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imreggroupwise

Groupwise deformable registration

Description

The imreggroupwise function uses the total variation method to perform deformable registration of slices in a series of grayscale images. You can use this function to reduce sliding motion between slices in a series of medical images, such as a timeseries. Registering all slices of the series to one of the slices using deformable registration in a for loop can introduce bias towards the artifacts of one slice in all the slices. In contrast, the imreggroupwise function reduces the overall range of sliding motion across all slices.

[dispField,reg] = imreggroupwise(moving) transforms the slices in the image series moving so that they are groupwise registered, and returns the displacement field dispField and the registered image series reg.

example

[dispField,reg] = imreggroupwise(moving,Name=Value) specifies options for the total variation method using one or more optional name-value arguments.

Examples

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Load an MRI volume into the workspace.

imgs = load("mristack.mat");
imgs = squeeze(imgs.mristack);

Pad the slices of the MRI volume to allow for rotation.

imgs = padarray(imgs,[10 10],"both");

Extract the 10th slice of the MRI volume, to use to generate the moving image series.

paddedSlice = imgs(:,:,10);

Generate the moving image series by rotating the slice by different angles.

moving = zeros(276,276,27);
for i = 1:27
  moving(:,:,i) = imrotate(paddedSlice,i,"crop");
end

Perform groupwise registration of the slices of the moving image series.

[dispField,reg] = imreggroupwise(moving,GridRegularization=0.05);
--------------------------- Pyramid Level = 3 -------------------------------- 
                                                     Closeness to 
 Iteration         f(x)         Step-size           optimal solution
     1        160720.92          11.50                 18.19431
     2        146622.17          41.61                 31.55621
     3        137582.30          54.80                 37.51630
     4        131892.89          21.32                 30.22352
     5        129146.80          12.05                 27.98123
     6        126260.51          18.80                 34.57209
     7        123292.77          21.42                 32.76271
     8        119756.72          34.44                 26.53227
     9        117145.16          27.64                 33.13160
    10        114257.37          28.72                 39.06536
    11        111212.99          50.30                 35.02401
    12        108848.93          28.47                 27.27366
    13        106838.15          16.68                 21.59996
    14        104141.37          48.40                 29.34133
    15        103034.70          43.98                 36.78617
    16        101421.24          11.33                 21.98658
    17         99846.91          25.65                 19.28558
    18         98950.73          20.29                 22.02194
    19         97683.82          55.50                 23.47823
    20         97058.47          35.79                 56.52787
    21         95693.10          12.29                 39.94096
    22         94308.28          31.93                 50.77296
    23         93620.93          21.01                 23.42839
    24         92756.49          43.04                 26.44428
    25         92160.48          39.07                 20.02188
    26         91649.86          20.14                 23.32969
    27         90848.45          52.28                 12.75790
    28         90785.24          35.18                 50.98939
    29         89193.25          13.04                 24.02603
    30         87913.57          26.84                 23.86608
    31         87261.74          13.25                 27.18752
    32         86609.40          28.99                 20.23212
    33         86403.18          36.29                 19.85028
    34         86171.97          12.29                 14.73627
    35         85991.59          43.41                 19.17823
    36         85880.43          31.97                 52.82440
    37         84848.06          22.60                 38.11074
    38         83896.58          24.78                 26.63796
    39         83221.23          17.79                 31.42078
    40         82422.75          15.26                 17.38349
    41         82386.70          42.07                 30.26392
    42         82118.45          10.10                 20.60638
    43         81714.94          31.01                 27.63559
    44         81475.85          25.61                 35.72504
    45         81219.57          11.81                 30.83450
    46         80900.59          42.13                 21.99698
    47         80701.15          27.56                 46.08761
    48         79735.79          18.84                 29.77860
    49         78885.47          19.72                 21.33987
    50         78443.85          14.00                 33.84345
    51         78025.38          19.61                 21.81821
    52         77820.46          10.80                 27.58759
    53         77566.30          14.89                 14.12064
    54         77356.17          16.30                 24.02455
    55         77210.20          17.62                 13.38399
    56         77175.39          16.57                 13.65389
    57         77139.47          16.67                 14.31732
    58         77103.48          16.91                 14.75186
    59         77052.18          18.54                 13.45865
    60         77007.15          17.58                 11.45708
    61         76995.53           6.92                 12.12129

