Abstract
Differentiable rendering is a technique to connect 3D scenes with corresponding 2D images. Since it is differentiable, processes during image formation can be learned. Previous approaches to differentiable rendering focus on mesh-based representations of 3D scenes, which is inappropriate for medical applications where volumetric, voxelized models are used to represent anatomy. We propose a novel Projective Spatial Transformer module that generalizes spatial transformers to projective geometry, thus enabling differentiable volume rendering. We demonstrate the usefulness of this architecture on the example of 2D/3D registration between radiographs and CT scans. Specifically, we show that our transformer enables end-to-end learning of an image processing and projection model that approximates an image similarity function that is convex with respect to the pose parameters, and can thus be optimized effectively using conventional gradient descent. To the best of our knowledge, we are the first to describe the spatial transformers in the context of projective transmission imaging, including rendering and pose estimation. We hope that our developments will benefit related 3D research applications. The source code is available at https://github.com/gaocong13/Projective-Spatial-Transformers.
Supported by NIH R01EB023939, NIH R21EB020113, NIH R21EB028505 and Johns Hopkins University Applied Physics Laboratory internal funds.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
It is worth mentioning that this problem can be circumvented via ray casting-based implementations if one is interested in but not in [25].
References
Ferrante, E., Oktay, O., Glocker, B., Milone, D.H.: On the adaptability of unsupervised CNN-based deformable image registration to unseen image domains. In: Shi, Y., Suk, H.-I., Liu, M. (eds.) MLMI 2018. LNCS, vol. 11046, pp. 294–302. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00919-9_34
Gibson, E., et al.: Automatic multi-organ segmentation on abdominal CT with dense V-networks. IEEE Trans. Med. Imaging 37(8), 1822–1834 (2018)
Grupp, R., et al.: Automatic annotation of hip anatomy in fluoroscopy for robust and efficient 2D/3D registration. arXiv preprint arXiv:1911.07042 (2019)
Hansen, N., Müller, S.D., Koumoutsakos, P.: Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). Evol. Comput. 11(1), 1–18 (2003)
Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge University Press, Cambridge (2003)
Haskins, G., Kruger, U., Yan, P.: Deep learning in medical image registration: a survey. Mach. Vis. Appl. 1–18 (2020). https://doi.org/10.1007/s00138-020-01060-x
Henderson, P., Ferrari, V.: Learning single-image 3D reconstruction by generative modelling of shape, pose and shading. Int. J. Comput. Vis. 128, 835–854 (2020). https://doi.org/10.1007/s11263-019-01219-8
Hou, B., et al.: Predicting slice-to-volume transformation in presence of arbitrary subject motion. In: Descoteaux, M., Maier-Hein, L., Franz, A., Jannin, P., Collins, D.L., Duchesne, S. (eds.) MICCAI 2017. LNCS, vol. 10434, pp. 296–304. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66185-8_34
Jaderberg, M., Simonyan, K., Zisserman, A., et al.: Spatial transformer networks. In: Advances in Neural Information Processing Systems, pp. 2017–2025 (2015)
Krčah, M., Székely, G., Blanc, R.: Fully automatic and fast segmentation of the femur bone from 3D-CT images with no shape prior. In: 2011 IEEE International Symposium on Biomedical Imaging: from Nano to Macro, pp. 2087–2090. IEEE (2011)
Krebs, J., et al.: Robust non-rigid registration through agent-based action learning. In: Descoteaux, M., Maier-Hein, L., Franz, A., Jannin, P., Collins, D.L., Duchesne, S. (eds.) MICCAI 2017. LNCS, vol. 10433, pp. 344–352. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66182-7_40
Kuang, D., Schmah, T.: FAIM – a ConvNet method for unsupervised 3D medical image registration. In: Suk, H.-I., Liu, M., Yan, P., Lian, C. (eds.) MLMI 2019. LNCS, vol. 11861, pp. 646–654. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-32692-0_74
Liao, R., et al.: An artificial agent for robust image registration. In: Thirty-First AAAI Conference on Artificial Intelligence (2017)
Liu, S., Li, T., Chen, W., Li, H.: Soft rasterizer: a differentiable renderer for image-based 3D reasoning. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 7708–7717 (2019)
Loper, M.M., Black, M.J.: OpenDR: an approximate differentiable renderer. In: Fleet, D., Pajdla, T., Schiele, B., Tuytelaars, T. (eds.) ECCV 2014. LNCS, vol. 8695, pp. 154–169. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10584-0_11
Maes, F., Collignon, A., Vandermeulen, D., Marchal, G., Suetens, P.: Multimodality image registration by maximization of mutual information. IEEE Trans. Med. Imaging 16(2), 187–198 (1997)
Mahendran, S., Ali, H., Vidal, R.: 3D pose regression using convolutional neural networks. In: Proceedings of the IEEE International Conference on Computer Vision Workshops, pp. 2174–2182 (2017)
Miao, S., et al.: Dilated FCN for multi-agent 2D/3D medical image registration. In: Thirty-Second AAAI Conference on Artificial Intelligence (2018)
Miao, S., Wang, Z.J., Liao, R.: A CNN regression approach for real-time 2D/3D registration. IEEE Trans. Med. Imaging 35(5), 1352–1363 (2016)
Miolane, N., Mathe, J., Donnat, C., Jorda, M., Pennec, X.: Geomstats: a python package for riemannian geometry in machine learning. arXiv preprint arXiv:1805.08308 (2018)
Penney, G.P., Weese, J., Little, J.A., Desmedt, P., Hill, D.L., et al.: A comparison of similarity measures for use in 2-D-3-D medical image registration. IEEE Trans. Med. Imaging 17(4), 586–595 (1998)
Roth, H.R., et al.: A new 2.5D representation for lymph node detection using random sets of deep convolutional neural network observations. In: Golland, P., Hata, N., Barillot, C., Hornegger, J., Howe, R. (eds.) MICCAI 2014. LNCS, vol. 8673, pp. 520–527. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10404-1_65
Salehi, S.S.M., Khan, S., Erdogmus, D., Gholipour, A.: Real-time deep registration with geodesic loss. arXiv preprint arXiv:1803.05982 (2018)
Smith, L.N.: Cyclical learning rates for training neural networks. In: 2017 IEEE Winter Conference on Applications of Computer Vision (WACV), pp. 464–472. IEEE (2017)
Würfl, T., et al.: Deep learning computed tomography: learning projection-domain weights from image domain in limited angle problems. IEEE Trans. Med. Imaging 37(6), 1454–1463 (2018)
Yan, X., Yang, J., Yumer, E., Guo, Y., Lee, H.: Perspective transformer nets: learning single-view 3D object reconstruction without 3D supervision. In: Advances in Neural Information Processing Systems, pp. 1696–1704 (2016)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Gao, C. et al. (2020). Generalizing Spatial Transformers to Projective Geometry with Applications to 2D/3D Registration. In: Martel, A.L., et al. Medical Image Computing and Computer Assisted Intervention – MICCAI 2020. MICCAI 2020. Lecture Notes in Computer Science(), vol 12263. Springer, Cham. https://doi.org/10.1007/978-3-030-59716-0_32
Download citation
DOI: https://doi.org/10.1007/978-3-030-59716-0_32
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-59715-3
Online ISBN: 978-3-030-59716-0
eBook Packages: Computer ScienceComputer Science (R0)