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 |
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.
Citation: |
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 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 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
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 |
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 |
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° |
Table 3. Fields in the scan metadata
Field Name | Description |
projectName | Identifier of the CT scan, such as |
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. |
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 |
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 |
|
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. |
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 | 0.79085 | 0.44851 | 0.50565 | 0.44893 | 0.55401 | 0.43938 | 0.49096 | ||
0.69954 | 0.48696 | 0.35458 | 0.41472 | 0.52826 | 0.40087 | 0.47031 | |||
0.50118 | 0.36976 | 0.43939 | 0.39896 | 0.35415 | 0.34527 | 0.46894 | |||
1.99157 | 1.30523 | 1.29962 | 1.26261 | 1.43642 | 1.18552 | 1.43021 | 9th | ||
02-I | 0.96959 | 0.92622 | 0.95561 | 0.93696 | 0.94067 | 0.86811 | 0.68502 | ||
0.94863 | 0.92514 | 0.96670 | 0.88776 | 0.94187 | 0.80702 | 0.69134 | |||
0.96532 | 0.96928 | 0.96778 | 0.92211 | 0.96641 | 0.73418 | 0.70366 | |||
2.88354 | 2.82064 | 2.89009 | 2.74683 | 2.84895 | 2.40931 | 2.08002 | |||
02-II | 0.97916 | 0.93172 | 0.95766 | 0.94148 | 0.95152 | 0.87436 | 0.69228 | ||
0.96524 | 0.92857 | 0.95974 | 0.88134 | 0.94706 | 0.80140 | 0.69340 | |||
0.96757 | 0.96147 | 0.97187 | 0.92038 | 0.96676 | 0.73621 | 0.70237 | |||
2.91197 | 2.82176 | 2.88927 | 2.74320 | 2.86534 | 2.41197 | 2.08805 | 5th | ||
03 | 0.99242 | 0.98250 | 0.98088 | 0.97921 | 0.90589 | 0.87977 | 0.72839 | ||
0.98978 | 0.98003 | 0.96052 | 0.86968 | 0.94447 | 0.77897 | 0.68578 | |||
0.98363 | 0.99104 | 0.97194 | 0.95317 | 0.95462 | 0.63618 | 0.69520 | |||
2.96583 | 2.95357 | 2.91334 | 2.80206 | 2.80498 | 2.29492 | 2.10937 | 4th | ||
04 | 0.95802 | 0.89352 | 0.81804 | 0.84194 | 0.72393 | 0.73458 | 0.62915 | ||
0.89248 | 0.88292 | 0.67281 | 0.63267 | 0.80082 | 0.63951 | 0.65528 | |||
0.84620 | 0.94346 | 0.76756 | 0.78212 | 0.74274 | 0.52597 | 0.62538 | |||
2.69670 | 2.71990 | 2.25841 | 2.25673 | 2.26749 | 1.90006 | 1.90981 | 8th | ||
05 | 0.98991 | 0.86566 | 0.59670 | 0.74181 | 0.96497 | 0.85329 | 0.58669 | ||
0.98584 | 0.84429 | 0.50683 | 0.64274 | 0.68449 | 0.67221 | 0.75349 | |||
0.98032 | 0.70310 | 0.96522 | 0.65008 | 0.92236 | 0.56497 | 0.61420 | |||
2.95607 | 2.41305 | 2.06875 | 2.03463 | 2.57182 | 2.09047 | 1.95438 | 7th | ||
06-I | 0.99250 | 0.99149 | 0.98123 | 0.98376 | 0.98222 | 0.96424 | 0.77253 | ||
0.98314 | 0.98862 | 0.97817 | 0.96756 | 0.98041 | 0.89914 | 0.84657 | |||
0.98341 | 0.98884 | 0.97239 | 0.96508 | 0.96349 | 0.95129 | 0.79108 | |||
2.95905 | 2.96895 | 2.93179 | 2.91640 | 2.92612 | 2.81467 | 2.41018 | 1st | ||
06-II | 0.99394 | 0.98917 | 0.97883 | 0.97478 | 0.97979 | 0.96010 | 0.78061 | ||
