Explaining Convolutional Neural Networks for Area Estimation of Choroidal Neovascularization via Genetic Programming
Choroidal neovascularization (CNV), which will cause deterioration of the vision, is characterized by the growth of abnormal blood vessels in the choroidal layer. Estimating the area of CNV is important for proper treatment and prognosis of the disease. As a noninvasive imaging modality, optical coherence tomography (OCT) has become an important modality for assisting the diagnosis. Due to the number of acquired OCT volumes increases, automating the OCT image analysis is becoming increasingly relevant. In this paper, we train a convolutional neural network (CNN) with the raw images to estimate the area of CNV directly. Experimental results show that the performance of such a simple way is very competitive with the segmentation based methods. To explain the reason why the CNN performs well, we try to find the function being approximated by the CNN. Thus, for each layer in the CNN, we propose using a surrogate model, which is desired to have the same input and output with the layer while its mathematical expression is explicit, to fit the function approximated by this layer. Genetic programming (GP), which can automatically evolve both the structure and the parameters of the mathematical model from the data, is employed to derive the model. Primary results show that using GP to derive the surrogate models is a potential way to find the function being approximated by the CNN.
KeywordsChoroidal neovascularization Convolutional neural networks Surrogate model Genetic programming
This work has been supported by the National Basic Research Program of China (973 Program) under Grant 2014CB748600.
- 3.Huang, D., et al.: Optical coherence tomography. Science 254(5035), 1178–1181 (1991)Google Scholar
- 7.Manit, J., Schweikard, A., Ernst, F.: Deep convolutional neural network approach for forehead tissue thickness estimation. Curr. Dir. Biomed. Eng. 3(2), 103–107 (2017)Google Scholar
- 9.Poli, R., Langdon, W.B., McPhee, N.F., Koza, J.R.: A field guide to genetic programming, pp. 1–93. Lulu.com (2008). http://www.gp-field-guide.org.uk
- 10.Ronneberger, O., Fischer, P., Brox, T.: U-Net: convolutional networks for biomedical image segmentation. In: Navab, N., Hornegger, J., Wells, W.M., Frangi, A.F. (eds.) MICCAI 2015. LNCS, vol. 9351, pp. 234–241. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24574-4_28CrossRefGoogle Scholar
- 14.Zhen, X., Islam, A., Bhaduri, M., Chan, I., Li, S.: Direct and simultaneous four-chamber volume estimation by multi-output regression. In: Navab, N., Hornegger, J., Wells, W.M., Frangi, A.F. (eds.) MICCAI 2015. LNCS, vol. 9349, pp. 669–676. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24553-9_82CrossRefGoogle Scholar