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Helsinki tomography challenge 2022: Description of the competition and dataset

  • *Corresponding author: Alexander Meaney

    *Corresponding author: Alexander Meaney 
Abstract Full Text(HTML) Figure(15) / Table(5) Related Papers Cited by
  • Inverse problems involve extracting information from indirect measurements. Many of these problems are ill-posed, making the recovery process unstable and sensitive to errors and noise. Specially designed algorithms are essential for robust solutions in such cases. Computed tomography (CT), which aims to determine an object's interior structure from X-ray projections, is a widely used application that requires solving an ill-posed problem. In this work we present the Helsinki Tomography Challenge 2022 (HTC2022), aimed to foster algorithm development in the field of CT reconstruction. HTC2022 focused specifically on limited-angle tomography to produce segmented reconstructions of disc-shaped imaging phantoms with holes of varying complexity and with progressively reduced angular range in seven levels of difficulty. This work also presents the dataset used in the competition, now publicly available. Real data is crucial for testing algorithms against the complexities of real-world scenarios, and this dataset can now be used by the reconstruction algorithm development community. HTC2022 was a global competition, with nine teams from seven countries participating and submitting a total of 22 algorithms. The competition results indicate interesting solutions in limited-angle tomography, with high-quality reconstructions that demonstrated promising directions for future research.

    Mathematics Subject Classification: Primary: 65-11, 44A12, 78A46; Secondary: 78-05.

    Citation:

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  • Figure 1.  Comparison of the phantom and its reconstructions. a) Photograph of the phantom A at level 6 of the test data. The heterogeneity seen in the photograph is due to the protective adhesive paper that covers the phantoms and, therefore, does not represent the material of the disk; b) segmented filtered back-projection (FBP) reconstruction using full-angle data (ground truth); c) segmented reconstruction of the winning team using limited-angle data; d) segmented FBP reconstruction using limited-angle data

    Figure 2.  The phantoms in the training data

    Figure 7.  Comparison between the test phantoms (top) and their segmented full-angle FBP reconstructions (bottom). The columns denote the phantom difficulty levels 1-7, from left to right

    Figure 3.  Voronoi diagrams for various $ p $ and $ \alpha $ with 6 central Voronoi cells. The black marks indicate the central seed points, and the colored regions represent the cells. The white circumference represents the boundary of the disc. The red marks represent additional seeds of boundary cells, used to restrict the central cells to the interior of the disc

    Figure 4.  Phantom generation procedure applied to 3 samples (rows). From left to right: Voronoi diagram after Lloyd's algorithm, distance map $ D $, smoothed version of the map $ D_{\text{LP}} $, high-pass filtered map $ D_{\text{HP}} $, normalized and cleaned $ D_{\text{HP}} $, and final shape of the phantom after applying the threshold

    Figure 5.  (a) Diagram of the measurement setup. Abbreviations: $ D_{\text{sd}} $ = distance from source to detector, $ D_{\text{so}} $ = distance from source to origin, $ D_{\text{od}} $ = distance from origin to detector. In this geometry, the center of rotation is defined as the origin. (b) Photograph of the measurement setup

    Figure 6.  Sinogram construction process. (a) X-ray projection after dark-frame subtraction, flat-field correction and binning. (b) X-ray projection after log-transform. The center row has been highlighted. (c) Full sinogram containing the center rows of projection data from 721 directions

    Figure 8.  Reconstruction and segmentation. a) Full data reconstruction, FBP. b) Segmented ground truth image. c) Limited-angle reconstruction, FBP. d) Segmented limited-angle reconstruction. The phantom pictured is 4B, and the limited-angle data has an angular range of 60°. The angular range indicated in the image depicts the directions of the central rays of the cone beams. The reconstruction images have each been windowed between zero and the maximum grey value in that reconstruction

    Figure 9.  Reconstructions of level 1 A (top), B (middle), and C (bottom). First, second, and third places are highlighted in gold, silver, and bronze colors

    Figure 10.  Reconstructions of level 2 A (top), B (middle), and C (bottom). First, second, and third places are highlighted in gold, silver, and bronze colors

    Figure 11.  Reconstructions of level 3 A (top), B (middle), and C (bottom). First, second, and third places are highlighted in gold, silver, and bronze colors

    Figure 12.  Reconstructions of level 4 A (top), B (middle), and C (bottom). First, second, and third places are highlighted in gold, silver, and bronze colors

    Figure 13.  Reconstructions of level 5 A (top), B (middle), and C (bottom). First, second, and third places are highlighted in gold, silver, and bronze colors

    Figure 14.  Reconstructions of level 6 A (top), B (middle), and C (bottom). First, second, and third places are highlighted in gold, silver, and bronze colors

    Figure 15.  Reconstructions of level 7 A (top), B (middle), and C (bottom). First, second, and third places are highlighted in gold, silver, and bronze colors

