# PDF Motion Analysis and Image Sequence Processing

The deformation implies a force that constrains the shape to be smooth and a force that constrains the mesh to be close to the 3-D data-Internal forces determine the response of a physically based model to external constraints. The internal forces are expressed so that they be intrinsic viewpoint invariant and scale dependant. Similar types of constraints hold for contours. Hence, the cited publication provides a simple model for representing a 3-D object of interest.

It defines the forces to be applied in order to reshape and adjust the model onto the 3-D object of interest. The invention relates to an image processing method for processing a sequence of images of a distortable 3-D Object, each image being registered at a corresponding image instant within the interval of time of the sequence.

The inward motions of the 3-D Object boundary are called contractions and the outward motions are called relaxations. It is an object of the invention to propose such a processing method having steps to construct and display an image of said 3-D Object represented with regions, each region showing a quantified indication relating to its maximal contraction or relaxation within said interval of time.

The displayed image provides the advantage to yield an easy estimation of the propagation of the deformations over the 3-D Object boundary within the given interval of time. In the displayed image, each region may show a quantified indication of the phase of a predetermined periodic function representing the motion of the region, said phase indication corresponding to the image of the sequence in which the maximal contraction or relaxation of said region has been estimated.

In the displayed image, each region may show a quantified indication corresponding to the delay necessary for said region to attain its maximal contraction or relaxation from a predetermined reference. In the displayed image, each region may show a quantified indication of the image instant when said region have had its maximal contraction or relaxation between the image corresponding to said image instant and an adjacent image in the sequence. It is also an object of the invention to propose such an image processing method for processing a sequence of 3-D ultrasound images of a body organ having a wall with regions that move either inwardly or outwardly in the time, in order to construct and display a virtual image of the organ wall represented with regions, having such quantified indications.

## Motion estimation and analysis

It is also an object of the invention to propose such an image processing method wherein the quantified indications are given in a coded manner, preferably in a color coded manner. It is particularly an object of the invention to apply this method to 3-D ultrasound imaging, in order to yield quantified information relating to the maximum deformation of regions of the heart, in a color coded form, for easily estimating the propagation of the deformation during contraction and relaxation of cavities of the heart, from a sequence of images registered during the interval of time of a cardiac cycle.

So, the invention also relates to an ultrasound examination apparatus having image processing means and to a program product for carrying out the method. The invention is described hereafter in detail in reference to the following diagrammatic drawings, wherein:.

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The invention relates to an image processing method for analyzing the amplitude and direction of the displacements of wall regions of a distortable 3-D Object over a sequence of images, and for constructing and displaying a virtual image of said 3-D Object represented with the regions, each region showing a quantified indication relating to its maximal contraction or relaxation within the interval of time of the sequence of images. Said indications are preferably given in a coded manner, such as in a color-coded manner.

The invention may be applied to a sequence of 3-D ultrasound images of a body organ having a wall with regions that move either inwardly or outwardly in the time, said organ having nearly periodic motions, in order to construct and display a virtual image of the organ wall represented with regions, having such quantified indications. Using 3D-ultrasound imaging, this method permits of analyzing the contraction and relaxation of the heart. This method yields quantified information relating to the maximum deformation of regions of a cavity of the heart, in a color coded form, for easily estimating the propagation of local deformation over the heart wall during contraction and relaxation of said cavity, from a sequence of images registered during the interval of time of the cardiac cycle.

The displayed virtual image provides the advantage to yield an easy estimation of the propagation of the deformations over a 3-D Object boundary within a given interval of time. In the displayed virtual image, each region may show a quantified indication of the phase of a predetermined periodic function representing the motion of the region, said phase indication corresponding to the image of the sequence in which the maximal contraction or relaxation of said region has been estimated within said interval of time.

Alternately, in the displayed virtual image, each region may show a quantified indication corresponding to the delay necessary for said region to attain its maximal contraction or relaxation from a predetermined reference. In another embodiment, in the displayed virtual image, each region may show a quantified indication of the image instant within the sequence, when said region have had its maximal contraction or relaxation between the image corresponding to said image instant and an adjacent image of the sequence.

The quantitative estimation of local cardiac deformations, corresponding to contractions and relaxations of the heart wall regions represented in a 3-D image sequence, has important clinical implications for the assessment of the viability of cardiac muscle cells in said heart wall. The cardiac contractions and the cardiac relaxations are complex spatio-temporal phenomena, activated by the temporal changes of electrical potential in the cardiac muscular cells. During contraction, also occurs a twist motion of the heart wall. These considerations emphasize the complexity of the deformation, that may not be simply described as a temporal radial contraction or relaxation of the heart wall.

Hence, a good spatial resolution is required when studying the contraction or the relaxation. Moreover, not only the amplitude of the contraction should be studied, but also the phase, which indicates locally the time when contraction or relaxation happens, and the way it is propagating.

There are several cardio-pathologies due to conduction diseases: tachycardia and atrial or ventricular fibrillation are some examples. The analysis of the local cardiac contractions provides information about the condition of the heart and is useful for the study of such cardio-pathologies, as well as those inducing conduction abnormalities, such as the myocardial infarction for instance. The method can be carried out using reconstructed or real-time 3D echocardiography, the images being formed using a trans-thoracic or a trans-esophageal probe.

