Source: http://www.docstoc.com/docs/51438297/Three-dimensional-Reconstruction-Of-Intrabody-Organs---Patent-6456867
Timestamp: 2014-12-19 20:20:47
Document Index: 163576039

Matched Legal Cases: ['art 70', 'art 70', 'art 70', 'art 70', 'art 70', 'art 70', 'art 70', 'art\n70', 'art 70', 'art 70', 'art 70']

Three-dimensional Reconstruction Of Intrabody Organs - Patent 6456867
United States Patent: 6456867
A method of reconstructing a map of a volume, including determining
coordinates of a plurality of locations on a surface of the volume having
a configuration, generating a grid of points defining a reconstruction
surface in 3D space in proximity to the determined locations, for each of
the points on the grid, defining a respective vector, dependent on a
displacement between one or more of the points on the grid and one or more
of the locations, and adjusting the reconstruction surface by moving
substantially each of the points on the grid responsive to the respective
vector, so that the reconstruction surface is deformed to resemble the
configuration of the surface.
Reisfeld; Daniel (Haifa, IS)
09/789,427
122137Jul., 19986226542
600/407  ; 600/416; 600/425; 600/437; 600/481
G06T 17/20&amp;nbsp(20060101); A61B 5/04&amp;nbsp(20060101); A61B 5/0408&amp;nbsp(20060101); A61B 005/05&amp;nbsp()
128/920,923,848,899 382/128,154 600/416,424,473,474,371,372-374,380-384,407,417,481,425
4892104
Kizakevich et al.
Gerstenfeld E., Sahakian A., Baerman J., Ropella K., Swiryn S. (1991) &quot;Detection of Changes in Atrial Endocardial Activation With Use of an
Orthogonal Catheter&quot;, JACC. vol. 18, No. 4: 1034-42.
Gerstenfeld E., Sahakian A., Swiryn S. (1992) &quot;Evidence for Transient Linking of Atrial Excitation During Atrial Fibrillation in Humans&quot;, Circulation. vol. 86, No. 2: 375-382.
Kadish A., Spear J., Levine J., Hanich R., Prood C., Moore E.N. (1986) &quot;Vector Mapping of Myocardial Activation&quot;, Circulation. vol. 74, No. 3: 603-615..
This application is a division of application Ser. No. 09/122,137, filed
Jul. 24, 1998, now U.S. Pat. No. 6,226,542.
1.  A method of displaying values of a parameter which varies over a surface of a portion of the human body, comprising: determining a value of the parameter at each of a
plurality of points on the surface of the body;  and rendering an image of the surface to a display with a varying amount of transparency on different areas of the surface, responsive in each of the areas of the surface to the confidence value of the
parameter at one or more points in the area.
2.  A method according to claim 1, wherein determining the value comprises sampling a plurality of points and creating a map of the surface responsive thereto, and wherein rendering the image comprises rendering a graphic representation of the
3.  A method according to claim 2, wherein the plurality of points comprises sampled points and interpolated points, and further comprising the value comprises determining a measure of reliability of the map in each of the areas;  wherein
determining the measure of reliability comprises assigning measures of reliability to the interpolated points according to their respective distance from a closest sampled point.
4.  A method according to claim 1, wherein rendering the image comprises rendering one or more of the areas having a low measure of reliability relative to another one or more of the areas with a relatively greater degree of transparency.
Cardiac mapping is used to locate aberrant electrical pathways and currents within the heart, as well as mechanical and other aspects of cardiac activity.  Various methods and devices have been described for mapping the heart.  Such methods and
device are described, for example, in U.S.  Pat.  Nos.  5,471,982 and 5,391,199 and in PCT patent publications WO94/06349, WO96/05768 and WO97/24981.  U.S.  Pat.  No. 5,391,199, for example, describes a catheter including both electrodes for sensing
cardiac electrical activity and miniature coils for determining the position of the catheter relative to an externally-applied magnetic field.  Using this catheter a cardiologist may collect a set of sampled points within a short period of time, by
determining the electrical activity at a plurality of locations and determining the spatial coordinates of the locations.
In order to allow the surgeon to appreciate the determined data, a map, preferably a three dimensional (3D) map, including the sampled points is produced.  U.S.  Pat.  No. 5,391,199 suggests superimposing the map on an image of the heart.  The
positions of the locations are determined with respect to a frame of reference of the image.  However, it is not always desirable to acquire an image, nor is it generally possible to acquire an image in which the positions of the locations can be found
Various methods are known in the art for reconstructing a 3D map of a cavity or volume using the known position coordinates of a plurality of locations on the surface of the cavity or volume.  Some methods include triangulation, in which the map
is formed of a plurality of triangles which connect the sampled points.  In some cases a convex hull or an alpha-hull of the points is constructed to form the mesh, and thereafter the constructed mesh is shrunk down to fit on the sampled points within
the hull.  Triangulation methods do not provide a smooth surface and therefore require additional stages of smoothing.
Another method which has been suggested is forming a bounding ellipsoid which encloses the sampled points.  The sampled points are projected onto the ellipsoid, and the projected points are connected by a triangulation method.  The triangles are
thereafter moved with the sampled points back to their original locations, forming a crude piecewise linear approximation of the sampled surface.  However, this method may reconstruct only surfaces which have a star shape, i.e., a straight line
connecting a center of the reconstructed mesh to any point on the surface does not intersect the surface.  In most cases heart chambers do not have a star shape.
In addition, reconstruction methods known in the art require a relatively large number of sampled locations to achieve a suitable reconstructed map.  These methods were developed, for example, to work with CT and MRI imaging systems which provide
large numbers of points, and therefore generally work properly only on large numbers of points.  In contrast, determining the data at the locations using an invasive catheter is a time-consuming process which should be kept as short as possible,
especially when dealing with a human heart.  Therefore, reconstruction methods which require a large number of determined locations are not suitable.
It is another object of some aspects of the present invention to provide a simple, rapid method for reconstructing a 3D map of a volume in the human body from a plurality of sampled points, preferably using fewer sampled points than is feasible
using methods known the art.
It is another object of preferred embodiments of the present invention to provide a method for reconstructing a 3D map of a volume in the human body from a plurality of sampled points, without assuming any topological relationship between the
In preferred embodiments of the present invention, a processor reconstructs a 3D map of a volume or cavity in a patient&#39;s body (hereinafter referred to as the volume), from a plurality of sampled points on the volume whose position coordinates
have been determined.  In contrast to prior art reconstruction methods in which a large number of sampled points are used, the preferred embodiments of the present invention are directed to reconstruction of a surface based on a limited number of sampled
points.  The number of sampled points is generally less than 200 points and may be less than 50 points.  Preferably, ten to twenty sampled points are sufficient in order to perform a preliminary reconstruction of the surface to a satisfactory quality.
