Augmenting transformation knowledge onto a convolutional neural network's weights has often yielded significant improvements in performance. For rotational transformation augmentation, an important element to recent approaches has been the use of a steerable basis i.e. the circular harmonics. Here, we propose a scale-steerable filter basis for the locally scale-invariant CNN, denoted as log-radial harmonics. By replacing the kernels in the locally scale-invariant CNN lsi_cnn with scale-steered kernels, significant improvements in performance can be observed on the MNIST-Scale and FMNIST-Scale datasets. Training with a scale-steerable basis results in filters which show meaningful structure, and feature maps demonstrate which demonstrate visibly higher spatial-structure preservation of input. Furthermore, the proposed scale-steerable CNN shows on-par generalization to global affine transformation estimation methods such as Spatial Transformers, in response to test-time data distortions.
Scale-transformed weights were proposed in @cite_9 , where it was observed to improve performance over the normal baseline CNN, on MNIST-Scale. On the same dataset (with a 10k, 2k and 50k split), better performance was observed in @cite_3 , where in addition to forwarding the maximum filter response to a range of scales, the actual scale at which the response was obtained was also forwarded. In both works, weight scaling was only indirectly emulated, by rather scaling the input and the resizing back the convolution response to a fix size for max-pooling across scales.
@cite_9 @cite_3
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Because of the powerful learning capability of deep neural networks, counting performance via density map estimation has improved significantly during the past several years. However, it is still very challenging due to severe occlusion, large scale variations, and perspective distortion. Scale variations (from image to image) coupled with perspective distortion (within one image) result in huge scale changes of the object size. Earlier methods based on convolutional neural networks (CNN) typically did not handle this scale variation explicitly, until Hydra-CNN and MCNN. MCNN uses three columns, each with different filter sizes, to extract features at different scales. In this paper, in contrast to using filters of different sizes, we utilize an image pyramid to deal with scale variations. It is more effective and efficient to resize the input fed into the network, as compared to using larger filter sizes. Secondly, we adaptively fuse the predictions from different scales (using adaptively changing per-pixel weights), which makes our method adapt to scale changes within an image. The adaptive fusing is achieved by generating an across-scale attention map, which softly selects a suitable scale for each pixel, followed by a 1x1 convolution. Extensive experiments on three popular datasets show very compelling results. Incorporating multi-scale features in fully convolutional neural networks (FCNs) has been a key element to achieving state-of-the-art performance on semantic image segmentation. One common way to extract multi-scale features is to feed multiple resized input images to a shared deep network and then merge the resulting features for pixelwise classification. In this work, we propose an attention mechanism that learns to softly weight the multi-scale features at each pixel location. We adapt a state-of-the-art semantic image segmentation model, which we jointly train with multi-scale input images and the attention model. The proposed attention model not only outperforms average- and max-pooling, but allows us to diagnostically visualize the importance of features at different positions and scales. Moreover, we show that adding extra supervision to the output at each scale is essential to achieving excellent performance when merging multi-scale features. We demonstrate the effectiveness of our model with extensive experiments on three challenging datasets, including PASCAL-Person-Part, PASCAL VOC 2012 and a subset of MS-COCO 2014.