Maxout filter networks referencing morphological filters. Nakashizuka, M., Kobayashi, K., Ishikawa, T., & Itoi, K. In 2017 25th European Signal Processing Conference (EUSIPCO), pages 1599-1603, Aug, 2017.
Maxout filter networks referencing morphological filters [pdf]Paper  doi  abstract   bibtex   
This paper presents nonlinear filters that are obtained from extensions of morphological filters. The proposed nonlinear filter consists of a convex and concave filter that are extensions of the dilation and erosion of morphological filter with the maxout activation function. Maxout can approximate arbitrary convex functions as piecewise linear functions, including the max function of the morphological filters. The class of the convex function hence includes the morphological dilation and can be trained for specific image processing tasks. In this paper, the closing filter is extended to a convex-concave filter with maxout. The convex-concave filter is trained for noise and mask removal with a training set. The examples of noise and mask removal show that the convex-concave filter can obtain a recovered image, whose quality is comparable to in-painting by using the total variation minimization with reduced computational cost without mask information of the corrupted pixels.
@InProceedings{8081479,
  author = {M. Nakashizuka and K. Kobayashi and T. Ishikawa and K. Itoi},
  booktitle = {2017 25th European Signal Processing Conference (EUSIPCO)},
  title = {Maxout filter networks referencing morphological filters},
  year = {2017},
  pages = {1599-1603},
  abstract = {This paper presents nonlinear filters that are obtained from extensions of morphological filters. The proposed nonlinear filter consists of a convex and concave filter that are extensions of the dilation and erosion of morphological filter with the maxout activation function. Maxout can approximate arbitrary convex functions as piecewise linear functions, including the max function of the morphological filters. The class of the convex function hence includes the morphological dilation and can be trained for specific image processing tasks. In this paper, the closing filter is extended to a convex-concave filter with maxout. The convex-concave filter is trained for noise and mask removal with a training set. The examples of noise and mask removal show that the convex-concave filter can obtain a recovered image, whose quality is comparable to in-painting by using the total variation minimization with reduced computational cost without mask information of the corrupted pixels.},
  keywords = {convex programming;image denoising;image filtering;image processing;mathematical morphology;minimisation;nonlinear filters;piecewise linear techniques;morphological dilation;closing filter;convex-concave filter;maxout filter networks;morphological filter;nonlinear filter;maxout activation function;approximate arbitrary convex functions;image processing;mask removal;noise removal;total variation minimization;corrupted pixels;Training;Convex functions;Neural networks;Image processing;Morphology;Noise reduction;Mathematical morphology;maxout;noise removal;nonlinear filter;neural network},
  doi = {10.23919/EUSIPCO.2017.8081479},
  issn = {2076-1465},
  month = {Aug},
  url = {https://www.eurasip.org/proceedings/eusipco/eusipco2017/papers/1570347768.pdf},
}
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