Human Brain Mapp.

    (2000)
  • J. Ashburner et al.

    Nonlinear spatial normalization using basis functions

    Human Brain Mapp.

    (1999)
  • F.L. Bookstein

    Principal warps: thin-plate splines and the decomposition of deformations

    IEEE Trans. Pattern Anal. Mach. Intell.

    (1989)
  • I. Bricault et al.

    Registration of real and CT-derived virtual bronchoscopic images to assist transbronchial biopsy

    IEEE Trans. Med. Imag.

    (1998)
  • M. Bro-Nielsen et al.

    Fast fluid registration of medical images

  • L.G. Brown

    A survey of image registration techniques

    ACM Comput. Surveys

    (1992)
  • P. Cachier, Recalage non rigide d’images médicales volumiques: contributions aux approches iconiques et géométriques,...
  • P. Cachier, N. Ayache, Regularization in image non-rigid registration: I. Trade-off between smoothness and similarity,...
  • P. Cachier, N. Ayache, Isotropic energies, filters and splines for vector field regularization, J. Math. Imag. Vision...
  • P. Cachier et al.

    Multisubject non-rigid registration of brain MRI using intensity and geometric features

  • P. Cachier et al.

    3D non-rigid registration by gradient descent on a Gaussian-windowed similarity measure using convolutions

  • P. Cachier, X. Pennec, N. Ayache, Fast non-rigid matching by gradient descent: study and improvements of the “Demons”...
  • P. Cachier et al.

    Symmetrization of the non-rigid registration problem using inversion-invariant energies: application to multiple sclerosis

  • V. Camion et al.

    Geodesic interpolating splines

  • G.E. Christensen et al.

    Volumetric transformation of brain anatomy

    IEEE Trans. Med. Imag.

    (1997)
  • G.E. Christensen et al.

    Deformable templates using large deformation kinematics

    IEEE Trans. Image Process.

    (1996)
  • L.D. Cohen

    Auxiliary variables and two-step iterative algorithms in computer vision problems

    J. Math. Imag. Vision

    (1996)
  • A. Collignon et al.

    Automated multi-modality image registration based on information theory

  • D.L. Collins et al.

    ANIMAL validation and applications of nonlinear registration based segmentation

    Int. J. Pattern Recog. Artif. Intell.

    (1997)
  • D.L. Collins et al.

    Non-linear cerebral registration with sulcal constraints

  • B.M. Dawant et al.

    Brain atlas deformation in the presence of large space-occupying tumors

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