Beyond $\chi^2$ Difference: Learning Optimal Metric for Boundary   Detection
  This letter focuses on solving the challenging problem of detecting natural image boundaries. A boundary usually refers to the border between two regions with different semantic meanings. Therefore, a measurement of dissimilarity between image regions plays a pivotal role in boundary detection of natural images. To improve the performance of boundary detection, a Learning-based Boundary Metric (LBM) is proposed to replace $\chi^2$ difference adopted by the classical algorithm mPb. Compared with $\chi^2$ difference, LBM is composed of a single layer neural network and an RBF kernel, and is fine-tuned by supervised learning rather than human-crafted. It is more effective in describing the dissimilarity between natural image regions while tolerating large variance of image data. After substituting $\chi^2$ difference with LBM, the F-measure metric of mPb on the BSDS500 benchmark is increased from 0.69 to 0.71. Moreover, when image features are computed on a single scale, the proposed LBM algorithm still achieves competitive results compared with \emph{mPb}, which makes use of multi-scale image features. 
Fei He, Shengjin Wang
cs.CV