Rotation-invariant multiresolution texture analysis using radon and wavelet transforms

Novel method of image analysis that combines Radon and Fourier image transformations for the purpose of differentiating between malignant and benign colonic biopsies

Colorectal cancer is the third most common type of cancer. It develops slowly as a polyp that can turn into a cancerous tumor. This study aimed to develop a decision-making algorithm of microscopic images using texture analysis that is orientation free, to be used for automated classification of normal and neoplastic (malignant or premalignant) colonic biopsies. Forty-nine colonic adenocarcinomas, 41 adenomas and a control group of adjacent normal colonic mucosa were included in the texture analysis. Radon transform followed by the Fast Fourier transform were applied to the images. Subsequently, the gray level co-occurrence matrix (GLCM) transform was applied allowing the extraction of four textural variables (homogeneity, contrast, correlation, and entropy). For classification and prediction of the diagnosis, a statistical multivariate regression model and a neural network (NNET) model were used and compared. The statistical model provided a sensitivity of 71.3% and a specificity of 50% (Area under the ROC curve: 0.67) for classifying the neoplastic and the normal images, respectively. The NNET model was superior to the statistical model and produced a sensitivity of 97.9% and specificity of 88% (Area under the ROC curve: 0.92). To our knowledge, this is the first study that used a combination of Radon, FFT, and GLCM transformations in order to overcome the tissue orientation problem in texture analysis of microscopic images of colonic biopsies. The NNET classifier trained by the extracted textural features proved to be superior to the statistical classifier, thus predicting colonic neoplasia with high accuracy. RESEARCH HIGHLIGHTS: We propose a novel decision-making algorithm of orientation invariant image texture analysis, fast and easily implemented for automated differentiation between benign and neoplastic epithelial tumors of the colon. This method can reduce the turnaround time allowing to prioritize the biopsies during their examination and diagnosis by the pathologist.

Rotation equivariant and invariant neural networks for microscopy image analysis

MOTIVATION

Neural networks have been widely used to analyze high-throughput microscopy images. However, the performance of neural networks can be significantly improved by encoding known invariance for particular tasks. Highly relevant to the goal of automated cell phenotyping from microscopy image data is rotation invariance. Here we consider the application of two schemes for encoding rotation equivariance and invariance in a convolutional neural network, namely, the group-equivariant CNN (G-CNN), and a new architecture with simple, efficient conic convolution, for classifying microscopy images. We additionally integrate the 2D-discrete-Fourier transform (2D-DFT) as an effective means for encoding global rotational invariance. We call our new method the Conic Convolution and DFT Network (CFNet).

RESULTS

We evaluated the efficacy of CFNet and G-CNN as compared to a standard CNN for several different image classification tasks, including simulated and real microscopy images of subcellular protein localization, and demonstrated improved performance. We believe CFNet has the potential to improve many high-throughput microscopy image analysis applications.

AVAILABILITY AND IMPLEMENTATION

Source code of CFNet is available at: https://github.com/bchidest/CFNet.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Quasi Fourier-Mellin Transform for Affine Invariant Features

Fourier-Mellin transform (FMT) has been widely used for the extraction of rotation- and scale-invariant features. However, affine transform is a more reasonable approximation model for real viewpoint change. Due to shearing, the integral along the angular direction in the calculation of FMT cannot be used to extract the inherent features of an image undergoing affine transform. To eliminate the effect of shearing, whitening transform should be conducted on the integral along the radial direction. FMT can hardly be modified by conventional whitening-based methods with low computational cost due to additional processes. In this paper, two factors are constructed and embedded into FMT. Quasi Fourier-Mellin transform (QFMT) is proposed. The embedding of these factors is equivalent to whitening transform and can eliminate the effect of shearing in the affine transform. In particular, QFMT can also be calculated by integrating along the radial direction followed by integrating along the angular direction, as in FMT. Based on QFMT, the quasi Fourier-Mellin descriptor (QFMD) is constructed for the extraction of affine invariant features. Some experiments have also been conducted to test the performance of the proposed method.

Copy Move Forgery Image Detection via Discrete Radon and Polar Complex Exponential Transform-Based Moment Invariant Features

Copy move forgery with geometric distortions such as the rotational operation, the scaling operation, the mirror operation and the additive noise operation became more common. Existing methods are not competent for the detection of the copy move forgery with these distortions. In fact, the most critical issue for the detection of the forgery is the determination of the geometric features. This paper proposes an efficient Discrete Radon Polar Complex Exponential Transform (DRPCET)-based method for the extraction of the rotational and the scaling invariant features for the copy move forgery detection. First, the features obtained by the Radon transform (RT) and the Polar Complex Exponential Transform (PCET) are fused together. Then, these features are normalized. In order to achieve the scaling invariant property, an auxiliary circular template is introduced. With the auxiliary circular template, the translational moment invariant features, the rotational moment invariant features and the scaling moment invariant features are constructed for the extraction of the planar geometrical features. By further extracting some useful features for the representation of the image background, the interference of the background information can be reduced. After extracting the geometrical features, the lexicographic sorting is applied. Then, a correlation between the same part or similar parts of the image which are copied and moved to another image is computed. Based on the obtained correlations, these forgery parts can be identified and their composed positions can be located. Finally, these images are denoted as the forgery image. Extensive computer numerical simulations have been performed. The obtained results show that the proposed method can detect the copy move region in the forgery image precisely even though the forgery regions are suffered from the mixed geometric distortions.