An initial, generally arbitrary, closed 3D curved surface (also referred to herein for brevity as a curve) is defined in a reconstruction space in the volume of the sampled points.  The closed curve is roughly adjusted to a shape which resembles
a reconstruction of the sampled points.  Thereafter, a flexible matching stage is preferably repeatedly performed once or more to bring the closed curve to accurately resemble the shape of the actual volume being reconstructed.  Preferably, the 3D
surface is rendered to a video display or other screen for viewing by a physician or other user of the map.
In preferred embodiments of the present invention, the initial closed curved surface encompasses substantially all the sampled points or is interior to substantially all the sampled points.  However, it is noted that any curve in the vicinity of
the sampled points is suitable.  Preferably, the closed 3D curved surface comprises an ellipsoid, or any other simple closed curve.  Alternatively, a non-closed curve may be used, for example, when it is desired to reconstruct a single wall rather than
A grid of a desired density is defined on the curve, and adjustment of the curve is performed by adjusting the grid points.  The grid preferably divides the curved surface into quadrilaterals or any other polygons such that the grid evenly
defines points on the curve.  Preferably, the grid density is sufficient such that there are generally more grid points than sampled points in any arbitrary vicinity.  Further preferably, the grid density is adjustable according to a desired compromise
between reconstruction accuracy and speed.
In some preferred embodiments of the present invention, external information is used to choose an initial closed curve which is more closely related to the reconstructed volume, for example, using the image of the volume, as described above.
Thus, the reconstruction procedure may produce a more accurate reconstruction in less time.  Alternatively or additionally, a database of closed curves suitable for various volumes of the body is stored in a memory, and the curve to be used is chosen
according to the specific procedure.  In a further preferred embodiment of the present invention, a map of a reconstructed volume in a patient is used as a beginning curve for subsequent mapping procedures performed at later times on the same volume.
Preferably, the rough adjustment of the closed curve is performed in a single iteration, most preferably by calculating for each grid point an adjustment point, and moving the grid point a fraction of the distance to the adjustment point.
Preferably, the grid point is moved about 50-80% of the distance between its original point and the adjustment point, more preferably about 75%.
The adjustment point is preferably determined by taking a weighted sum over substantially all the sampled points.  Preferably, the weights are inversely related to the distances from the adjusted grid point to the sampled points, referred to
herein as grid distances.  In a preferred embodiment of the present invention, each weight is defined as the reciprocal of the sum of a small constant plus the grid distance, raised to a predetermined power, so that sampled points close to the grid point
are given a larger weight.  Preferably, the power is approximately between 4 to 9, most preferably 8.  The small constant is preferably smaller than the magnitude of the smallest grid distance, and is preferably of the size of the accuracy of the
determination of the coordinates of the sampled points.  The small constant is used to prevent division by zero when a grid-point is on a sampled point.
In some preferred embodiments of the present invention, the weights also include a factor which is indicative of the density of points in the vicinity of their corresponding point.  Preferably, the weight is multiplied by a density value between
zero and one, indicative of the density, such that isolated sampled points influence the sum more than sampled points in a dense area.  Preferably, the influence of the points is thus substantially independent of the density of points in their vicinity.
In a preferred embodiment of the present invention, the flexible matching step is performed by associating each sampled point with a corresponding grid-point, such that each sampled point is associated with the grid point which is closest to it.
A movement vector is calculated for each of the associated and non-associated grid-points.  Preferably, the movement vectors are calculated based on vectors from the associated grid points to their respective sampled points.  Further preferably, the
sampled points influence the value of the movement vector for a specific point according to their proximity to the specific point.  In addition, the function by which the movement vectors are calculated is preferably smooth and does not include
complicated calculations.  Preferably, the function is a weighted sum of the vectors from the associated grid points to their respective sampled points.  The grid points are then moved according to their respective movement vectors.
Additionally or alternatively, the associated grid points are moved toward their corresponding sampled points by a percentage of the distance between them.  Those grid points which are not associated with a sampled point are moved a distance
which is determined by interpolation between the distances which surrounding points on the grid are moved.  Preferably, the resulting grid is smoothed using a suitable smoothing transformation.  Preferably, the process of associating and moving is
repeated two or more times to allow finer adjustment of the closed curve.
In a preferred embodiment of the present invention, a user can adjust the number of times the flexible matching step is repeated according to a desired compromise between image quality and speed.  Alternatively or additionally, a quick
reconstruction is first provided to the user, and thereafter the calculation is repeated to receive a finer reconstruction.  Preferably, the weights of the weighted sum used in the flexible matching stage are adjusted according to the number of times the
matching is to be performed.  Alternatively or additionally, the weights are determined for each flexible matching step according to its place in the sequential order of the flexible matching steps.
Preferably, the distances used for the weights and/or for interpolation are Euclidean geometrical distances between the points.  The Euclidean distance is easily computed and causes points on opposite walls of the volume to mutually repel, so
that the walls do not intersect.  Alternatively, other distances, such as the distance along the original or adjusted grid, may be used.  In a preferred embodiment of the present invention, during the first flexible matching step the distance used is the
distance along the original grid while subsequent flexible matching steps use the Euclidean distance.
In some preferred embodiments of the present invention, a smoothing process is applied to the reconstructed surface, preferably by applying a surface convolution with a Gaussian-like kernel.  The smoothing process provides a better approximation
of the surface and allows easier performance of calculations based on the reconstructed surface.  However, applying the surface convolution results in some shrinkage of the surface, and therefore an affine transformation is preferably performed on the
smoothed surface.  The affine transformation is preferably chosen according to those sampled points which are external to the reconstructed surface.  The chosen affine transformation preferably minimizes the mean square distance of the external points to
Preferably, when the reconstruction is finished, each sampled point substantially coincides with a grid point.  In some preferred embodiments of the present invention, a final exact matching stage is performed.  Each sampled point is associated
with a closest grid point, and the associated grid point is moved onto the sampled point.  The rest of the grid points are preferably not moved.  Generally, most of the sampled points are by this stage very close to the reconstructed surface, and
therefore the smoothness of the surface is substantially not affected.  However, some outlier sampled points, i.e., sampled points which do not belong to the surface, may cause substantial changes to the surface.  Preferably, the user may determine
whether to move the surface onto points that are distanced from the surface by more than a predetermined maximum distance.  Alternatively or additionally, the entire exact matching step is optional and is applied only according to a user request.
