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Register a new userRadon cumulative distribution transform subspace modeling for image classification
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Added by
Mohammad Shifat-E-Rabbi
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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We present a new supervised image classification method applicable to a broad class of image deformation models. The method makes use of the previously described Radon Cumulative Distribution Transform (R-CDT) for image data, whose mathematical properties are exploited to express the image data in a form that is more suitable for machine learning. While certain operations such as translation, scaling, and higher-order transformations are challenging to model in native image space, we show the R-CDT can capture some of these variations and thus render the associated image classification problems easier to solve. The method -- utilizing a nearest-subspace algorithm in R-CDT space -- is simple to implement, non-iterative, has no hyper-parameters to tune, is computationally efficient, label efficient, and provides competitive accuracies to state-of-the-art neural networks for many types of classification problems. In addition to the test accuracy performances, we show improvements (with respect to neural network-based methods) in terms of computational efficiency (it can be implemented without the use of GPUs), number of training samples needed for training, as well as out-of-distribution generalization. The Python code for reproducing our results is available at https://github.com/rohdelab/rcdt_ns_classifier.
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Invertible image representation methods (transforms) are routinely employed as low-level image processing operations based on which feature extraction and recognition algorithms are developed. Most transforms in current use (e.g. Fourier, Wavelet, etc.) are linear transforms, and, by themselves, are unable to substantially simplify the representation of image classes for classification. Here we describe a nonlinear, invertible, low-level image processing transform based on combining the well known Radon transform for image data, and the 1D Cumulative Distribution Transform proposed earlier. We describe a few of the properties of this new transform, and with both theoretical and experimental results show that it can often render certain problems linearly separable in transform space.
Convolutional neural networks (CNNs) have achieved state-of-the-art results on many visual recognition tasks. However, current CNN models still exhibit a poor ability to be invariant to spatial transformations of images. Intuitively, with sufficient layers and parameters, hierarchical combinations of convolution (matrix multiplication and non-linear activation) and pooling operations should be able to learn a robust mapping from transformed input images to transform-invariant representations. In this paper, we propose randomly transforming (rotation, scale, and translation) feature maps of CNNs during the training stage. This prevents complex dependencies of specific rotation, scale, and translation levels of training images in CNN models. Rather, each convolutional kernel learns to detect a feature that is generally helpful for producing the transform-invariant answer given the combinatorially large variety of transform levels of its input feature maps. In this way, we do not require any extra training supervision or modification to the optimization process and training images. We show that random transformation provides significant improvements of CNNs on many benchmark tasks, including small-scale image recognition, large-scale image recognition, and image retrieval. The code is available at https://github.com/jasonustc/caffe-multigpu/tree/TICNN.
This paper presents a new mathematical signal transform that is especially suitable for decoding information related to non-rigid signal displacements. We provide a measure theoretic framework to extend the existing Cumulative Distribution Transform [ACHA 45 (2018), no. 3, 616-641] to arbitrary (signed) signals on $overline{mathbb{R}}$. We present both forward (analysis) and inverse (synthesis) formulas for the transform, and describe several of its properties including translation, scaling, convexity, linear separability and others. Finally, we describe a metric in transform space, and demonstrate the application of the transform in classifying (detecting) signals under random displacements.
In this paper, we propose a subspace representation learning (SRL) framework to tackle few-shot image classification tasks. It exploits a subspace in local CNN feature space to represent an image, and measures the similarity between two images according to a weighted subspace distance (WSD). When K images are available for each class, we develop two types of template subspaces to aggregate K-shot information: the prototypical subspace (PS) and the discriminative subspace (DS). Based on the SRL framework, we extend metric learning based techniques from vector to subspace representation. While most previous works adopted global vector representation, using subspace representation can effectively preserve the spatial structure, and diversity within an image. We demonstrate the effectiveness of the SRL framework on three public benchmark datasets: MiniImageNet, TieredImageNet and Caltech-UCSD Birds-200-2011 (CUB), and the experimental results illustrate competitive/superior performance of our method compared to the previous state-of-the-art.
In this paper, we propose a spectral-spatial graph reasoning network (SSGRN) for hyperspectral image (HSI) classification. Concretely, this network contains two parts that separately named spatial graph reasoning subnetwork (SAGRN) and spectral graph reasoning subnetwork (SEGRN) to capture the spatial and spectral graph contexts, respectively. Different from the previous approaches implementing superpixel segmentation on the original image or attempting to obtain the category features under the guide of label image, we perform the superpixel segmentation on intermediate features of the network to adaptively produce the homogeneous regions to get the effective descriptors. Then, we adopt a similar idea in spectral part that reasonably aggregating the channels to generate spectral descriptors for spectral graph contexts capturing. All graph reasoning procedures in SAGRN and SEGRN are achieved through graph convolution. To guarantee the global perception ability of the proposed methods, all adjacent matrices in graph reasoning are obtained with the help of non-local self-attention mechanism. At last, by combining the extracted spatial and spectral graph contexts, we obtain the SSGRN to achieve a high accuracy classification. Extensive quantitative and qualitative experiments on three public HSI benchmarks demonstrate the competitiveness of the proposed methods compared with other state-of-the-art approaches.
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