Most recent CNN architectures use average pooling as a final feature encoding step. In the field of fine-grained recognition, however, recent global representations like bilinear pooling offer improved performance. In this paper, we generalize average and bilinear pooling to "alpha-pooling", allowing for learning the pooling strategy during training. In addition, we present a novel way to visualize decisions made by these approaches. We identify parts of training images having the highest influence on the prediction of a given test image. It allows for justifying decisions to users and also for analyzing the influence of semantic parts. For example, we can show that the higher capacity VGG16 model focuses much more on the bird's head than, e.g., the lower-capacity VGG-M model when recognizing fine-grained bird categories. Both contributions allow us to analyze the difference when moving between average and bilinear pooling. In addition, experiments show that our generalized approach can outperform both across a variety of standard datasets.
The relationship of average pooling and pairwise matching of local features was presented by Bo al @cite_18 as an efficient encoding for matching a set of local features. This formulation was also briefly discussed in @cite_12 and used for deriving an explicit feature transformation, which approximates bilinear pooling. Bilinear encoding was first mentioned by Tenenbaum al @cite_7 and used, for example, by Carreira al @cite_3 and Lin al @cite_13 for image recognition tasks. Furthermore, the recent work of Murray al @cite_4 also analyzes orderless pooling approaches and proposes a technique to normalize the contribution of each local descriptor to resulting kernel values. In contrast, we show how the individual contributions can be used either for visualizing the classification decisions and for understanding the differences between generic and fine-grained tasks.
@cite_18 @cite_4 @cite_7 @cite_3 @cite_13 @cite_12
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In visual recognition, the images are frequently modeled as unordered collections of local features (bags). We show that bag-of-words representations commonly used in conjunction with linear classifiers can be viewed as special match kernels, which count 1 if two local features fall into the same regions partitioned by visual words and 0 otherwise. Despite its simplicity, this quantization is too coarse, motivating research into the design of match kernels that more accurately measure the similarity between local features. However, it is impractical to use such kernels for large datasets due to their significant computational cost. To address this problem, we propose efficient match kernels (EMK) that map local features to a low dimensional feature space and average the resulting vectors to form a set-level feature. The local feature maps are learned so their inner products preserve, to the best possible, the values of the specified kernel function. Classifiers based on EMK are linear both in the number of images and in the number of local features. We demonstrate that EMK are extremely efficient and achieve the current state of the art in three difficult computer vision datasets: Scene-15, Caltech-101 and Caltech-256. We consider the design of an image representation that embeds and aggregates a set of local descriptors into a single vector. Popular representations of this kind include the bag-of-visual-words, the Fisher vector and the VLAD. When two such image representations are compared with the dot-product, the image-to-image similarity can be interpreted as a match kernel. In match kernels, one has to deal with interference , i.e., with the fact that even if two descriptors are unrelated, their matching score may contribute to the overall similarity. We formalise this problem and propose two related solutions, both aimed at equalising the individual contributions of the local descriptors in the final representation. These methods modify the aggregation stage by including a set of per-descriptor weights. They differ by the objective function that is optimised to compute those weights. The first is a “democratisation” strategy that aims at equalising the relative importance of each descriptor in the set comparison metric. The second one involves equalising the match of a single descriptor to the aggregated vector. These concurrent methods give a substantial performance boost over the state of the art in image search with short or mid-size vectors, as demonstrated by our experiments on standard public image retrieval benchmarks. Perceptual systems routinely separate “content” from “style,” classifying familiar words spoken in an unfamiliar accent, identifying a font or handwriting style across letters, or recognizing a familiar face or object seen under unfamiliar viewing conditions. Yet a general and tractable computational model of this ability to untangle the underlying factors of perceptual observations remains elusive (Hofstadter, 1985). Existing factor models (Mardia, Kent, & Bibby, 1979; Hinton & Zemel, 1994; Ghahramani, 1995; Bell & Sejnowski, 1995; Hinton, Dayan, Frey, & Neal, 1995; Dayan, Hinton, Neal, & Zemel, 1995; Hinton & Ghahramani, 1997) are either insufficiently rich to capture the complex interactions of perceptually meaningful factors such as phoneme and speaker accent or letter and font, or do not allow efficient learning algorithms. We present a general framework for learning to solve two-factor tasks using bilinear models, which provide sufficiently expressive representations of factor interactions but can nonetheless be fit to data using efficient algorithms based on the singular value decomposition and expectation-maximization. We report promising results on three different tasks in three different perceptual domains: spoken vowel classification with a benchmark multi-speaker database, extrapolation of fonts to unseen letters, and translation of faces to novel illuminants. Feature extraction, coding and pooling, are important components on many contemporary object recognition paradigms. In this paper we explore novel pooling techniques that encode the second-order statistics of local descriptors inside a region. To achieve this effect, we introduce multiplicative second-order analogues of average and max-pooling that together with appropriate non-linearities lead to state-of-the-art performance on free-form region recognition, without any type of feature coding. Instead of coding, we found that enriching local descriptors with additional image information leads to large performance gains, especially in conjunction with the proposed pooling methodology. We show that second-order pooling over free-form regions produces results superior to those of the winning systems in the Pascal VOC 2011 semantic segmentation challenge, with models that are 20,000 times faster. Bilinear models has been shown to achieve impressive performance on a wide range of visual tasks, such as semantic segmentation, fine grained recognition and face recognition. However, bilinear features are high dimensional, typically on the order of hundreds of thousands to a few million, which makes them impractical for subsequent analysis. We propose two compact bilinear representations with the same discriminative power as the full bilinear representation but with only a few thousand dimensions. Our compact representations allow back-propagation of classification errors enabling an end-to-end optimization of the visual recognition system. The compact bilinear representations are derived through a novel kernelized analysis of bilinear pooling which provide insights into the discriminative power of bilinear pooling, and a platform for further research in compact pooling methods. Experimentation illustrate the utility of the proposed representations for image classification and few-shot learning across several datasets.