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Convolutional neural networks (CNNs) have demonstrated encouraging results in image classification tasks. However, the prohibitive computational cost of CNNs hinders the deployment of CNNs onto resource-constrained embedded devices. To address this issue, we propose EdgeCompress, a comprehensive compression framework to reduce the computational overhead of CNNs. In EdgeCompress, we first introduce dynamic image cropping (DIC), where we design a lightweight foreground predictor to accurately crop the most informative foreground object of input images for inference, which avoids redundant computation on background regions. Subsequently, we present compound shrinking (CS) to collaboratively compress the three dimensions (depth, width, and resolution) of CNNs according to their contribution to accuracy and model computation. DIC and CS together constitute a multidimensional CNN compression framework, which is able to comprehensively reduce the computational redundancy in both input images and neural network architectures, thereby improving the inference efficiency of CNNs. Further, we present a dynamic inference framework to efficiently process input images with different recognition difficulties, where we cascade multiple models with different complexities from our compression framework and dynamically adopt different models for different input images, which further compresses the computational redundancy and improves the inference efficiency of CNNs, facilitating the deployment of advanced CNNs onto embedded hardware. Experiments on ImageNet-1K demonstrate that EdgeCompress reduces the computation of ResNet-50 by 48.8% while improving the top-1 accuracy by 0.8%. Meanwhile, we improve the accuracy by 4.1% with similar computation compared to HRank, the state-of-the-art compression framework. The source code and models are available at this https URL