can be included into standard CNNs to provide dynamic, adaptive downsampling and upsampling capabilities; to the best of our knowledge, IndexNet is one of the first attempts towards the design of generic upsampling operators;

-   We instantiate, and investigate five designs of IndexNet and demonstrate their effectiveness on four vision tasks.

A preliminary conference version of this work appeared in [@hao2019indexnet]. We extend [@hao2019indexnet] by i) further investigating two light-weight IndexNets; ii) comparing properties and computational complexity of IndexNets; iii) presenting a taxonomy of upsampling operators with the notion of guided upsampling and blind upsampling; and iv) designing image reconstruction experiments on synthetic data to compare two upsampling paradigms in recovering spatial information. Besides image matting in [@hao2019indexnet], we now v) apply IndexNets to a few more vision tasks including image denoising, semantic segmentation and monocular depth estimation and report extensive experimental results, not only between index networks but also across different vision tasks.

Literature Review
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We review upsampling operators and a closely-related group of networks: dynamic networks.

[**Upsampling in Deep Networks.**]{} Compared with other components in the design of deep networks, downsampling and upsampling of feature maps are relatively less studied. Since learning a CNN without sacrificing the 