    Table 1.  Limited-angle tomography difficulty level specifications

    Level Angular range Angular increment Number of projections
    1 90° 0.5° 181
    2 80° 0.5° 161
    3 70° 0.5° 141
    4 60° 0.5° 121
    5 50° 0.5° 101
    6 40° 0.5° 81
    7 30° 0.5° 61
     | Show Table
    DownLoad: CSV

    Table 2.  Summary of the scanner hardware properties and scan parameters

    X-ray target Molybdenum
    Tube voltage 45.0kV
    Tube current 1.0mA
    X-ray filter 0.5mm Al
    Detector scintillator material CsI
    Detector pixel size 50µm
    Detector rows 2368
    Detector columns 2240
    Hardware binning 1$ \times $1 pixels
    Exposure time per projection 1200 ms
    Number of averages per projection 1
    Source-to-origin distance 410.66 mm
    Source-to-detector distance 553.74 mm
    Geometric magnification 1.3484
    Number of projections 721
    Angular increment 0.5°
     | Show Table
    DownLoad: CSV

    Table 3.  Fields in the scan metadata

    Field Name Description
    projectName Identifier of the CT scan, such as $ \texttt{htc2022_01a_}$.
    scanner The CT scanner used to measure the data.
    measurers Names of the people who conducted the CT scan.
    date The measurement date.
    dateFormat The measurement date format.
    geometryType The measurement geometry of the CT scanner.
    distanceSourceOrigin Distance from the X-ray focal spot to the center of rotation.
    distanceSourceDetector Distance from the X-ray focal spot to the X-ray detector.
    distanceUnit The unit of length in which distances are given.
    geometricMagnification The geometric magnification resulting from the measurement geometry.
    numberImages The number of X-ray projection images.
    angles The angular positions for each X-ray projection.
    detector The X-ray detector.
    detectorType The X-ray detector type. $ \texttt{EID}$ means energy-integrating detector and
    $ \texttt{PCD}$ means photon-counting detector.
    binning The binning factor used for the detector during the measurements.
    pixelSize The pixel size for the raw data. This depends on the physical detector
    pixel size and the detector binning.
    exposureTime The detector exposure time used for a single X-ray projection.
    exposureTimeUnit The unit of time for the exposure time.
    tube The X-ray tube model used in the scanner.
    target The X-ray target material in the X-ray tube.
    voltage The acceleration voltage used in the X-ray tube.
    voltageUnit The unit of measurement for the acceleration voltage.
    current The X-ray tube current.
    currentUnit The unit of measurement for the X-ray tube current.
    xRayFilter The X-ray filter material.
    xRayFilterThickness The X-ray filter thickness in millimeters.
    detectorRows The number of pixel rows in a single X-ray projection. This refers to
    the raw data coming from the detector and it is affected by the
    detector binning.
    detectorCols The number of pixel columns in a single X-ray projection. This refers
    to the raw data coming from the detector and it is affected by the
    detector binning.
    freeRayAtDetector The detector area used to determine the free-ray intensity $ I_0 $. The field
    consists of four positive integer coordinates indicating the first and last
    rows and columns used to extract a free-ray area from each projection
    image. This is done prior to any post-scan binning. Any such
    binning is also applied to the free-ray data.
    binningPost The binning factor used in processing the data during sinogram
    creation. Its values are limited to the set $ \{1, 2, 4, 8, 16, 32\} $.
    pixelSizePost The physical equivalent pixel size in the sinogram after possible
    binning during sinogram creation.
    effectivePixelSizePost The effective pixel size in the sinogram, taking into account the
    magnification from the measurement geometry.
    numDetectorsPost The number of detector pixels for each projection direction in the final
    2D sinogram.
     | Show Table
    DownLoad: CSV