0.98194 | 0.98740 | 0.97284 | 0.96118 | 0.97278 | 0.83665 | 0.82159 | |||
0.98353 | 0.98543 | 0.97436 | 0.95744 | 0.95659 | 0.93214 | 0.78771 | |||
2.95941 | 2.96200 | 2.92603 | 2.89340 | 2.90916 | 2.72889 | 2.38991 |
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 | 0.98704 | 0.98299 | 0.96427 | 0.96778 | 0.97126 | 0.93130 | 0.79519 | ||
0.97766 | 0.98070 | 0.94868 | 0.92216 | 0.94202 | 0.82103 | 0.80375 | |||
0.96797 | 0.97881 | 0.96417 | 0.92472 | 0.91882 | 0.86344 | 0.73844 | |||
2.93267 | 2.94250 | 2.87712 | 2.81466 | 2.83210 | 2.61577 | 2.33738 | |||
07-I | 0.98201 | 0.98062 | 0.92540 | 0.71639 | 0.57536 | 0.63074 | 0.59809 | ||
0.98312 | 0.97610 | 0.84620 | 0.67985 | 0.48684 | 0.59686 | 0.61696 | |||
0.95713 | 0.95077 | 0.91221 | 0.45057 | 0.63181 | 0.63061 | 0.54338 | |||
2.92226 | 2.90749 | 2.68381 | 1.84681 | 1.69401 | 1.85821 | 1.75843 | |||
07-II | 0.99697 | 0.99606 | 0.99065 | 0.98886 | 0.98904 | 0.95231 | 0.77239 | ||
0.99589 | 0.99517 | 0.98424 | 0.98041 | 0.98019 | 0.83785 | 0.83181 | |||
0.99441 | 0.99322 | 0.98846 | 0.97956 | 0.97344 | 0.89885 | 0.80129 | |||
2.98727 | 2.98445 | 2.96335 | 2.94883 | 2.94267 | 2.68901 | 2.40549 | 2nd | ||
07-III | 0.98942 | 0.97097 | 0.94119 | 0.95775 | 0.95655 | 0.95146 | 0.77007 | ||
0.96900 | 0.96441 | 0.93918 | 0.91330 | 0.97665 | 0.84366 | 0.80307 | |||
0.96473 | 0.95997 | 0.92522 | 0.94574 | 0.97219 | 0.84846 | 0.69877 | |||
2.92315 | 2.89535 | 2.80559 | 2.81679 | 2.90539 | 2.64358 | 2.27191 | |||
07-IV | 0.99314 | 0.98653 | 0.96766 | 0.97638 | 0.97218 | 0.92918 | 0.74209 | ||
0.99327 | 0.98629 | 0.96073 | 0.97320 | 0.95656 | 0.82330 | 0.79864 | |||
0.99220 | 0.98664 | 0.96277 | 0.97253 | 0.96058 | 0.88876 | 0.75758 | |||
2.97861 | 2.95946 | 2.89116 | 2.92211 | 2.88932 | 2.64124 | 2.29831 | |||
08-I | 0.95879 | 0.93977 | 0.93084 | 0.94198 | 0.92899 | 0.89870 | 0.67264 | ||
0.95392 | 0.93519 | 0.90612 | 0.92537 | 0.93182 | 0.77484 | 0.71968 | |||
0.93383 | 0.94839 | 0.91226 | 0.92934 | 0.92509 | 0.80276 | 0.66689 | |||
2.84654 | 2.82335 | 2.74922 | 2.79669 | 2.78590 | 2.47630 | 2.05921 | 6th | ||
08-II | 0.97973 | 0.92047 | 0.95188 | 0.94905 | 0.92163 | 0.90634 | 0.66310 | ||
0.96617 | 0.93489 | 0.93393 | 0.86119 | 0.92725 | 0.75551 | 0.69765 | |||
0.95255 | 0.97096 | 0.94675 | 0.86357 | 0.88353 | 0.78538 | 0.64905 | |||
2.89845 | 2.82632 | 2.83256 | 2.67381 | 2.73241 | 2.44723 | 2.00980 | |||
08-III | 0.98680 | 0.92298 | 0.94821 | 0.93463 | 0.91588 | 0.90119 | 0.65785 | ||
0.96365 | 0.92695 | 0.93543 | 0.86027 | 0.93396 | 0.76908 | 0.69393 | |||
0.95144 | 0.96038 | 0.93863 | 0.86539 | 0.89081 | 0.76683 | 0.65320 | |||
2.90189 | 2.81031 | 2.82227 | 2.66029 | 2.74065 | 2.43710 | 2.00498 | |||
08-IV | 0.97616 | 0.94031 | 0.95342 | 0.94636 | 0.91434 | 0.90544 | 0.66266 | ||
0.96326 | 0.93597 | 0.95119 | 0.90666 | 0.91938 | 0.76940 | 0.70863 | |||
0.95627 | 0.96854 | 0.94678 | 0.92256 | 0.91451 | 0.79796 | 0.65654 | |||
2.89569 | 2.84482 | 2.85139 | 2.77558 | 2.74823 | 2.47280 | 2.02783 | |||