The method of the invention can also be applied to a sequence of 3-D images of other organs of the body that can be formed by ultrasound systems or ultrasound apparatus, or by other medical imaging systems known of those skilled in the art. In the example described hereafter, analysis of the cardiac wall motion is performed from a sequence of 3-D simplified models of the left ventricular volume, which are obtained from the segmentation of 3-D ultrasound images of the heart.

For the construction of the virtual image to be displayed and for the estimation of quantified indications relating to the contraction or relaxation of regions of the heart to be represented in said virtual image, the sequence of 3-D segmented images is further processed using one of two different techniques or both those techniques.

The first technique consists in a Fourier analysis of the motion over the models of the 3-D segmented sequence. A first model, called reference model of the left ventricle, is first chosen in an image called first image among the different successive images of the sequence of 3-D simplified models. The volume of the left ventricle varies from one image to the following image.

So, the corresponding models vary from one image to the following image. This first technique comprises, for each region of the virtual image or model to be displayed, a definition of corresponding region on each model of the image sequence. Then, this first technique comprises a computation of the motion between the corresponding region defined on each model of the images of the sequence and the corresponding region on the reference model of the first image, based on the assumption that this motion is periodic.

This first technique further comprises a definition of a periodic function of motion and a derivation of the phase associated to the motion from a Fourier analysis, for estimating a continuous information of phase from the set of images forming the sequence. The continuous information of phase indicates the delay for attaining the maximum of contraction or relaxation, for each region of the virtual model, from the reference model.

The second technique comprises a computation of the amplitude of motion between corresponding regions of two successive models, called couple of models, of two successive images of the sequence, instead of considering each model of the sequence with respect to a reference model. To each couple of model is associated an instant of time: for instance, the image instant when the last in time of the two images of the couple is registered in the interval of time of the sequence.

The image instant within the interval of time of the sequence when this motion is maximal corresponds to a maximum of contraction or relaxation, between corresponding regions on the considered models of a couple. These two techniques are complementary: the first one gives local quantified information of phase based on a global time-analysis of the motion throughout the sequence and on the assumption that the cardiac motion is periodic; and the second one gives local quantified information of the instant of time when a maximum of motion occurs between two models, so is based on an analysis of the motion that is more precise in the temporal dimension.

In order to represent the local quantified information of maximal contraction or relaxation in the sequence of images, a predefined color-map is used. Said color-map associates the instant of maximal contraction or relaxation related to each region as estimated according to the second technique, or the phase related to each region as estimated according to the first proposed technique, to a color, and then fits the color on the corresponding regions of a generic or mean model, called virtual model, of the left ventricle, thus yielding the information of the way the contraction or relaxation propagates in the myocardium.

Furthermore, the path of propagation of the contraction or relaxation can be superimposed on this representation. In an example, 3-D images of a heart cavity wall, for example the wall of the heart left ventricle, are acquired using an ultrasound examination apparatus. These images are assembled in a sequence of images. The sequence images can be acquired at a rate of 15 to 30 or 50 images per second, each image of the sequence being preferably associated to an instant of the cardiac cycle. Other examples of forming sequences of 3-D images of different organs, whose shape or dimensions vary over time, may be found by operators of ultrasound apparatus or of other systems of image acquisition.

After the acquisition of the image sequence, the images are segmented. Any method of segmentation, which is able to segment the 3-D object in the images of the sequence, may be used. The result of the segmentation operation permits of locating the voxels of the wall of the 3-D Object, for instance the internal wall of the left ventricle.

## Motion Analysis and Image Sequence Processing - Google книги

Referring to FIG. This Simplex Mesh Technique has been previously described in relation to the publication above cited as the state of the art. In the case of a heart cavity, an elementary 3-D Mesh Model, which may be for example a sphere, is set inside the 3-D cavity, then it is deformed and reshaped using the above-described internal and external forces, until it is mapped unto the internal wall of the cavity. This operation is performed for each image of the sequence, so that a sequence of images representing segmented 3-D objects is formed.

In each of these images, the wall of the object of interest is represented by a Simplex Mesh Model with faces and edges. The faces are generally not planar. It is to be noted that in the process of segmentation, the segmented 3-D Object is represented by the faces and edges of the Mesh Model. The faces define regions of the 3-D Object. For refining the mapping of the Mesh Model onto the 3-D Object, the faces may be divided. So, the number of faces may differ from a model in a given image to the model in another image of the sequence. In order to avoid difficulties due to a varying number of faces of the models representing the segmented 3-D Object from one image to another, a unique number of faces corresponding to a given level of segmentation is preferably chosen for all the models of the images of the sequence, thus defining the number of regions to be considered.

These segmented images may be processed in order to transform each model representing the 3-D segmented Object into a binary model. For instance, the voxels inside the model are attributed the value 1, the voxels outside the model are attributed the value 0. The boundary of the 3-D binary model is located between the 0 and 1 regions and represents the location of the organ wall.