--------------------------- Pyramid Level = 2 -------------------------------- 
                                                     Closeness to 
 Iteration         f(x)         Step-size           optimal solution
     1         90397.57           9.98                 16.07776
     2         88598.63          13.10                 23.03916
     3         86659.87          23.18                 36.97704
     4         85346.69          26.94                 46.28403
     5         83821.96           9.70                 20.80432
     6         82514.48          16.43                 25.34133
     7         81522.62          18.21                 27.43884
     8         80714.91          45.26                 44.56642
     9         79515.86          16.33                 17.96243
    10         78667.76          10.10                 25.12929
    11         77756.18          24.19                 27.73775
    12         77571.40          32.06                 51.91825
    13         76629.12           7.86                 22.85993
    14         75929.67          19.14                 31.05180
    15         75590.59          16.23                 14.57161
    16         75563.08          47.79                 52.11658
    17         74964.02          19.25                 34.85287
    18         74383.90           8.57                 36.63964
    19         73887.61          25.26                 20.34162
    20         73676.18           8.94                 12.66080
    21         73360.07          26.43                 19.09864
    22         73190.90          31.92                 33.94272
    23         73032.36          10.59                 20.21763
    24         72764.07          32.08                 14.04518
    25         72626.99          24.21                 27.84766
    26         72493.83          30.79                 28.66531
    27         72090.89          18.12                 17.14031
    28         71660.52          18.11                 11.76067
    29         71269.90          15.98                 24.21175
    30         71067.73          22.38                 15.58385
    31         70985.12           8.50                 14.58411
    32         70888.81          11.41                 13.56274
    33         70796.71          14.63                 12.23691
    34         70729.12          15.27                 12.57831
    35         70721.71          14.16                 12.59730
    36         70716.14           5.36                 12.87683

--------------------------- Pyramid Level = 1 -------------------------------- 
                                                     Closeness to 
 Iteration         f(x)         Step-size           optimal solution
     1         80123.51          13.71                 13.80900
     2         78453.64          14.18                 11.56824
     3         76729.32          27.24                 26.34447
     4         75799.10          26.53                 37.72128
     5         74508.05           9.21                 19.73064
     6         73460.13          20.96                 27.40239
     7         72800.90          16.67                 26.18356
     8         71919.69          32.43                 14.43351
     9         71545.75          30.56                 32.57132
    10         70717.01          15.97                 18.49375
    11         70052.45          19.04                 22.48044
    12         69587.50          17.23                 23.88982
    13         69094.55          28.76                 22.76715
    14         68720.48          24.05                 24.80507
    15         68212.79          16.41                 14.46844
    16         67766.80          23.74                 14.20388
    17         67589.19          23.70                 29.27166
    18         67121.86          14.29                 13.96609
    19         66779.83          23.35                 12.63738
    20         66611.24          19.61                 21.53575
    21         66390.03          23.81                 15.41449
    22         66226.75           9.53                 10.36505
    23         66174.37          35.33                 14.71976
    24         66046.98           6.29                 11.75380
    25         65777.74          20.41                 21.22998
    26         65694.36          26.64                 37.03862
    27         65478.70           9.46                 33.20081
    28         65330.62          28.51                 30.64879
    29         65193.94          14.45                 30.87433
    30         64969.61          20.04                 27.73873
    31         64863.63           7.47                 23.45422
    32         64742.49          10.56                 18.98134
    33         64655.24          11.63                 19.72796
    34         64589.34          12.86                 11.98109
    35         64575.96           6.52                 13.75064
    36         64563.45           8.01                 13.59998
    37         64558.37           3.78                 12.33042

Visualize the output of the groupwise registration. The mean image of the moving image series shows that the slices are misaligned. In contrast, the mean image of the registered image series indicates alignment across slices.

figure
imshow([paddedSlice,mean(moving,3),mean(reg,3)])
title("Original Image | Mean Image of Moving Image Series | Mean Image of Registered Image Series")

Figure contains an axes object. The axes object with title Original Image | Mean Image of Moving Image Series | Mean Image of Registered Image Series contains an object of type image.

Input Arguments

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Image series to be registered, specified as a 3-D numeric array. The slices in the image series must capture the same anatomical slice of the body. For example, the image series can be a collection of the same slice imaged at different times.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: [dispField,reg] = imreggroupwise(moving,NumPyramidLevels=6) registers the slices of moving using six pyramid levels.

Grid spacing, specified as a two-element numeric vector. Smaller values of GridSpacing specify a finer grid resolution.

Data Types: double

Pixel size, specified as a two-element numeric vector. Values are in millimeters.

Data Types: double

Number of multiresolution pyramid levels, specified as a positive integer.

If moving is of size M-by-N-by-P, then the value of NumPyramidlevels must satisfy the condition min([M N P]) > (2^NumPyramidLevels)*0.7.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Weighing factor for grid displacement regularization, specified as a nonnegative scalar.

A large value for GridRegularization can create a smooth output displacement field, whereas a small value can create more localized displacements.

Data Types: double

Progress information output, specified as a numeric or logical 1 (true) or 0 (false). Specify DisplayProgress as true to display information such as the number of iterations, normalized root mean square error (RMSE), function local minima, step size, and closeness to optimal solution.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical

Output Arguments

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Displacement field, returned as a 4-D numeric array.

If moving is of size M-by-N-by-P, the displacement field dispField is a 4-D numeric array of size M-by-N-by-2-by-P, where dispField(:,:,1,:) and dispField(:,:,2,:) contain the displacements for each of the slices in the X- and Y- directions, respectively.

Registered image series, returned with the same size and data type as moving.

References

[1] Vishnevskiy, Valery, Tobias Gass, Gabor Szekely, Christine Tanner, and Orcun Goksel. “Isotropic Total Variation Regularization of Displacements in Parametric Image Registration.” IEEE Transactions on Medical Imaging 36, no. 2 (February 2017): 385–95. https://doi.org/10.1109/TMI.2016.2610583.

Version History

Introduced in R2022b