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Convolutional networks are not aware of an object's geometric variations,which leads to inefficient utilization of model and data capacity. To overcomethis issue, recent works on deformation modeling seek to spatially reconfigurethe data towards a common arrangement such that semantic recognition suffersless from deformation. This is typically done by augmenting static operatorswith learned free-form sampling grids in the image space, dynamically tuned tothe data and task for adapting the receptive field. Yet adapting the receptivefield does not quite reach the actual goal -- what really matters to thenetwork is the "effective" receptive field (ERF), which reflects how much eachpixel contributes. It is thus natural to design other approaches to adapt theERF directly during runtime.  In this work, we instantiate one possible solution as Deformable Kernels(DKs), a family of novel and generic convolutional operators for handlingobject deformations by directly adapting the ERF while leaving the receptivefield untouched. At the heart of our method is the ability to resample theoriginal kernel space towards recovering the deformation of objects. Thisapproach is justified with theoretical insights that the ERF is strictlydetermined by data sampling locations and kernel values. We implement DKs asgeneric drop-in replacements of rigid kernels and conduct a series of empiricalstudies whose results conform with our theories. Over several tasks andstandard base models, our approach compares favorably against prior works thatadapt during runtime. In addition, further experiments suggest a workingmechanism orthogonal and complementary to previous works.

Deformable Kernels: Adapting Effective Receptive Fields for Object Deformation