segmentation models, such as DeepLabv3+ [@chen18v3] and RefineNet [@lin2017refine], to this task, we observe that they tend to fail to recover boundary details (Fig. \[fig:alpha\_mattes\]). A plausible explanation is that, compared to the bilinearly upsampled feature map, unpooling uses max-pooling indices to guide upsampling. Since boundaries in the shallow layers usually have the maximum responses, indices extracted from these responses record the boundary locations. The feature map projected by the indices thus shows improved boundary delineation.

![Alpha mattes of different models for the task of image matting. From left to right, Deeplabv3+ [@chen18v3], RefineNet [@lin2017refine], Deep Matting [@xu2017deep] and IndexNet (Ours). Bilinear upsampling tends to fail to recover subtle details, while unpooling and our learned upsampling operator can produce much clear mattes with good local contrast. []{data-label="fig:alpha_mattes"}](mattes_intro.pdf){width="\linewidth"}

We thus believe that different upsampling operators may exhibit different characteristics, and we expect a specific behavior of the upsampling operator when dealing with specific image content for a particular vision task. A question of interest is: *Can we design a generic operator to upsample feature maps that better predict boundaries and regions simultaneously?* A key observation of this work is that unpooling, bilinear interpolation or other *upsampling operators are some forms of 