Further alternatively or additionally, the grid points are brought to a fixed distance from the sampled points.  Leaving such a fixed distance may be desired, for example, when the sampled coordinates are of locations close to a distal tip of a
sampling catheter rather than at the distal tip itself.
In preferred embodiments of the present invention, data regarding the sampled points are acquired by positioning a catheter within the volume which is to be reconstructed, for example, within a chamber of the heart.  The catheter is positioned
with a distal end thereof in contact with each of the sampled points in turn, and the coordinates of the points and, optionally, values of one or more physiological parameters are sensed at a distal end of the catheter.  Preferably, the catheter
comprises a coordinate sensor close to its distal end, which outputs signals indicative of the coordinates of the tip of the catheter.  Preferably, the coordinate sensor determines the position by transmitting and receiving electromagnetic waves, as
described, for example, in PCT publications GB93/01736, WO94/04938, WO97/24983 and WO96/05768, or in U.S.  Pat.  No. 5,391,199, commonly owned by the present assignee and which are all incorporated herein by reference.
In some preferred embodiments of the present invention, the reconstructed volume is in movement, for example, due to beating of the heart.  In such embodiments, the sampled points are preferably registered with a reference frame fixed to the
heart.  Preferably, a reference catheter is fixed in the heart, and the sampled points are determined together with the position of the reference catheter which is used to register the points, as described, for example, in the above-mentioned U.S.  Pat.
No. 5,391,199 and PCT publication WO96/05768.
Alternatively or additionally, when at least part of the movement is a cyclic movement, as in the heart, acquisition of the sampled points is synchronized to a specific time point of the cycle.  Preferably, when the sampled volume is in the
heart, an ECG signal is received and is used to synchronize the acquisition of the sampled points.  For example, the sampled points may be acquired at end diastole.  Further alternatively or additionally, the coordinates of each of the sampled points are
determined together with an indication of the time point relative to the cyclic movement in which the coordinates were acquired.  Preferably, the indication includes the relative time from the beginning of the cycle and the frequency of the cyclic
movement.  According to the frequency and the relative time, the determined coordinates are corrected to end diastole, or any other point in the cyclic movement.
In some preferred embodiments of the present invention, for each sampled point a plurality of coordinates are determined at different time points of the cyclic movement.  In one of these preferred embodiments, each sampled point has two
coordinates which define the range of movement of the point.  Preferably, if the plurality of coordinates of different points are associated with different cycle frequencies, the coordinates are transformed so as to correspond to a set of coordinates in
a single-frequency cyclic movement.  Further preferably, the coordinates are processed so as to reduce or substantially eliminate any contribution due to movement other than the specific (cardiac) cyclic movement, such as movement of the chest due to
respiration.  Reconstruction is performed for a plurality of configurations of the volume at different time points of the cyclic movement.  Preferably, a first reconstruction is performed as described above to form an anchor reconstruction surface, and
reconstruction of surfaces for other time points of the cycle are performed relative to the anchor reconstruction surface.
Preferably, for each further time point of the cyclic movement, the anchor surface is adjusted according to the coordinates of the sampled points at the further time point relative to the coordinates of the sampled points of the anchor surface.
Preferably, the anchor surface is adjusted by a quadratic transformation which minimizes a mean square error, the error representing the distances between the sampled points of the further time point and the adjusted surface.  Alternatively or
additionally, an affine transformation is used instead of the quadratic transformation.  Further alternatively or additionally, a simple transformation is used for surfaces having relatively few sampled points, while surfaces with a relatively large
number of sampled points a quadratic transformation is used.  The simple transformation may be an affine transformation, a scaling and rotation transformation, a rotation transformation, or any other suitable transformation.
Alternatively or additionally, the reconstruction is performed separately for each of the further time points.  Further alternatively or additionally, a first reconstruction of the surfaces for the further time points is performed relative to the
anchor surface, and afterwards a more accurate reconstructed is performed for each time point independently.
In some preferred embodiments of the present invention, one or more physiological parameters are acquired at each sampled point.  The physiological parameters for the heart may comprise a measure of cardiac electrical activity, for example,
and/or may comprise any other type of local information relating to the heart, as described in the PCT patent publication WO97/24981, also owned by the present assignee and further incorporated herein by reference.  The one or more physiological
parameters may be either scalars or vectors and may comprise, for example, a voltage, temperature, pressure, or any other desired value.
Preferably, after the volume is reconstructed based on the coordinates, values of the physiological parameter are determined for each of the grid points based on interpolation of the parameter value at surrounding sampled points.  Preferably, the
interpolation of the physiological parameter is performed in a manner proportional to the aggregate interpolation of the coordinates.  Alternatively, the physiological parameters are interpolated according to the geometrical distance between the points
on the grid.  Alternatively or additionally, the physiological parameters are interpolated in a manner similar to the flexible matching step described hereinabove.
The reconstructed surface may be displayed in movement, and/or a physician may request a display of a specific time point of the cycle.  Preferably, the physiological parameter is displayed on the reconstructed surface based on a predefined color
scale.  In a preferred embodiment of the present invention, the reliability of reconstruction of regions of the reconstructed surface is indicated on the displayed surface.  Preferably, regions which are beneath a user-defined threshold are displayed as
semi-transparent, using known methods such as .alpha.-blending.  Preferably, the reliability at any grid point is determined according to its proximity to sampled points.  Those points on the grid which are beyond a predetermined distance from the
nearest sampled point are less reliable.
In some preferred embodiments of the present invention, acquired images such as LV-grams and fluoroscopic images are used together with the sampled points to enhance the speed and/or accuracy of the reconstruction.  Preferably, the processor
performs an object recognition procedure on the image to determine the shape of the closed 3D curved surface to use in constructing the initial grid of the reconstruction.  Alternatively or additionally, the image is used by the physician to select areas
in which it is most desired to receive sampled points.
In some preferred embodiments of the present invention, the physician may define points, lines, or areas on the grid which must remain fixed and are not to be adjusted.  Alternatively or additionally, some points may be acquired as interior
points which are not to be on the map since they are not on a surface of the volume.  The reconstruction procedure is performed accordingly so that the closed curve is not moved too close to the interior points.