Hybrid k -Nearest Neighbor Classifier

Conventional k -nearest neighbor (KNN) classification approaches have several limitations when dealing with some problems caused by the special datasets, such as the sparse problem, the imbalance problem, and the noise problem. In this paper, we first perform a brief survey on the recent progress of the KNN classification approaches. Then, the hybrid KNN (HBKNN) classification approach, which takes into account the local and global information of the query sample, is designed to address the problems raised from the special datasets. In the following, the random subspace ensemble framework based on HBKNN (RS-HBKNN) classifier is proposed to perform classification on the datasets with noisy attributes in the high-dimensional space. Finally, the nonparametric tests are proposed to be adopted to compare the proposed method with other classification approaches over multiple datasets. The experiments on the real-world datasets from the Knowledge Extraction based on Evolutionary Learning dataset repository demonstrate that RS-HBKNN works well on real datasets, and outperforms most of the state-of-the-art classification approaches.

Rotation invariant texture retrieval considering the scale dependence of Gabor wavelet

Obtaining robust and efficient rotation-invariant texture features in content-based image retrieval field is a challenging work. We propose three efficient rotation-invariant methods for texture image retrieval using copula model based in the domains of Gabor wavelet (GW) and circularly symmetric GW (CSGW). The proposed copula models use copula function to capture the scale dependence of GW/CSGW for improving the retrieval performance. It is well known that the Kullback-Leibler distance (KLD) is the commonly used similarity measurement between probability models. However, it is difficult to deduce the closed-form of KLD between two copula models due to the complexity of the copula model. We also put forward a kind of retrieval scheme using the KLDs of marginal distributions and the KLD of copula function to calculate the KLD of copula model. The proposed texture retrieval method has low computational complexity and high retrieval precision. The experimental results on VisTex and Brodatz data sets show that the proposed retrieval method is more effective compared with the state-of-the-art methods.

A scale- and orientation-adaptive extension of Local Binary Patterns for texture classification

Local Binary Patterns (LBPs) have been used in a wide range of texture classification scenarios and have proven to provide a highly discriminative feature representation. A major limitation of LBP is its sensitivity to affine transformations. In this work, we present a scale- and rotation-invariant computation of LBP. Rotation-invariance is achieved by explicit alignment of features at the extraction level, using a robust estimate of global orientation. Scale-adapted features are computed in reference to the estimated scale of an image, based on the distribution of scale normalized Laplacian responses in a scale-space representation. Intrinsic-scale-adaption is performed to compute features, independent of the intrinsic texture scale, leading to a significantly increased discriminative power for a large amount of texture classes. In a final step, the rotation- and scale-invariant features are combined in a multi-resolution representation, which improves the classification accuracy in texture classification scenarios with scaling and rotation significantly.

A classification sensor based on compressed optical Radon transform

We present a thin-film sensor that optically measures the Radon transform of an image focussed onto it. Measuring and classifying directly in Radon space, rather than in image space, is fast and yields robust and high classification rates. We explain how the number of integral measurements required for a given classification task can be reduced by several orders of magnitude. Our experiments achieve classification rates of 98%-99% for complex hand gesture and motion detection tasks with as few as 10 photosensors. Our findings have the potential to stimulate further research towards a new generation of application-oriented classification sensors for use in areas such as biometry, security, diagnostics, surface inspection, and human-computer interfaces.

Localized Radon Polar Harmonic Transform (LRPHT) Based Rotation Invariant Analysis of Textured Images

In this paper, the authors propose a method to analyze and capture the information from texture regardless their geometric deformation. Input image is transformed to radon space and multiresolution is achieved within the radon space using Gaussian derivative wavelet. The transformed image is applied to the polar harmonic transform (PHT). The proposed method is tested against additive Gaussian noise and impulse noise with different rotations. A k- nearest neighbor classifier is employed to classify the texture. To test and evaluate correct classification percentage of the method, several sets of texture are evaluated with different rotation angle under different noisy condition. Experimental results show superiority of method in comparison to recent invariant texture analysis method.

