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...nition architectures. 1. Introduction Finding good image features is critical in modern approaches to category-level image classification. Many methods first extract low-level descriptors (e.g., SIFT =-=[18]-=- or HOG descriptors [5]) at interest point locations, or nodes in a dense grid. This paper considers the problem of combining these local features into a global image representation suited to recognit...

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... Introduction Finding good image features is critical in modern approaches to category-level image classification. Many methods first extract low-level descriptors (e.g., SIFT [18] or HOG descriptors =-=[5]-=-) at interest point locations, or nodes in a dense grid. This paper considers the problem of combining these local features into a global image representation suited to recognition using a common clas...

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... Laboratoire d’Informatique de l’Ecole Normale Supérieure, ENS/INRIA/CNRS UMR 8548. them as mid-level features. Popular examples of mid-level features include bags of features [25], spatial pyramids =-=[12]-=-, and the upper units of convolutional networks [13] or deep belief networks [8, 23]. Extracting these mid-level features involves the same sequence of interchangeable modules as identified by Winder ...

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...o 4WILLOW project-team, Laboratoire d’Informatique de l’Ecole Normale Supérieure, ENS/INRIA/CNRS UMR 8548. them as mid-level features. Popular examples of mid-level features include bags of features =-=[25]-=-, spatial pyramids [12], and the upper units of convolutional networks [13] or deep belief networks [8, 23]. Extracting these mid-level features involves the same sequence of interchangeable modules a...

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... the limit when β → ∞). This amounts to coding as in the E-step of the expectationmaximization algorithm to learn a Gaussian mixture model, using codewords of the dictionary as centers. Sparse coding =-=[22]-=- uses a linear combination of a small number of codewords to approximate the xi. Yang et al. [31] have obtained state-of-the-art results by using sparse coding and max pooling: αi = argmin α L(α,D) , ...

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...nsional SIFT descriptors [18] of 16 × 16 patches. The descriptors are extracted on a dense grid rather than at interest points, as this procedure has been shown to yield superior scene classification =-=[17]-=-. Pooling regions m comprise the cells of 4×4, 2×2 and 1×1 grids (forming a three-level pyramid). We use the SPAMS toolbox [1] to compute sparse codes. 3.1. Interaction Between Modules Here, we perfor...

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...48. them as mid-level features. Popular examples of mid-level features include bags of features [25], spatial pyramids [12], and the upper units of convolutional networks [13] or deep belief networks =-=[8, 23]-=-. Extracting these mid-level features involves the same sequence of interchangeable modules as identified by Winder and Brown for local image descriptors [29]. In this paper, we focus on two types of ...

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...ral recognition schemes using a single type of descriptors. Bold numbers in parentheses preceding the method description indicate methods reimplemented in this paper. SP: spatial pyramid. Caltech-101 =-=[6]-=- and Scenes datasets [12] as benchmarks. These datasets respectively comprise 101 object categories (plus a ”background” category) and fifteen scene categories. Following the usual procedure [12, 31],...

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... convolutional nets [13], bag-of-features methods, and HOG descriptors; max pooling is found in convolutional nets [16, 23], HMAX nets [24], and state-of-the-art variants of the spatial pyramid model =-=[31]-=-. The final global vector is formed by concatenating with suitable weights the semi-local vectors obtained for each pooling region. High levels of performance have been reported for specific pairings ...

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...f h over examples from positive and negative classes (henceforth denoted by + and−) to be well separated. We model the distribution of image patches of a given class as a mixture of two distributions =-=[21]-=-: patches are taken from the actual class distribution (foreground) with probability (1 − w), and from a clutter distribution (background) with probability w, with clutter patches being present in bot...

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...dictionary trained by minimizing the average of L(αi,D) over all samples, alternatively over D and the αi. It is well known that the ℓ1 penalty induces sparsity and makes the problem tractable (e.g., =-=[15, 19]-=-). 3. Systematic Evaluation of UnsupervisedMidLevel Features This section offers comprehensive comparisons of unsupervised coding schemes. In all experiments, we use the Method Caltech-101, 30 trainin...

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...s can be plugged into various architectures. For example, average pooling is found in convolutional nets [13], bag-of-features methods, and HOG descriptors; max pooling is found in convolutional nets =-=[16, 23]-=-, HMAX nets [24], and state-of-the-art variants of the spatial pyramid model [31]. The final global vector is formed by concatenating with suitable weights the semi-local vectors obtained for each poo...

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...inative codebooks. Lazebnik and Raginsky [11] incorporate discriminative information by minimizing the loss of mutual information between features and labels during the quantization step. Winn et al. =-=[30]-=- prune a large codebook iteratively by fusing codewords that do not contribute to discrimination. However these methods are optimized for vector quantization. Mairal et al. [20] have proposed an algor...

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...o various architectures. For example, average pooling is found in convolutional nets [13], bag-of-features methods, and HOG descriptors; max pooling is found in convolutional nets [16, 23], HMAX nets =-=[24]-=-, and state-of-the-art variants of the spatial pyramid model [31]. The final global vector is formed by concatenating with suitable weights the semi-local vectors obtained for each pooling region. Hig...