In some preferred embodiments of the present invention, the reconstruction surface is used to determine an accurate estimate of the volume of the cavity.  The surface is divided by the grid points into quadrilaterals, and each quadrilateral is
further divided into two triangles.  Based on these triangles the volume defined by the surface is estimated.  Alternatively, the volume is calculated using a volumetric representation.  Other measurements, such as geodesic surface measurements on the
surface, may also be performed using the reconstructed surface.
There is therefore provided in accordance with a preferred embodiment of the present invention, a method of reconstructing a map of a volume, including determining coordinates of a plurality of locations on a surface of the volume having a
configuration, generating a grid of points defining a reconstruction surface in 3D space in proximity to the determined locations, for each of the points on the grid, defining a respective vector, dependent on a displacement between one or more of the
points on the grid and one or more of the locations, and adjusting the reconstruction surface by moving substantially each of the points on the grid responsive to the respective vector, so that the reconstruction surface is deformed to resemble the
Preferably, moving each point in the rough adjustment stage includes defining, for each of the points on the grid, a respective rough adjustment vector which includes a weighted sum of vectors from the point to each of the determined locations
and moving the points a distance proportional to the respective vector.
Preferably, the flexible matching stage includes selecting a grid point to be associated respectively with each of the determined locations.  Preferably, selecting the grid point includes finding for each determined location a point on the grid
that is substantially closest thereto.
Preferably, the distances include geometrical distances.  Alternatively or additionally, the distances include a length of the reconstruction surface between the grid points.
Preferably, generating the grid and adjusting the reconstruction surface are performed for a first group of coordinates determined in a first phase of the cyclic motion, and the reconstructed surface of the first group is adjusted to form a
reconstructed surface in one or more additional phases.
Preferably, the method includes a final stage in which each determined location is associated with a respective grid point, and the associated grid points are moved onto the determined locations while non-associated grid points are substantially
Preferably, estimating the measure of the volume includes choosing an arbitrary point inside the grid and calculating the volumes of tetrahedrons defined by the arbitrary point and groups of three points on the grid which cover the entire grid
There is further provided in accordance with a preferred embodiment of the present invention, apparatus for reconstructing a map of a volume from coordinates of a plurality of determined locations on a surface of the volume having a
configuration, including a processor, which receives the coordinates and generates a grid of points defining a reconstruction surface in 3D space in proximity to the determined locations, and which defines a respective vector for each of the points on
the grid, dependent on a displacement between one or more of the points on the grid and one or more of the locations, and which adjusts the reconstruction surface by moving each of the points on the grid responsive to the respective vector, so that the
reconstruction surface is deformed to resemble the configuration of the surface of the volume.
Preferably, the processor calculates the center of mass using a weight that is substantially proportional for each location to the inverse of the sum of a small constant and the distance between the point and the location raised to a power
Preferably, the distances include geometrical distances.  Preferably, the apparatus includes a probe, which is brought into engagement with the surface to determine the locations thereon.
There is further provided in accordance with a preferred embodiment of the present invention, a method of displaying values of a parameter which varies over a surface, including determining a value of the parameter at each of a plurality of
points on the surface, and rendering an image of the surface to a display with a different degree of transparency in different areas of the surface, responsive in each of the areas to the value of the parameter at one or more points in the area.
FIG. 1 shows a mapping system 18 for mapping of a volume in a patient&#39;s body, in accordance with a preferred embodiment of the present invention.  System 18 comprises an elongate probe, preferably a catheter 20, for insertion into the human body. A distal end 22 of catheter 20 includes a functional portion 24 for performing diagnostic and/or therapeutic functions, adjacent to a distal tip 26.  Functional portion 24 preferably comprises electrodes (not shown in the figure) for performing
electrophysiological measurements, as described, for example, in U.S.  Pat.  No. 5,391,199 or in PCT publication WO97/24983, which are incorporated herein by reference.  Alternatively or additionally, functional portion 24 may include other diagnostic
apparatus for recording parameter values at points within the body.  Such apparatus may include a chemical sensor, a temperature sensor, a pressure sensor and/or any other desired sensor.  Functional portion 24 may determine for each point a single value
of the parameter, or alternatively a plurality of values dependent on the time of their acquisition.  Functional portion 24 may also include therapeutic apparatus, as is known in the art.
Distal end 22 of catheter 20 further includes a device 28 that generates signals used to determine the position and, preferably, orientation of the catheter within the body.  Device 28 is preferably adjacent to functional portion 24, in a fixed
relation with tip 26.  Device 28 preferably comprises three non-concentric coils, such as described in PCT patent publication WO96/05768, whose disclosure is incorporated herein by reference.  This device enables continuous generation of six dimensions
of position and orientation information with respect to an externally-applied magnetic field.  Alternatively, device 28 comprises other position and/or coordinate sensors as described in U.S.  Pat.  No. 5,391,199, U.S.  Pat.  No. 5,443,489 and PCT
publication WO94/04938, which are incorporated herein by reference.  Further alternatively or additionally, tip 26 is marked with a marker whose position can be determined from outside of the body, for example, a radio-opaque marker for use with a
Catheter 20 preferably includes a handle 30, having controls 32 which are used by a surgeon to steer distal end 22 of the catheter in a desired direction, so as to position and/or orient it as desired.  Catheter 20 preferably comprises a steering
mechanism in distal end 22, as is known in the art, so that repositioning of tip 26 is facilitated.
Catheter 20 is coupled, via an extension cable 21, to a console 34 which enables the user to observe and regulate the functions of catheter 20.  Console 34 preferably includes a computer 36, keyboard 38, signal processing circuits 40, which are
typically inside the computer, and display 42.  Signal processing circuits 40 typically receive, amplify, filter and digitize signals from catheter 20, including signals generated by position signal generating device 28, whereupon these digitized signals
are received and used by computer 36 to compute the position and orientation of the catheter.  Alternatively, appropriate circuitry may be associated with the catheter itself so that circuits 40 receive signals that are already amplified, filtered and/or
digitized.  Preferably, computer 36 includes a memory for storing positions and determined parameters of the points.  Computer 36 preferably also includes dedicated graphic hardware for polygon manipulation, which allows performing reconstruction stages
described hereinbelow using fast computer graphic techniques.
Preferably, system 18 also includes an ECG monitor 73, coupled to receive signals from one or more body surface electrodes 52 and to convey the signals to computer 36.  Alternatively, the ECG monitoring function may be performed by circuits 40.