Other possibility for attributing a boundary to a binary object may be used as known of those skilled in the art. The formation of a sequence of binary models is optional, but permits of minimizing the amount of calculation in the further steps of the image processing method. In the segmented images, the 3-D Object that has been segmented using the Simplex Mesh Model, has faces denoted by Z having a center of gravity denoted by ZC. The point ZC may alternately be a reference point of a region of the simplified model.

The local analysis of the heart wall motions during contraction and relaxation is performed using the above cited two different complementary techniques. The volume of the models varies periodically for physiological reasons. In the present example, the volume of the left ventricle varies periodically in function of the pulse during the cardiac cycle. Referring to FIGS. This information of distance is defined in order to permit of estimating the amplitudes of movement of each face or region of the model in function of time.

Some faces may show great amplitudes of movement during the cardiac cycle; some other faces may show very small amplitudes of movement during said cardiac cycle; some may have regular amplitudes of movement over several cardiac cycles; other faces may have irregular amplitudes of movement over several cardiac cycles. The centers of gravity C 0 , C 1 , C 2 ,. C N , of the models in the segmented images of the sequence are also considered. If they are not located in coincidence, an operation of translation may be performed to superimpose those points C 0 , C 1.

In this first technique, the 3-D object of interest, for example the heart left ventricle, is first considered in one segmented or binary image of the sequence called first segmented image. Once the first segmented image is chosen, the other segmented or binary images of the sequence where the left ventricle varies in shape and dimension during the cardiac cycle are further considered one by one.

In this first technique, two processes are proposed, as examples, for obtaining the information of motion, during the cardiac cycle, of the regions that have been defined and delineated on the virtual image. In a first process, corresponding regions are selected on the different models, these regions also corresponding to the regions of the virtual image.

This distance is denoted by D 0. Then, referring to FIG. This distance is denoted by D 1. In a second process, the different models are all binary models.

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The centers of gravity of these models and of the virtual model may be superimposed forming a common center of gravity. Then, as illustrated by FIGS. A function called function of motion is further estimated from these calculated distances. Assuming that the variation of said distances for the corresponding regions of the different volumes is periodic, the estimated function is a periodic function. For each face or region of a model, the phase of said function is derived from a Fourier analysis.

Then a continuous information of phase is estimated over the corresponding faces or regions from the set of images forming the image sequence. This continuous information of phase permits of estimating the delay to attain the maximal contraction or relaxation for each face or for each region of the Models. The phase may be estimated in degrees or grades or radians. The delay may be estimated in unity of time or in function of the instant of image acquisition in the sequence.

In this technique of phase calculation, the information of phase may thus be used to estimate the instant of the maximum of contraction or the maximum of relaxation of the heart left ventricle. This technique of Fourier analysis, based on a global time-analysis of the motion throughout the sequence, gives an information based on the assumption that the cardiac motion is periodic.

In this technique, the different distances between the different models of the different segmented images are calculated. The information of the distance between two successive volumes is used for computing the amplitude of motion between these two volumes. This technique permits of analyzing the motion more precisely in the temporal dimension. An image of the virtual model is constructed having a given number of faces or regions, which may correspond to the faces or regions of the successive models of the sequence, providing a predetermined level of segmentation of the models as above described.

Using this color-coding operation, different colors may be associated to the different image instants of the sequence registered during a cardiac cycle in unity of time or in time divisions of the cardiac cycle ; or the values of phase in degree, grade or radian ; or the delays of time in unity of time or in time divisions of the cardiac cycle.

Numerous other color-coding techniques may be used by those skilled in the art for performing this step. Using the color-coded Map defined by the color-coding operation, the appropriate colors, corresponding to the quantified indications of the maximum of contraction or relaxation, are fitted to the faces or regions of the virtual model, in order that each region or face be represented with a quantified indication as above calculated either with the first or the second technique. These indications may be the instant when a face or region has had its maximum of contraction or relaxation as measured in the second technique; or the phase value corresponding to its maximum of contraction or relaxation as measured in the first proposed technique; or the delay to attain its maximum of contraction or relaxation as measured in the first proposed technique.

This operation of coloring the faces or regions in function of the color-coded Map yields the information of the way the contraction or relaxation propagates in the myocardium. Each face or each zone Z of the model representing the object of interest is attributed a color specific of the quantified indications. The color-coded virtual image is displayed for example on a screen.

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It may be registered or memorized. Belfor, R. Lagendijk, J. Nicoulin, M. Mattavelli, W. Li, A. Basso, A. Popat, M. Mersereau, M. Smith, C. Kim, F. Kossentini, K. Buck, N. Aizawa, C. Choi, H. Harashima, T. Woods, J. Ozkan, M. Sezan, A. Erdem, A. Viero, Y. Apostolopoulos, J. See All Customer Reviews. Shop Textbooks. Add to Wishlist. USD Sign in to Purchase Instantly. Temporarily Out of Stock Online Please check back later for updated availability. Overview The range of applications in the area of motion analysis and image sequence processing is expanding with the steady increase in the use of video and television systems in a variety of different fields.