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Register a new userWavelet and Curvelet Moments for Image Classification: Application to Aggregate Mixture Grading
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Added by
Fionn Murtagh
Publication date
2008
fields
Informatics Engineering
and research's language is
English
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We show the potential for classifying images of mixtures of aggregate, based themselves on varying, albeit well-defined, sizes and shapes, in order to provide a far more effective approach compared to the classification of individual sizes and shapes. While a dominant (additive, stationary) Gaussian noise component in image data will ensure that wavelet coefficients are of Gaussian distribution, long tailed distributions (symptomatic, for example, of extreme values) may well hold in practice for wavelet coefficients. Energy (2nd order moment) has often been used for image characterization for image content-based retrieval, and higher order moments may be important also, not least for capturing long tailed distributional behavior. In this work, we assess 2nd, 3rd and 4th order moments of multiresolution transform -- wavelet and curvelet transform -- coefficients as features. As analysis methodology, taking account of image types, multiresolution transforms, and moments of coefficients in the scales or bands, we use correspondence analysis as well as k-nearest neighbors supervised classification.
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Convolutional Neural Networks (CNNs) are generally prone to noise interruptions, i.e., small image noise can cause drastic changes in the output. To suppress the noise effect to the final predication, we enhance CNNs by replacing max-pooling, strided-convolution, and average-pooling with Discrete Wavelet Transform (DWT). We present general DWT and Inverse DWT (IDWT) layers applicable to various wavelets like Haar, Daubechies, and Cohen, etc., and design wavelet integrated CNNs (WaveCNets) using these layers for image classification. In WaveCNets, feature maps are decomposed into the low-frequency and high-frequency components during the down-sampling. The low-frequency component stores main information including the basic object structures, which is transmitted into the subsequent layers to extract robust high-level features. The high-frequency components, containing most of the data noise, are dropped during inference to improve the noise-robustness of the WaveCNets. Our experimental results on ImageNet and ImageNet-C (the noisy version of ImageNet) show that WaveCNets, the wavelet integrat
Though widely used in image classification, convolutional neural networks (CNNs) are prone to noise interruptions, i.e. the CNN output can be drastically changed by small image noise. To improve the noise robustness, we try to integrate CNNs with wavelet by replacing the common down-sampling (max-pooling, strided-convolution, and average pooling) with discrete wavelet transform (DWT). We firstly propose general DWT and inverse DWT (IDWT) layers applicable to various orthogonal and biorthogonal discrete wavelets like Haar, Daubechies, and Cohen, etc., and then design wavelet integrated CNNs (WaveCNets) by integrating DWT into the commonly used CNNs (VGG, ResNets, and DenseNet). During the down-sampling, WaveCNets apply DWT to decompose the feature maps into the low-frequency and high-frequency components. Containing the main information including the basic object structures, the low-frequency component is transmitted into the following layers to generate robust high-level features. The high-frequency components are dropped to remove most of the data noises. The experimental results show that %wavelet accelerates the CNN training, and WaveCNets achieve higher accuracy on ImageNet than various vanilla CNNs. We have also tested the performance of WaveCNets on the noisy version of ImageNet, ImageNet-C and six adversarial attacks, the results suggest that the proposed DWT/IDWT layers could provide better noise-robustness and adversarial robustness. When applying WaveCNets as backbones, the performance of object detectors (i.e., faster R-CNN and RetinaNet) on COCO detection dataset are consistently improved. We believe that suppression of aliasing effect, i.e. separation of low frequency and high frequency information, is the main advantages of our approach. The code of our DWT/IDWT layer and different WaveCNets are available at https://github.com/CVI-SZU/WaveCNet.
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.
Supervised classification and representation learning are two widely used classes of methods to analyze multivariate images. Although complementary, these methods have been scarcely considered jointly in a hierarchical modeling. In this paper, a method coupling these two approaches is designed using a matrix cofactorization formulation. Each task is modeled as a factorization matrix problem and a term relating both coding matrices is then introduced to drive an appropriate coupling. The link can be interpreted as a clustering operation over a low-dimensional representation vectors. The attribution vectors of the clustering are then used as features vectors for the classification task, i.e., the coding vectors of the corresponding factorization problem. A proximal gradient descent algorithm, ensuring convergence to a critical point of the objective function, is then derived to solve the resulting non-convex non-smooth optimization problem. An evaluation of the proposed method is finally conducted both on synthetic and real data in the specific context of hyperspectral image interpretation, unifying two standard analysis techniques, namely unmixing and classification.
We propose a convolutional neural network (CNN) architecture for image classification based on subband decomposition of the image using wavelets. The proposed architecture decomposes the input image spectra into multiple critically sampled subbands, extracts features using a single CNN per subband, and finally, performs classification by combining the extracted features using a fully connected layer. Processing each of the subbands by an individual CNN, thereby limiting the learning scope of each CNN to a single subband, imposes a form of structural regularization. This provides better generalization capability as seen by the presented results. The proposed architecture achieves best-in-class performance in terms of total multiply-add-accumulator operations and nearly best-in-class performance in terms of total parameters required, yet it maintains competitive classification performance. We also show the proposed architecture is more robust than the regular full-band CNN to noise caused by weight-and-bias quantization and input quantization.
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