FIG. 2 shows a distal portion of mapping catheter 20 within a heart 70 of a patient, in accordance with a preferred embodiment of the present invention.  Catheter 20 is inserted into heart 70 and tip 26 is brought into contact with a plurality of
locations, such as locations 75 and 77 on an inner surface 72 of heart 70.  Surface 72 bounds the volume to be reconstructed, and it is locations on this surface which are to be sampled.  At each of the plurality of locations, the coordinates of tip 26
are determined by device 28, preferably together with physiological information determined by functional portion 24.  The determined coordinates and, optionally, physiological information form a local data point.  The local data points from a plurality
of locations are used for producing a map of heart 70, or of a portion of the heart.
At least one reference catheter 78 is preferably inserted into heart 70 and is placed in a fixed position relative to the heart.  By comparing the positions of catheters 20 and 78, the position of tip 26 is accurately determined relative to the
heart, irrespective of heart motion.  Alternatively, any other suitable method may be used to compensate for movement of heart 70.
Preferably, the coordinates of tip 26 at the plurality of locations are determined at a common time-point in the cardiac cycle, preferably at end-diastole.  Alternatively or additionally, each determined position is recorded together with a
time-point, preferably relative to a predetermined time-point in the cardiac cycle, and together with indication of the current heart rate.  The relative time-point and the rate of the cycle are used to correct for the movement of the heart.  Thus, it is
possible to determine positions of a large number of points, simply, in a limited time period.
Further alternatively or additionally, the position of tip 26 is determined at each location at two or more time-points in the cardiac cycle, such that for each location, a range of positions are determined.  Thus, a geometric map of the
plurality of locations may comprise a plurality of &quot;snapshots&quot; of heart 70, each snapshot associated with a different phase of the cardiac cycle.  The cardiac cycle is preferably determined using ECG monitor 73, according to physiological readings from
functional portion 24, or according to movements of reference catheter 78.  Preferably, each position is determined together with the heart rate at the time of determination.  A frequency and phase shift transformation is preferably applied to the
plurality of positions at each location to bring the positions to a state as if they were determined at common time-points with respect to a common predetermined heart rate.
Preferably, the transformation applied to the positions also serves to reduce or eliminate the effects of any movement of the heart that is not due to the cardiac cycle, particularly chest movement due to respiration or other movements of the
patient.  These effects are removed by defining a cyclic trajectory of the points associated with each location, and then filtering out of the trajectory frequencies of motion other than frequencies associated with the heart rate.  Preferably, any
frequencies whose corresponding wavelengths do not evenly divide the cardiac cycle length, as determined from the ECG, are filtered out.  The result for each location is a modified trajectory, including a corrected end-diastolic point, which is then used
in reconstructing the map of the heart, as described hereinbelow.
Preferably, at each location at which tip 26 is positioned, it is verified that catheter 20 is in contact with the surface, using any suitable method, for example, as described in PCT publication WO97/24981, which is incorporated herein by
FIG. 3 is a flow chart illustrating the process of point sampling and reconstruction of a map, in accordance with a preferred embodiment of the present invention.  As described above, catheter 20 is brought into contact with surface 72 of heart
70, and signals are received from the catheter to form a local data point characteristic of the location of tip 26.  The local data point preferably includes coordinates of the point at a plurality of time points and one or more values, associated with
the point, of at least one physiological parameter.  Preferably, as mentioned above, the local data point includes an indication of the heart rate and time point in the heart cycle for each determined coordinate.  The parameter values may be associated
with specific time points or may be associated generally with the point.
Preferably, the contact between tip 26 and surface 72 is verified and the point is added to the map only if there is sufficient contact between the tip and the surface.  In a preferred embodiment of the present invention, points for which proper
contact does not exist are added to a database of interior points.  These points are interior to the reconstructed surface and indicate areas on the map which are not part of the reconstructed surface.  Alternatively or additionally, the user may
indicate sampled points which are not to be used as part of the reconstructed surface, for example because they are outstandingly outside of the area of the other sampled points.  Tip 26 is then moved to an additional location on surface 72 and data are
likewise determined regarding the additional point.  This procedure is repeated for a plurality of sampled points until data are determined for a sufficient number of points to make the map, or for a predetermined amount of time.  Preferably, computer 36
counts the number of sampled points and compares the number of points to a predetermined required minimum number of points.  Preferably, the predetermined number of points is between about ten to twenty points for fast procedures and is up to 100 points
for longer procedures.  Alternatively or additionally, the physician notifies computer 36 when a sufficient number of points have been sampled.
A map of heart 70 or of a volume within the heart is reconstructed, as described below, and the physician decides whether the map includes sufficient detail and appears to be accurate.  If the map is not sufficient, more points are acquired and
the map is accordingly updated or is again reconstructed.  The reconstructed map is thereafter used for analysis of the functioning of heart 70, and the physician may decide on a required treatment accordingly.
FIG. 4 is a flow chart illustrating a reconstruction procedure, in accordance with a preferred embodiment of the present invention.  Reconstruction is initially performed for positions determined at an anchor time point (t.sub.0) of the heart
cycle, such as end diastole.  In a first stage of the initial reconstruction, a grid enclosing the sampled points is constructed.  Thereafter, a stage of model distortion is applied to the grid, in which the grid is roughly adjusted to the shape defined
by the sampled points.  Subsequently, a preferably iterative stage of flexible matching is carried out finely adjusting the grid points according to the coordinates of the sampled points.  Final adjustment is preferably applied to the grid including
smoothing, an affine transformation and/or an exact matching stage which brings the grid to include substantially all the sampled points.  The parameter values associated with the sampled points are preferably interpolated to all the grid points and the
grid is subsequently displayed.  This procedure is described in greater detail hereinbelow with reference to the figures that follow.
FIGS. 5A-5E are simplified, two-dimensional graphs illustrating the reconstruction procedure for a single time-point, in accordance with a preferred embodiment of the present invention.  For clarity of illustration, the figures and the following
description refer to a simplified, two dimensional example.  The extension of the principles illustrated herein to 3D reconstruction will be clear to those skilled in the art.  Points S.sub.i are sampled points on the surface of the volume to be
reconstructed, whose coordinates were received during the above-described sampling process.
As shown in FIG. 5A, in the first stage, an initial grid 90 is defined in a vicinity of the sampled points, preferably enclosing the sampled points.  Alternatively, grid 90 may be interior to the sampled points or pass between the points.
Preferably, grid 90 comprises a number of points substantially greater than the number of sampled points.  The density of the points is preferably sufficient to produce a map of sufficient accuracy for any required medical procedure.  In a preferred
embodiment of the present invention, the physician can adjust the density of points on the grid according to a desired compromise between reconstruction speed and accuracy.  Preferably, grid 90 has an ellipsoidal shape or any other simple closed shape.
