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In this paper, we focus on devising a versatile framework for dense pixelwise prediction whose goal is to assign a discrete or continuous label to each pixel for an image. It is well-known that the reduced feature resolution due to repeated subsampling operations poses a serious challenge to Fully Convolutional Network (FCN) based models. In contrast to the commonly-used strategies, such as dilated convolution and encoder-decoder structure, we introduce the Flattening Module to produce high-resolution predictions without either removing any subsampling operations or building a complicated decoder module. In addition, the Flattening Module is lightweight and can be easily combined with any existing FCNs, allowing the model builder to trade off among model size, computational cost and accuracy by simply choosing different backbone networks. We empirically demonstrate the effectiveness of the proposed Flattening Module through competitive results in human pose estimation on MPII, semantic segmentation on PASCAL-Context and object detection on PASCAL VOC. We hope that the proposed approach can serve as a simple and strong alternative of current dominant dense pixelwise prediction frameworks.

This paper offers a novel mathematical approach, the modified Fractional-order Steepest Descent Method (FSDM) for training BackPropagation Neural Networks (BPNNs); this differs from the majority of the previous approaches and as such. A promising mathematical method, fractional calculus, has the potential to assume a prominent role in the applications of neural networks and cybernetics because of its inherent strengths such as long-term memory, nonlocality, and weak singularity. Therefore, to improve the optimization performance of classic first-order BPNNs, in this paper we study whether it could be possible to modified FSDM and generalize classic first-order BPNNs to modified FSDM based Fractional-order Backpropagation Neural Networks (FBPNNs). Motivated by this inspiration, this paper proposes a state-of-the-art application of fractional calculus to implement a modified FSDM based FBPNN whose reverse incremental search is in the negative directions of the approximate fractional-order partial derivatives of the square error. At first, the theoretical concept of a modified FSDM based FBPNN is described mathematically. Then, the mathematical proof of the fractional-order global optimal convergence, an assumption of the structure, and the fractional-order multi-scale global optimization of a modified FSDM based FBPNN are analysed in detail. Finally, we perform comparative experiments and compare a modified FSDM based FBPNN with a classic first-order BPNN, i.e., an example function approximation, fractional-order multi-scale global optimization, and two comparative performances with real data. The more efficient optimal searching capability of the fractional-order multi-scale global optimization of a modified FSDM based FBPNN to determine the global optimal solution is the major advantage being superior to a classic first-order BPNN.