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We study the Solid Isotropic Material Penalization (SIMP) method with a density field generated by a fully-connected neural network, taking the coordinates as inputs. In the large width limit, we show that the use of DNNs leads to a filtering effect similar to traditional filtering techniques for SIMP, with a filter described by the Neural Tangent Kernel (NTK). This filter is however not invariant under translation, leading to visual artifacts and non-optimal shapes. We propose two embeddings of the input coordinates, which lead to (approximate) spatial invariance of the NTK and of the filter. We empirically confirm our theoretical observations and study how the filter size is affected by the architecture of the network.

Object detection plays a crucial role in the field of computer vision by autonomously locating and identifying objects of interest. The You Only Look Once (YOLO) model is an effective single-shot detector. However, YOLO faces challenges in cluttered or partially occluded scenes and can struggle with small, low-contrast objects. We propose a new method that integrates spatial transformer networks (STNs) into YOLO to improve performance. The proposed STN-YOLO aims to enhance the model's effectiveness by focusing on important areas of the image and improving the spatial invariance of the model before the detection process. Our proposed method improved object detection performance both qualitatively and quantitatively. We explore the impact of different localization networks within the STN module as well as the robustness of the model across different spatial transformations. We apply the STN-YOLO on benchmark datasets for Agricultural object detection as well as a new dataset from a state-of-the-art plant phenotyping greenhouse facility. Our code and dataset are publicly available.

Compared to natural images, medical images usually show stronger visual patterns and therefore this adds flexibility and elasticity to resource-limited clinical applications by injecting proper priors into neural networks. In this paper, we propose spatially covariant pixel-aligned classifier (SCP) to improve the computational efficiency and meantime maintain or increase accuracy for lesion segmentation. SCP relaxes the spatial invariance constraint imposed by convolutional operations and optimizes an underlying implicit function that maps image coordinates to network weights, the parameters of which are obtained along with the backbone network training and later used for generating network weights to capture spatially covariant contextual information. We demonstrate the effectiveness and efficiency of the proposed SCP using two lesion segmentation tasks from different imaging modalities: white matter hyperintensity segmentation in magnetic resonance imaging and liver tumor segmentation in contrast-enhanced abdominal computerized tomography. The network using SCP has achieved 23.8%, 64.9% and 74.7% reduction in GPU memory usage, FLOPs, and network size with similar or better accuracy for lesion segmentation.

Previous work generally believes that improving the spatial invariance of convolutional networks is the key to object counting. However, after verifying several mainstream counting networks, we surprisingly found too strict pixel-level spatial invariance would cause overfit noise in the density map generation. In this paper, we try to use locally connected Gaussian kernels to replace the original convolution filter to estimate the spatial position in the density map. The purpose of this is to allow the feature extraction process to potentially stimulate the density map generation process to overcome the annotation noise. Inspired by previous work, we propose a low-rank approximation accompanied with translation invariance to favorably implement the approximation of massive Gaussian convolution. Our work points a new direction for follow-up research, which should investigate how to properly relax the overly strict pixel-level spatial invariance for object counting. We evaluate our methods on 4 mainstream object counting networks (i.e., MCNN, CSRNet, SANet, and ResNet-50). Extensive experiments were conducted on 7 popular benchmarks for 3 applications (i.e., crowd, vehicle, and plant counting). Experimental results show that our methods significantly outperform other state-of-the-art methods and achieve promising learning of the spatial position of objects.

Convolutional neural networks are among the most successful architectures in deep learning. This success is at least partially attributable to the efficacy of spatial invariance as an inductive bias. Locally connected layers, which differ from convolutional layers in their lack of spatial invariance, usually perform poorly in practice. However, these observations still leave open the possibility that some degree of relaxation of spatial invariance may yield a better inductive bias than either convolution or local connectivity. To test this hypothesis, we design a method to relax the spatial invariance of a network layer in a controlled manner. In particular, we create a \textit{low-rank} locally connected layer, where the filter bank applied at each position is constructed as a linear combination of basis set of filter banks. By varying the number of filter banks in the basis set, we can control the degree of departure from spatial invariance. In our experiments, we find that relaxing spatial invariance improves classification accuracy over both convolution and locally connected layers across MNIST, CIFAR-10, and CelebA datasets. These results suggest that spatial invariance in convolution layers may be overly restrictive.