Alternatively or additionally, grid 90 has a shape based on known characteristics of the volume on whose surface the sampled points are located, for example, a shape determined by processing an LV-gram or other fluoroscopic or ultrasound image of
the heart.  In a preferred embodiment of the present invention, computer 36 contains a data-base of initial grids according to commonly-sampled volumes.  The physician indicates, preferably via keyboard 38, which volume is being sampled and initial grid
90 is chosen accordingly.  The chosen grid may be initially aligned with the sample points using any method known in the art, for example as described in Paul J. Besl and Neil D. McKay, &quot;A method for registration of 3-D shapes,&quot; IEEE Transactions on
Pattern Analysis and Machine Intelligence, 14(2):239-258, February 1992, which is incorporated herein by reference.  The initial grid may alternatively be chosen from the grid library using geometric hashing or alignment, as described, for example, in
Haim J. Wolfson, &quot;Model-based object recognition by geometric hashing,&quot; in: O. Faugeras, ed., Computer Vision-ECCV90 (First European Conference on Computer Vision, Antibes, France, Apr.  23-27, 1990), Springer, Berlin, 1990, 526-536, or in P.
Huttenlocher and S. Ullman, &quot;Recognizing solid objects by alignment with an image,&quot; International Journal of Computer Vision, 5: 195-212, 1990, which are incorporated herein by reference.  After the initial alignment, the method of the present invention
proceeds, preferably as shown in FIG. 4 and described further hereinbelow.
As shown in FIG. 5B, grid 90 is transformed to a grid 92 of points G&#39;, which is a rough adjustment toward the structure of the sampled volume.  For each point Gj on grid 90, an adjustment vector V.sub.j is constructed, and point Gj is replaced by
a corresponding point Gj&#39; on grid 92, which is displaced by V.sub.j from point Gj on grid 90.  Adjustment vector V.sub.j is preferably a weighted sum of vectors V.sub.ji from Gj to the sampled points S.sub.i, as shown in FIG. 5A.  Preferably, the weights
of vectors V.sub.ji in the sum are strongly inversely dependent on the magnitude of the vectors.  Preferably, the weights are inversely dependent on the magnitude raised to a power (k), wherein k preferably ranges between 4 and 10, and is most preferably
either between 6 and 8.  In a preferred embodiment of the present invention, adjustment vectors V.sub.j are calculated according to equation (1): ##EQU1##
In equation (1), epsilon is a small scalar, preferably, smaller than the magnitude of the smallest vector which is not zero, and is preferably of the size of the accuracy of the determination of the sampled points, for example, about 10.sup.-6.
Epsilon is used to prevent division by zero when the grid point is on a sampled point, and therefore the magnitude of the vector is zero.  C.sub.f is a constant factor between 0.1 and 1, preferably between 0.5 and 0.9 most preferably about 0.75, which is
adjusted to determine how closely the points G.sub.j &#39; will approach points S.sub.i in the rough adjustment.
In a preferred embodiment, the influence of a sampled point Si on grid point Gj, takes into account not only the distance between the sampled point Si and Gj, as shown above in equation (1) but also the density of sampled points S in the vicinity
of Si.  Hence, the weighting factor applied to each sampled point, ##EQU2##
is multiplied by a density value .quadrature..sub.i, which preferably takes on values between 0 and 1.  Preferably, .delta..sub.i is as defined in equation (2): ##EQU3##
The more points there are in the vicinity of S, the smaller value .delta.  takes on and the less influence each point has.  Preferably, the sum of influences of a plurality of points in a close vicinity is the same as the influence of a single
isolated point, which preferably has a density value .delta.  of about 1.
FIG. 5C illustrates a first part of a flexible matching step, in which each of sampled points S.sub.i is associated with a grid point Gj from roughly adjusted grid 92.  The associated grid points are moved toward their respective sampled points,
while the rest of the G&#39; points on the roughly adjusted grid are moved according to interpolation of the movements of neighboring points on grid 92, as described further hereinbelow.  Preferably, each sampled point S.sub.i is associated with the closest
grid point.  For example, the closest grid point to S.sub.1 is G.sub.1 &#39;, and these points are therefore associated.  Preferably, computer 36 creates a memory list in which these pairs of points are listed.  For clarity of this explanation, the
associated points are marked by dashed ovals 96 in FIG. 5C.
Preferably, a transformation function f, which moves the associated grid points toward their respective sampled points, is generated.  The non-associated grid points are also moved according to function f. Function f is preferably easily
calculated, and transforms the grid to a smooth form.  Preferably, function f is a weighted sum of the distances between the associated pairs of sampled and grid points, such that pairs of associated points close to the grid point influence its
displacement more than pairs of associated points far from the grid point.  Function f is preferably as given in equation (3) below, with w.sub.i (Gj) dependent on the distances between the grid point Gj and the associated grid points Gi, preferably as
defined in equation (4).  Alternatively, w.sub.i (Gj) is dependent on the distance between the grid point Gj and the sampled points Si, as in equation (1).  In the flexible matching stage, k is preferably smaller than the power law in the rough
adjustment stage in order to generate a smoother grid surface.  Preferably, k in the flexible matching stage is between 2 and 6 and is most preferably 4.  Preferably, k is an even number in order to simplify the calculations.  Although the equations
below are stated for convenience in scalar notation, it will be understood that S.sub.i, G.sub.i and f(G.sub.j) are vector quantities, as in equation (1) above: ##EQU4##
The constant C determines how close the associated grid points are moved toward their associated sampled points.  For very small values of C, the associated grid points G.sub.i are moved substantially onto the sampled points S.sub.i.  Preferably,
C is between 0.3 and 0.7, more preferably about 0.5.  Alternatively or additionally, C is changed according to the number of times the flexible matching is to be performed.  Further alternatively or additionally, in the first flexible matching step, C is
relatively large, while in subsequent flexible matching steps C is gradually reduced.
The distance definition used in equations (2), (3) and (4) is preferably the Euclidean distance in R.sup.3, due to its simplicity in calculation and the fact that it causes points on opposite walls of the reconstructed volume to repel one
In an alternative preferred embodiment of the present invention, the grid points which have an associated sampled point are moved toward their associated sampled points by a portion of the distance between them.  Preferably, the points are moved
a percentage of the distance between the associated pair.  For example, in FIG. 5C the points are moved about 2/3 of the distance.  Alternatively, the grid points are moved by any other amount dependent on the distance between the associated pair.
