  The cup-to-disc ratio (CDR) is one of the most significant indicator for
glaucoma diagnosis. Different from the use of costly fully supervised learning
formulation with pixel-wise annotations in the literature, this study
investigates the feasibility of accurate CDR measurement in fundus images using
only tight bounding box supervision. For this purpose, we develop a two-task
network named as CDRNet for accurate CDR measurement, one for weakly supervised
image segmentation, and the other for bounding-box regression. The weakly
supervised image segmentation task is implemented based on generalized multiple
instance learning formulation and smooth maximum approximation, and the
bounding-box regression task outputs class-specific bounding box prediction in
a single scale at the original image resolution. To get accurate bounding box
prediction, a class-specific bounding-box normalizer and an expected
intersection-over-union are proposed. In the experiments, the proposed approach
was evaluated by a testing set with 1200 images using CDR error and $F_1$ score
for CDR measurement and dice coefficient for image segmentation. A grader study
was conducted to compare the performance of the proposed approach with those of
individual graders. The experimental results indicate that the proposed
approach outperforms the state-of-the-art performance obtained from the fully
supervised image segmentation (FSIS) approach using pixel-wise annotation for
CDR measurement. Its performance is also better than those of individual
graders. In addition, the proposed approach gets performance close to the
state-of-the-art obtained from FSIS and the performance of individual graders
for optic cup and disc segmentation. The codes are available at
\url{https://github.com/wangjuan313/CDRNet}.