    Table 4.  Scores and final leaderboard

    Team ID Scores Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Rank
    01 $ S_n^A $ 0.79085 0.44851 0.50565 0.44893 0.55401 0.43938 0.49096
    $ S_n^B $ 0.69954 0.48696 0.35458 0.41472 0.52826 0.40087 0.47031
    $ S_n^C $ 0.50118 0.36976 0.43939 0.39896 0.35415 0.34527 0.46894
    $ S_n $ 1.99157 1.30523 1.29962 1.26261 1.43642 1.18552 1.43021 9th
    02-I $ S_n^A $ 0.96959 0.92622 0.95561 0.93696 0.94067 0.86811 0.68502
    $ S_n^B $ 0.94863 0.92514 0.96670 0.88776 0.94187 0.80702 0.69134
    $ S_n^C $ 0.96532 0.96928 0.96778 0.92211 0.96641 0.73418 0.70366
    $ S_n $ 2.88354 2.82064 2.89009 2.74683 2.84895 2.40931 2.08002
    02-II $ S_n^A $ 0.97916 0.93172 0.95766 0.94148 0.95152 0.87436 0.69228
    $ S_n^B $ 0.96524 0.92857 0.95974 0.88134 0.94706 0.80140 0.69340
    $ S_n^C $ 0.96757 0.96147 0.97187 0.92038 0.96676 0.73621 0.70237
    $ S_n $ 2.91197 2.82176 2.88927 2.74320 2.86534 2.41197 2.08805 5th
    03 $ S_n^A $ 0.99242 0.98250 0.98088 0.97921 0.90589 0.87977 0.72839
    $ S_n^B $ 0.98978 0.98003 0.96052 0.86968 0.94447 0.77897 0.68578
    $ S_n^C $ 0.98363 0.99104 0.97194 0.95317 0.95462 0.63618 0.69520
    $ S_n $ 2.96583 2.95357 2.91334 2.80206 2.80498 2.29492 2.10937 4th
    04 $ S_n^A $ 0.95802 0.89352 0.81804 0.84194 0.72393 0.73458 0.62915
    $ S_n^B $ 0.89248 0.88292 0.67281 0.63267 0.80082 0.63951 0.65528
    $ S_n^C $ 0.84620 0.94346 0.76756 0.78212 0.74274 0.52597 0.62538
    $ S_n $ 2.69670 2.71990 2.25841 2.25673 2.26749 1.90006 1.90981 8th
    05 $ S_n^A $ 0.98991 0.86566 0.59670 0.74181 0.96497 0.85329 0.58669
    $ S_n^B $ 0.98584 0.84429 0.50683 0.64274 0.68449 0.67221 0.75349
    $ S_n^C $ 0.98032 0.70310 0.96522 0.65008 0.92236 0.56497 0.61420
    $ S_n $ 2.95607 2.41305 2.06875 2.03463 2.57182 2.09047 1.95438 7th
    06-I $ S_n^A $ 0.99250 0.99149 0.98123 0.98376 0.98222 0.96424 0.77253
    $ S_n^B $ 0.98314 0.98862 0.97817 0.96756 0.98041 0.89914 0.84657
    $ S_n^C $ 0.98341 0.98884 0.97239 0.96508 0.96349 0.95129 0.79108
    $ S_n $ 2.95905 2.96895 2.93179 2.91640 2.92612 2.81467 2.41018 1st
    06-II $ S_n^A $ 0.99394 0.98917 0.97883 0.97478 0.97979 0.96010 0.78061
    $ S_n^B $ 0.98194 0.98740 0.97284 0.96118 0.97278 0.83665 0.82159
    $ S_n^C $ 0.98353 0.98543 0.97436 0.95744 0.95659 0.93214 0.78771
    $ S_n $ 2.95941 2.96200 2.92603 2.89340 2.90916 2.72889 2.38991
     | Show Table
    DownLoad: CSV

    Table 5.  Scores and final leaderboard (cont.)