As shown in FIG. 5D, those grid points G&#39;.sub.k which are not associated with sampled points S.sub.i are then moved according to a movement vector V.sub.k which is dependent on the movements of the grid points G&#39;.sub.l surrounding the point.
Preferably, the non-associated points G&#39;.sub.k are moved a distance which is a linear interpolation of the movements of the surrounding points G&#39;.sub.l.  Preferably, the distance between the grid points is determined as the geometrical distance between
the points as they are on the present adjusted grid.  For example, the geometrical distance between G&#39;.sub.15 and G&#39;.sub.16 is indicated by X.sub.2, and may be calculated according to the coordinates of the two points.  Alternatively or additionally, the
distance used is the grid-distance X.sub.2 along the present adjusted grid, the grid-distance L.sub.2 along the original grid, or the geometrical distance L.sub.2 on the original grid.  In a preferred embodiment of the present invention, in a first
flexible matching step, the distance used is the grid-distance--either l.sub.2 or X.sub.2 --while in subsequent flexible matching steps the distance used is the geometrical distance X.sub.2.
For example, as shown in FIG. 5D, point G&#39;.sub.15 is moved a distance defined by a vector, which is a weighted sum of vectors ##EQU5##
of grid points G&#39;.sub.14, and G&#39;.sub.16, respectively.  Preferably, ##EQU7##
is as described in equation (2) below, in which d.sub.1 is a selected type of distance between G.sub.15 and G.sub.14, and may include X.sub.1, X.sub.1, l.sub.1 or any other suitable distance definition.  Likewise, d.sub.2 is a selected type of
distance between G.sub.15 and G.sub.16 and may include X.sub.2, X.sub.2, l.sub.2, or any other distance definition.  Preferably, in the first flexible matching step illustrated in FIG. 5D, d.sub.1 and d.sub.2 are taken as X.sub.1 and X.sub.2
respectively.  ##EQU8##
Preferably, during the flexible matching stage, flexible matching steps are repeated a few times (N.sub.0 times, as shown in FIG. 4).  Each time, grid points are associated with the sampled points, and the associated and non-associated grid
points are moved accordingly.
The rough adjustment and flexible matching tend to cause the grid to become non-uniform.  Therefore, during a final adjustment stage the grid is preferably smoothed, for example, by applying a surface convolution with a Gaussian-like kernel.
Preferably, the kernel is a 3.times.3 Gaussian kernel, and is applied to the grid a plurality of times, preferably between five and ten times.  Alternatively, a larger kernel may be used in which case it may be applied to the grid fewer times, most
preferably only once.  The surface convolution, however, generally causes shrinkage of the surface, and therefore a simple transformation, preferably an affine transformation, is applied to the grid to cancel the shrinkage and improve the matching of the
grid to the sampled points.  The affine transformation is preferably chosen as the transformation which minimizes the mean square distance between sampled points outside of the grid and a surface defined by the grid.  This choice of the transformation
causes substantially all the sampled points to be on or inside the surface defined by the grid.  This choice is in accordance with the anatomical structure of the heart in which outliers, i.e., points not on the sampled surface, are generally inside the
sampled surface, i.e. inside a cardiac chamber rather than on the myocardial wall.  Thus, the reconstructed grid is properly reconstructed by ignoring outliers which otherwise may deform the grid incorrectly.
To conclude the final adjustment stage, the user may optionally request an exact matching stage in which the grid surface is deformed to include substantially all the sampled points.  Preferably, for each sampled point not on the grid surface as
a result of prior stages, a closest grid point is chosen and moved to the position of the sampled point.  The rest of the grid points are preferably not moved.  Preferably, internal points which are beyond a certain distance from the grid surface are not
moved in this stage and are regarded as outliers.  It is noted that external points are not generally distanced from the grid surface due to the affine transformation described above.
Alternatively or additionally, a last flexible matching step is performed in which the associated grid points are moved onto the sampled points, as shown in FIG. 5E.  Curved line 100 in FIG. 5E represents the final grid configuration and
comprises an accurate approximation of the sampled volume.
Alternatively, the flexible matching is performed in one step, and the associated points from the rough adjustment grid are immediately moved onto the sampled points.  In a preferred embodiment of the present invention, computer 36 first produces
an approximate map, in which the flexible matching is performed in one step.  The approximate map is used by the physician to decide if more sampled points are needed.  Once the physician decided that no more points are needed, computer 36 reconstructs a
more accurate map in which the flexible matching is performed a plurality of times.  Meanwhile, the physician may use the approximate map in order to save time.  In further preferred embodiments, the first reconstructed map is produced with a relatively
low density of points on the grid, while later reconstructions use a more dense grid.
Referring back to FIG. 4, when the sampled points include data from more than one time point, the reconstructed grid of the anchor time point (hereinafter referred to as the anchor grid) is preferably used to quickly reconstruct the grid for
other time points t.sub.i.  For each of the other time points, a simple transformation is performed on the anchor grid to bring the grid close to the form of the sampled points of time t.sub.i.  The simple transformation is preferably a quadratic
transformation or an affine transformation.  Alternatively, the transformation comprises a rotation and/or scaling transformation.  In some preferred embodiments of the present invention, the transformation is chosen according to the number of sampled
points.  Preferably, when there are a relatively large number of sampled points, a quadratic transformation is applied, while for fewer sampled points, simpler transformations are employed.
Flexible matching is then preferably performed on the transformed grid one or more times (N.sub.T), preferably fewer times than were required in reconstruction of the anchor-time grid (N.sub.T &amp;gt;N.sub.0), most preferably twice.  Final
adjustments are then preferably applied to the grid, and the resulting grid at time t.sub.i may be displayed.  The parameter value may also be interpolated separately for time t.sub.i, substantially as described above with respect to the anchor grid.
When reconstruction for all of the time points is concluded, the reconstructed grids may be displayed in sequence as a function of time, or in any other manner.  Preferably, the reconstruction process continues while the anchor grid is displayed, so that
a physician may use the reconstructed data without delay.
Preferably, as noted hereinabove, each data point includes at least one physiological parameter, such as an indicator of the electrical activity in the heart, measured using functional portion 24 of catheter 20.  After the map is constructed, as
described above, the points on the grid, G.sub.1, G&#39;.sub.4, G&#39;.sub.7, etc., that were associated with sampled points S.sub.1, S.sub.2, S.sub.6, etc., are assigned the physiological parameter value of their respective sampled points.  The non-associated
grid points receive parameter values by interpolation between the values of the parameters of neighboring associated grid points in a manner similar to that described above.  Alternatively or additionally, the non-associated grid points receive parameter
values in a manner similar to the way they received their coordinates in flexible matching.
