deformable convolution

**Deformable Convolution** is a **convolution with learnable spatial offsets applied to the sampling grid** — allowing the kernel to sample from irregular, input-dependent positions rather than a fixed rectangular grid, adapting the receptive field to object shapes. **How Does Deformable Convolution Work?** - **Standard Conv**: Samples at fixed grid positions ${(-1,-1), (-1,0), ..., (1,1)}$ for a 3×3 kernel. - **Deformable**: Each position gets a learned 2D offset: $p_k + Delta p_k$ where $Delta p_k$ is predicted by a parallel conv layer. - **Bilinear Interpolation**: Since offsets are fractional, bilinear interpolation samples the feature map at non-integer positions. - **Paper**: Dai et al. (2017), v2: Zhu et al. (2019). **Why It Matters** - **Shape Adaptation**: The receptive field adapts to object geometry — larger for large objects, deformed for non-rectangular shapes. - **Detection**: Significantly improves object detection (especially for non-rigid objects) in DETR, Mask R-CNN. - **v2**: Adds learnable modulation scalars to weight each sampling point's contribution. **Deformable Convolution** is **convolution with a flexible sampling grid** — letting the network learn where to look instead of using a fixed rectangular window.