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...riptors on the same dataset are shown on Table 2. Note that better performance has been reported with multiple descriptor types (e.g., methods using multiple kernel learning have achieved 77.7% ± 0.3 =-=[7]-=- and 78.0% ± 0.3 [28, 2] on Caltech-101 with 30 training examples), or subcategory learning (83% on Caltech101 [26]). The coding and pooling module combinations used in [27, 31] are included in our co...

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...ion is that the superiority of max pooling over average pooling generalizes to many combinations of coding schemes and classifiers. Several authors have already stressed the efficiency of max pooling =-=[10, 31]-=-, but they have not given theoretical explanations to their findings. In this section, we study max pooling in more details theoretically and experimentally. 5.1.ATheoreticalComparison ofPooling Strat...

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...dictionary trained by minimizing the average of L(αi,D) over all samples, alternatively over D and the αi. It is well known that the ℓ1 penalty induces sparsity and makes the problem tractable (e.g., =-=[15, 19]-=-). 3. Systematic Evaluation of UnsupervisedMidLevel Features This section offers comprehensive comparisons of unsupervised coding schemes. In all experiments, we use the Method Caltech-101, 30 trainin...

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... it is constant, we can compute the gradient: ∂αk ∂Dij = biAjk −αjCik, (18) A , (Dα T Dα) −1, (19) b , x−α, (20) C , ADα T . (21) We train the discriminative dictionary by stochastic gradient descent =-=[4, 14]-=-. Recomputing the sparse decompositions αi at each location of a training image at each iteration is computationally costly. To simplify the computation while remaining closer to global image statisti...

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...tion step. Winn et al. [30] prune a large codebook iteratively by fusing codewords that do not contribute to discrimination. However these methods are optimized for vector quantization. Mairal et al. =-=[20]-=- have proposed an algorithm to train discriminative dictionaries for sparse coding, but it requires each encoded vector to be labelled. Instead, the approach we propose is adapted to global image stat...

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... networks [13] or deep belief networks [8, 23]. Extracting these mid-level features involves the same sequence of interchangeable modules as identified by Winder and Brown for local image descriptors =-=[29]-=-. In this paper, we focus on two types of modules: • Coding: Input features are locally transformed into representations that have some desirable properties such as compactness, sparseness (i.e., most...

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...48. them as mid-level features. Popular examples of mid-level features include bags of features [25], spatial pyramids [12], and the upper units of convolutional networks [13] or deep belief networks =-=[8, 23]-=-. Extracting these mid-level features involves the same sequence of interchangeable modules as identified by Winder and Brown for local image descriptors [29]. In this paper, we focus on two types of ...

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...y and macrofeatures giving the best performance for sparse coding. Method Caltech 15 tr. Caltech 30 tr. Scenes Boiman et al. [3] Nearest neighbor + spatial correspondence 65.0± 1.1 70.4 - Jain et al. =-=[9]-=- Fast image search for learned metrics 61.0 69.6 - Lazebnik et al. [12] (1) SP + hard quantization + kernel SVM 56.4 64.4 ± 0.8 81.4 ± 0.5 van Gemert et al. [27] (2) SP + soft quantization + kernel SV...

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... it is constant, we can compute the gradient: ∂αk ∂Dij = biAjk −αjCik, (18) A , (Dα T Dα) −1, (19) b , x−α, (20) C , ADα T . (21) We train the discriminative dictionary by stochastic gradient descent =-=[4, 14]-=-. Recomputing the sparse decompositions αi at each location of a training image at each iteration is computationally costly. To simplify the computation while remaining closer to global image statisti...

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...e classification task. In this section, we introduce a novel supervised method to learn the dictionary. Several authors have proposed methods to obtain discriminative codebooks. Lazebnik and Raginsky =-=[11]-=- incorporate discriminative information by minimizing the loss of mutual information between features and labels during the quantization step. Winn et al. [30] prune a large codebook iteratively by fu...

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...criptor types (e.g., methods using multiple kernel learning have achieved 77.7% ± 0.3 [7] and 78.0% ± 0.3 [28, 2] on Caltech-101 with 30 training examples), or subcategory learning (83% on Caltech101 =-=[26]-=-). The coding and pooling module combinations used in [27, 31] are included in our comparative evaluation (bold numbers in parentheses on Tables 1 and 2). Overall, our results confirm the experimental...

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... pooling + linear SVM 67.0± 0.5 73.2± 0.5 80.3 ± 0.9 Yang et al. [31] (4) SP + sparse codes + max pooling + kernel SVM 60.4±1.0 − 77.7±0.7 Zhang et al. [32] kNN-SVM 59.1± 0.6 66.2 ± 0.5 - Zhou et al. =-=[33]-=- SP + Gaussian mixture − − 84.1± 0.5 Table 2. Results obtained by several recognition schemes using a single type of descriptors. Bold numbers in parentheses preceding the method description indicate ...