    Team ID Scores Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Rank
    06-III $ S_n^A $ 0.98704 0.98299 0.96427 0.96778 0.97126 0.93130 0.79519
    $ S_n^B $ 0.97766 0.98070 0.94868 0.92216 0.94202 0.82103 0.80375
    $ S_n^C $ 0.96797 0.97881 0.96417 0.92472 0.91882 0.86344 0.73844
    $ S_n $ 2.93267 2.94250 2.87712 2.81466 2.83210 2.61577 2.33738
    07-I $ S_n^A $ 0.98201 0.98062 0.92540 0.71639 0.57536 0.63074 0.59809
    $ S_n^B $ 0.98312 0.97610 0.84620 0.67985 0.48684 0.59686 0.61696
    $ S_n^C $ 0.95713 0.95077 0.91221 0.45057 0.63181 0.63061 0.54338
    $ S_n $ 2.92226 2.90749 2.68381 1.84681 1.69401 1.85821 1.75843
    07-II $ S_n^A $ 0.99697 0.99606 0.99065 0.98886 0.98904 0.95231 0.77239
    $ S_n^B $ 0.99589 0.99517 0.98424 0.98041 0.98019 0.83785 0.83181
    $ S_n^C $ 0.99441 0.99322 0.98846 0.97956 0.97344 0.89885 0.80129
    $ S_n $ 2.98727 2.98445 2.96335 2.94883 2.94267 2.68901 2.40549 2nd
    07-III $ S_n^A $ 0.98942 0.97097 0.94119 0.95775 0.95655 0.95146 0.77007
    $ S_n^B $ 0.96900 0.96441 0.93918 0.91330 0.97665 0.84366 0.80307
    $ S_n^C $ 0.96473 0.95997 0.92522 0.94574 0.97219 0.84846 0.69877
    $ S_n $ 2.92315 2.89535 2.80559 2.81679 2.90539 2.64358 2.27191
    07-IV $ S_n^A $ 0.99314 0.98653 0.96766 0.97638 0.97218 0.92918 0.74209
    $ S_n^B $ 0.99327 0.98629 0.96073 0.97320 0.95656 0.82330 0.79864
    $ S_n^C $ 0.99220 0.98664 0.96277 0.97253 0.96058 0.88876 0.75758
    $ S_n $ 2.97861 2.95946 2.89116 2.92211 2.88932 2.64124 2.29831
    08-I $ S_n^A $ 0.95879 0.93977 0.93084 0.94198 0.92899 0.89870 0.67264
    $ S_n^B $ 0.95392 0.93519 0.90612 0.92537 0.93182 0.77484 0.71968
    $ S_n^C $ 0.93383 0.94839 0.91226 0.92934 0.92509 0.80276 0.66689
    $ S_n $ 2.84654 2.82335 2.74922 2.79669 2.78590 2.47630 2.05921 6th
    08-II $ S_n^A $ 0.97973 0.92047 0.95188 0.94905 0.92163 0.90634 0.66310
    $ S_n^B $ 0.96617 0.93489 0.93393 0.86119 0.92725 0.75551 0.69765
    $ S_n^C $ 0.95255 0.97096 0.94675 0.86357 0.88353 0.78538 0.64905
    $ S_n $ 2.89845 2.82632 2.83256 2.67381 2.73241 2.44723 2.00980
    08-III $ S_n^A $ 0.98680 0.92298 0.94821 0.93463 0.91588 0.90119 0.65785
    $ S_n^B $ 0.96365 0.92695 0.93543 0.86027 0.93396 0.76908 0.69393
    $ S_n^C $ 0.95144 0.96038 0.93863 0.86539 0.89081 0.76683 0.65320
    $ S_n $ 2.90189 2.81031 2.82227 2.66029 2.74065 2.43710 2.00498
    08-IV $ S_n^A $ 0.97616 0.94031 0.95342 0.94636 0.91434 0.90544 0.66266
    $ S_n^B $ 0.96326 0.93597 0.95119 0.90666 0.91938 0.76940 0.70863
    $ S_n^C $ 0.95627 0.96854 0.94678 0.92256 0.91451 0.79796 0.65654
    $ S_n $ 2.89569 2.84482 2.85139 2.77558 2.74823 2.47280 2.02783
    09-I $ S_n^A $ 0.98374 0.96736 0.96609 0.97050 0.94631 0.88205 0.71029
    $ S_n^B $ 0.99128 0.94881 0.96081 0.88746 0.92336 0.83275 0.67963
    $ S_n^C $ 0.96644 0.98850 0.97670 0.96987 0.95999 0.75667 0.70135
    $ S_n $ 2.94146 2.90467 2.90360 2.82783 2.82966 2.47147 2.09127
    09-II $ S_n^A $ 0.98518 0.96942 0.97095 0.97136 0.94977 0.88437 0.73497
    $ S_n^B $ 0.99234 0.95069 0.97232 0.89339 0.92751 0.84959 0.69966
    $ S_n^C $ 0.95641 0.98981 0.97937 0.97094 0.96374 0.74646 0.74373
    $ S_n $ 2.93393 2.90992 2.92264 2.83569 2.84102 2.48042 2.17836 3rd
    09-III $ S_n^A $ 0.98179 0.96248 0.96325 0.96344 0.91993 0.87032 0.74162
    $ S_n^B $ 0.99111 0.94443 0.95812 0.88225 0.91729 0.83250 0.67339
    $ S_n^C $ 0.95633 0.98696 0.97680 0.96605 0.95186 0.78638 0.69944
    $ S_n $ 2.92923 2.89387 2.89817 2.81174 2.78908 2.48920 2.11445
    09-IV $ S_n^A $ 0.98163 0.96679 0.96800 0.96887 0.93218 0.88161 0.72963
    $ S_n^B $ 0.99135 0.95200 0.96634 0.88077 0.91841 0.83673 0.67064
    $ S_n^C $ 0.95833 0.98680 0.97595 0.96558 0.95466 0.76779 0.69916
    $ S_n $ 2.93131 2.90559 2.91029 2.81522 2.80525 2.48613 2.09943
    09-V $ S_n^A $ 0.96127 0.94991 0.94647 0.93172 0.91745 0.86055 0.65961
    $ S_n^B $ 0.98542 0.93619 0.93851 0.85737 0.90958 0.76827 0.64573
    $ S_n^C $ 0.94298 0.97707 0.95182 0.93682 0.91935 0.70725 0.66359
    $ S_n $ 2.88967 2.86317 2.83680 2.72591 2.74638 2.33607 1.96893
     | Show Table
    DownLoad: CSV
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