  We propose MonoBox, an innovative box-supervised segmentation method
constrained by monotonicity to liberate its training from the user-unfriendly
box-tightness assumption. In contrast to conventional box-supervised
segmentation, where the box edges must precisely touch the target boundaries,
MonoBox leverages imprecisely-annotated boxes to achieve robust pixel-wise
segmentation. The 'linchpin' is that, within the noisy zones around box edges,
MonoBox discards the traditional misguiding multiple-instance learning loss,
and instead optimizes a carefully-designed objective, termed monotonicity
constraint. Along directions transitioning from the foreground to background,
this new constraint steers responses to adhere to a trend of monotonically
decreasing values. Consequently, the originally unreliable learning within the
noisy zones is transformed into a correct and effective monotonicity
optimization. Moreover, an adaptive label correction is introduced, enabling
MonoBox to enhance the tightness of box annotations using predicted masks from
the previous epoch and dynamically shrink the noisy zones as training
progresses. We verify MonoBox in the box-supervised segmentation task of
polyps, where satisfying box-tightness is challenging due to the vague
boundaries between the polyp and normal tissues. Experiments on both public
synthetic and in-house real noisy datasets demonstrate that MonoBox exceeds
other anti-noise state-of-the-arts by improving Dice by at least 5.5% and 3.3%,
respectively. Codes are at https://github.com/Huster-Hq/MonoBox.
