Resolution Learning in Deep Convolutional Networks Using Scale-Space Theory.

Resolution in deep convolutional neural networks (CNNs) is typically bounded by the receptive field size through filter sizes, and subsampling layers or strided convolutions on feature maps. The optimal resolution may vary significantly depending on the dataset. Modern CNNs hard-code their resolution hyper-parameters in the network architecture which makes tuning such hyper-parameters cumbersome. We propose to do away with hard-coded resolution hyper-parameters and aim to learn the appropriate resolution from data. We use scale-space theory to obtain a self-similar parametrization of filters and make use of the N-Jet: a truncated Taylor series to approximate a filter by a learned combination of Gaussian derivative filters. The parameter σ of the Gaussian basis controls both the amount of detail the filter encodes and the spatial extent of the filter. Since σ is a continuous parameter, we can optimize it with respect to the loss. The proposed N-Jet layer achieves comparable performance when used in state-of-the art architectures, while learning the correct resolution in each layer automatically. We evaluate our N-Jet layer on both classification and segmentation, and we show that learning σ is especially beneficial when dealing with inputs at multiple sizes.

Divide and Count: Generic Object Counting by Image Divisions.

We propose a general object counting method that does not use any prior category information. We learn from local image divisions to predict global image-level counts without using any form of local annotations. Our method separates the input image into a sets of image divisions - each fully covering the image. Each image division is composed of a set of region proposals or uniform grid cells. Our approach learns in an endto- end deep learning architecture to predict global image-level counts from local image divisions. The method incorporates a counting layer which predicts object counts in the complete image, by enforcing consistency in counts when dealing with overlapping image regions. Our counting layer is based on the inclusion-exclusion principle from set theory. We analyze the individual building blocks of our proposed approach on Pascal- VOC2007 and evaluate our method on the MS-COCO large scale generic object dataset as well as on three class-specific counting datasets: UCSD pedestrian dataset, and CARPK and PUCPR+ car datasets.