09-I | 0.98374 | 0.96736 | 0.96609 | 0.97050 | 0.94631 | 0.88205 | 0.71029 | ||
0.99128 | 0.94881 | 0.96081 | 0.88746 | 0.92336 | 0.83275 | 0.67963 | |||
0.96644 | 0.98850 | 0.97670 | 0.96987 | 0.95999 | 0.75667 | 0.70135 | |||
2.94146 | 2.90467 | 2.90360 | 2.82783 | 2.82966 | 2.47147 | 2.09127 | |||
09-II | 0.98518 | 0.96942 | 0.97095 | 0.97136 | 0.94977 | 0.88437 | 0.73497 | ||
0.99234 | 0.95069 | 0.97232 | 0.89339 | 0.92751 | 0.84959 | 0.69966 | |||
0.95641 | 0.98981 | 0.97937 | 0.97094 | 0.96374 | 0.74646 | 0.74373 | |||
2.93393 | 2.90992 | 2.92264 | 2.83569 | 2.84102 | 2.48042 | 2.17836 | 3rd | ||
09-III | 0.98179 | 0.96248 | 0.96325 | 0.96344 | 0.91993 | 0.87032 | 0.74162 | ||
0.99111 | 0.94443 | 0.95812 | 0.88225 | 0.91729 | 0.83250 | 0.67339 | |||
0.95633 | 0.98696 | 0.97680 | 0.96605 | 0.95186 | 0.78638 | 0.69944 | |||
2.92923 | 2.89387 | 2.89817 | 2.81174 | 2.78908 | 2.48920 | 2.11445 | |||
09-IV | 0.98163 | 0.96679 | 0.96800 | 0.96887 | 0.93218 | 0.88161 | 0.72963 | ||
0.99135 | 0.95200 | 0.96634 | 0.88077 | 0.91841 | 0.83673 | 0.67064 | |||
0.95833 | 0.98680 | 0.97595 | 0.96558 | 0.95466 | 0.76779 | 0.69916 | |||
2.93131 | 2.90559 | 2.91029 | 2.81522 | 2.80525 | 2.48613 | 2.09943 | |||
09-V | 0.96127 | 0.94991 | 0.94647 | 0.93172 | 0.91745 | 0.86055 | 0.65961 | ||
0.98542 | 0.93619 | 0.93851 | 0.85737 | 0.90958 | 0.76827 | 0.64573 | |||
0.94298 | 0.97707 | 0.95182 | 0.93682 | 0.91935 | 0.70725 | 0.66359 | |||
2.88967 | 2.86317 | 2.83680 | 2.72591 | 2.74638 | 2.33607 | 1.96893 |
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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
The phantoms in the training data
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
Voronoi diagrams for various
Phantom generation procedure applied to 3 samples (rows). From left to right: Voronoi diagram after Lloyd's algorithm, distance map
(a) Diagram of the measurement setup. Abbreviations:
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
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
Reconstructions of level 1 A (top), B (middle), and C (bottom). First, second, and third places are highlighted in gold, silver, and bronze colors
Reconstructions of level 2 A (top), B (middle), and C (bottom). First, second, and third places are highlighted in gold, silver, and bronze colors
Reconstructions of level 3 A (top), B (middle), and C (bottom). First, second, and third places are highlighted in gold, silver, and bronze colors
Reconstructions of level 4 A (top), B (middle), and C (bottom). First, second, and third places are highlighted in gold, silver, and bronze colors
Reconstructions of level 5 A (top), B (middle), and C (bottom). First, second, and third places are highlighted in gold, silver, and bronze colors
Reconstructions of level 6 A (top), B (middle), and C (bottom). First, second, and third places are highlighted in gold, silver, and bronze colors
Reconstructions of level 7 A (top), B (middle), and C (bottom). First, second, and third places are highlighted in gold, silver, and bronze colors