Deformable Convolutional Networks (DCNs) are a variant of convolutional neural networks (CNNs) designed to enhance the ability of standard convolutions to handle geometric transformations, such as translations, rotations, and scale variations, in image data. DCNs were introduced in the paper “Deformable Convolutional Networks” by X. Dai et al., in 2017, to address the limitations of traditional convolutional layers, which apply fixed receptive fields and are therefore limited when it comes to capturing complex object deformations or spatial variations.

Here’s an overview of the key concepts and how they work:

1. Traditional Convolutions vs. Deformable Convolutions

• In standard convolution operations, each pixel in the output feature map is computed by applying a fixed kernel (a small filter) to a region of pixels in the input image. The kernel is applied at regular intervals (stride) across the image, and each pixel in the input contributes equally to the output, with no flexibility to shift or adapt based on local image characteristics.
• In contrast, deformable convolutions introduce additional learnable offsets (displacements) for each position in the…