Further alternatively or additionally, the non-associated grid points are given parameter values using a zero-order-hold filling in method.  Starting from the sampled points, all the surrounding grid points are given the same parameter value as
the sampled point has, propagating outward until another grid point with a different parameter value is encountered.  Thereafter, a Gaussian smoothing process is preferably applied to the parameter values.  Thus, parameter values are given in a very
simple method to all the grid points substantially without forfeiting visual clarity.
Thus, a 3D map is reconstructed showing both the geometrical shape of the heart chamber and local electrical parameters or other physiological parameters as a function of position in the heart.  The local parameters may include electrogram
amplitude, activation time, direction and/or amplitude of the electrical conduction vector, or other parameters, and may be displayed using pseudocolor or other means of graphic realization, as is known in the art.  Preferably, a predefined color scale
is associated with the parameter, setting a first color, e.g., blue, for high values of the parameter, and a second color, e.g., red, for low values of the parameter.
FIG. 6 is a schematic illustration of a displayed reconstructed heart volume 130, in accordance with a preferred embodiment of the present invention.  A plurality of sampled points 134 are used to reconstruct a surface 132 of volume 130.  A grid
(not shown) is adjusted as described above to form surface 132.  Preferably, each point on the grid receives a reliability value indicative of the accuracy of the determination.  Further preferably, the reliability value is a function of the distance
from the grid point to the closest sampled point on surface 132 and/or of a density of sampled points 134 in a vicinity of the grid point.  Preferably, areas of surface 132 covered by less-reliable grid points, such as an area 140, are displayed as
semi-transparent, preferably using color-blending.  Due to the transparency, points 136 on an inner surface of volume 130 are displayed, being seen through volume 130.  Preferably, the user may define the predetermined distance and/or sample density
defining less-reliable points.  Alternatively or additionally, different levels of semi-transparency are used together with a multi-level reliability scale.
FIG. 7 is a schematic illustration of a volume estimation method, in accordance with a preferred embodiment of the present invention.  In some cases it is desired to estimate the volume encompassed by one or more reconstructed surfaces, for
example, to compare the volume of a heart chamber at different time-points of the heart cycle.  In FIG. 7 the reconstructed grid surface is represented, for clarity, by a ball 150.  The surface of ball 150 is partitioned into quadrilaterals by the grid
points, and these quadrilaterals are used for volume estimation.  An arbitrary point O, in a vicinity of the surface, preferably within the volume, most preferably close to the center of mass of ball 150, is chosen, thus defining a pyramid 152 for each
quadrilateral on the surface of ball 150.  An estimate of the sum of the volumes of pyramids 152 accurately represents the volume of ball 150.
Preferably, each quadrilateral is divided into two triangles, and the volume is estimated by summing the volumes of tetrahedrons defined by these triangles as bases and vertex O apex.  Let A.sub.m, B.sub.m, C.sub.m, denote the vertices of the
m-th triangle arranged clockwise, so that the normals of the triangles point outward from the surface of ball 150.  The volume V of ball 150 is estimated by equation (6): ##EQU9##
FIG. 8 is an illustration of a reconstruction procedure, in accordance with another preferred embodiment of the present invention.  In this preferred embodiment the sampled points are known to be on a single, open surface, rather than surrounding
a 3D volume, and therefore the beginning grid may comprise an open plane, rather than a closed curve.  Catheter 20 is brought into contact with a plurality of locations on an inner wall 76 of heart 70, and the coordinates of these locations are
determined to give sampled points 120.  Preferably, a physician indicates to console 34 the direction from which catheter 20 contacts surface 76.  Computer 36 accordingly generates an initial grid 122, which includes a plurality of grid points 124, such
that all the grid points are preferably on one side of the sampled points.  The adjustment procedure is performed substantially as described above, bringing grid points 124 to maximally resemble surface 76.
It is noted that although the above description assumes that the data regarding the sampled points are acquired by the system which performs the reconstruction, the reconstruction procedure may also be performed on points received from any
source, such as from a different computer, a library database or an imaging system.  Furthermore, although preferred embodiments are described herein with reference to mapping of the heart, it will be appreciated that the principles and methods of the
present invention may similarly be applied to 3D reconstruction of other physiological structure and cavities, as well as in non-medical areas of 3D image reconstruction.
Three-dimensional reconstruction of intrabody organs, Reisfeld, Daniel Reisfeld, Application number 09 789-427, Surgery, patent search, Patent Community, Atrial Fibrillation, Page Range, control apparatus, Company Search, Circulation Journal, Patent Inventor, Patent Attorney, English Español
The present invention relates generally to systems and methods for mapping, and specifically to methods of mapping of intrabody organs.BACKGROUND OF THE INVENTIONCardiac mapping is used to locate aberrant electrical pathways and currents within the heart, as well as mechanical and other aspects of cardiac activity. Various methods and devices have been described for mapping the heart. Such methods anddevice are described, for example, in U.S. Pat. Nos. 5,471,982 and 5,391,199 and in PCT patent publications WO94/06349, WO96/05768 and WO97/24981. U.S. Pat. No. 5,391,199, for example, describes a catheter including both electrodes for sensingcardiac electrical activity and miniature coils for determining the position of the catheter relative to an externally-applied magnetic field. Using this catheter a cardiologist may collect a set of sampled points within a short period of time, bydetermining the electrical activity at a plurality of locations and determining the spatial coordinates of the locations.In order to allow the surgeon to appreciate the determined data, a map, preferably a three dimensional (3D) map, including the sampled points is produced. U.S. Pat. No. 5,391,199 suggests superimposing the map on an image of the heart. Thepositions of the locations are determined with respect to a frame of reference of the image. However, it is not always desirable to acquire an image, nor is it generally possible to acquire an image in which the positions of the locations can be foundwith sufficient accuracy.Various methods are known in the art for reconstructing a 3D map of a cavity or volume using the known position coordinates of a plurality of locations on the surface of the cavity or volume. Some methods include triangulation, in which the mapis formed of a plurality of triangles which connect the sampled points. In some cases a convex hull or an alpha-hull of the points is constructed to form the mesh, and thereafter the constructed mesh is shrunk
Three-dimensional Reconstruction Of An Object From Projection Photographs - Patent 8098919