LDConv: Linear deformable convolution for improving convolutional neural networks

Neural networks based on convolutional operations have achieved remarkable results in the field of deep learning, but there are two inherent flaws in standard convolutional operations. On the one hand, the convolution operation is confined to a local window, so it cannot capture information from other locations, and its sampled shapes is fixed. On the other hand, the size of the convolutional kernel are fixed to k $\times$ k, which is a fixed square shape, and the number of parameters tends to grow squarely with size. Although Deformable Convolution (Deformable Conv) address the problem of fixed sampling of standard convolutions, the number of parameters also tends to grow in a squared manner. In response to the above questions, the Linear Deformable Convolution (LDConv) is explored in this work, which gives the convolution kernel an arbitrary number of parameters and arbitrary sampled shapes to provide richer options for the trade-off between network overhead and performance. In LDConv, a novel coordinate generation algorithm is defined to generate different initial sampled positions for convolutional kernels of arbitrary size. To adapt to changing targets, offsets are introduced to adjust the shape of the samples at each position. LDConv corrects the growth trend of the number of parameters for standard convolution and Deformable Conv to a linear growth. Moreover, it completes the process of efficient feature extraction by irregular convolutional operations and brings more exploration options for convolutional sampled shapes. Object detection experiments on representative datasets COCO2017, VOC 7+12, and VisDrone-DET2021 fully demonstrate the advantages of LDConv. LDConv is a plug-and-play convolutional operation that can replace the convolutional operation to improve network performance. The code for the relevant tasks can be found at https://github.com/CV-ZhangXin/LDConv.