Rotation invariant local frequency descriptors for texture classification

This paper presents a novel rotation invariant method for texture classification based on local frequency components. The local frequency components are computed by applying 1-D Fourier transform on a neighboring function defined on a circle of radius R at each pixel. We observed that the low frequency components are the major constituents of the circular functions and can effectively represent textures. Three sets of features are extracted from the low frequency components, two based on the phase and one based on the magnitude. The proposed features are invariant to rotation and linear changes of illumination. Moreover, by using low frequency components, the proposed features are very robust to noise. While the proposed method uses a relatively small number of features, it outperforms state-of-the-art methods in three well-known datasets: Brodatz, Outex, and CUReT. In addition, the proposed method is very robust to noise and can remarkably improve the classification accuracy especially in the presence of high levels of noise.

A fully automated approach to prostate biopsy segmentation based on level-set and mean filtering

With modern automated microscopes and digital cameras, pathologists no longer have to examine samples looking through microscope binoculars. Instead, the slide is digitized to an image, which can then be examined on a screen. This creates the possibility for computers to analyze the image. In this work, a fully automated approach to region of interest (ROI) segmentation in prostate biopsy images is proposed. This will allow the pathologists to focus on the most important areas of the image. The method proposed is based on level-set and mean filtering techniques for lumen centered expansion and cell density localization respectively. The novelty of the technique lies in the ability to detect complete ROIs, where a ROI is composed by the conjunction of three different structures, that is, lumen, cytoplasm, and cells, as well as regions with a high density of cells. The method is capable of dealing with full biopsies digitized at different magnifications. In this paper, results are shown with a set of 100 H and E slides, digitized at 5×, and ranging from 12 MB to 500 MB. The tests carried out show an average specificity above 99% across the board and average sensitivities of 95% and 80%, respectively, for the lumen centered expansion and cell density localization. The algorithms were also tested with images at 10× magnification (up to 1228 MB) obtaining similar results.

A wavelet multiscale denoising algorithm for magnetic resonance (MR) images

Based on the Radon transform, a wavelet multiscale denoising method is proposed for MR images. The approach explicitly accounts for the Rician nature of MR data. Based on noise statistics we apply the Radon transform to the original MR images and use the Gaussian noise model to process the MR sinogram image. A translation invariant wavelet transform is employed to decompose the MR 'sinogram' into multiscales in order to effectively denoise the images. Based on the nature of Rician noise we estimate noise variance in different scales. For the final denoised sinogram we apply the inverse Radon transform in order to reconstruct the original MR images. Phantom, simulation brain MR images, and human brain MR images were used to validate our method. The experiment results show the superiority of the proposed scheme over the traditional methods. Our method can reduce Rician noise while preserving the key image details and features. The wavelet denoising method can have wide applications in MRI as well as other imaging modalities.

Wavelet method for CT colonography computer-aided polyp detection

Computed tomographic colonography (CTC) computer aided detection (CAD) is a new method to detect colon polyps. Colonic polyps are abnormal growths that may become cancerous. Detection and removal of colonic polyps, particularly larger ones, has been shown to reduce the incidence of colorectal cancer. While high sensitivities and low false positive rates are consistently achieved for the detection of polyps sized 1 cm or larger, lower sensitivities and higher false positive rates occur when the goal of CAD is to identify "medium"-sized polyps, 6-9 mm in diameter. Such medium-sized polyps may be important for clinical patient management. We have developed a wavelet-based postprocessor to reduce false positives for this polyp size range. We applied the wavelet-based postprocessor to CTC CAD findings from 44 patients in whom 45 polyps with sizes of 6-9 mm were found at segmentally unblinded optical colonoscopy and visible on retrospective review of the CT colonography images. Prior to the application of the wavelet-based postprocessor, the CTC CAD system detected 33 of the polyps (sensitivity 73.33%) with 12.4 false positives per patient, a sensitivity comparable to that of expert radiologists. Fourfold cross validation with 5000 bootstraps showed that the wavelet-based postprocessor could reduce the false positives by 56.61% (p <0.001), to 5.38 per patient (95% confidence interval [4.41, 6.34]), without significant sensitivity degradation (32/45, 71.11%, 95% confidence interval [66.39%, 75.74%], p=0.1713). We conclude that this wavelet-based postprocessor can substantially reduce the false positive rate of our CTC CAD for this important polyp size range.

Reduced complexity rotation invariant texture classification using a blind deconvolution approach

In this paper, we present a texture classification procedure that makes use of a blind deconvolution approach. Specifically, the texture is modeled as the output of a linear system driven by a binary excitation. We show that features computed from one-dimensional slices extracted from the two-dimensional autocorrelation function (ACF) of the binary excitation allows representing the texture for rotation-invariant classification purposes. The two-dimensional classification problem is thus reconduced to a more simple one-dimensional one, which leads to a significant reduction of the classification procedure computational complexity.

Radon transform orientation estimation for rotation invariant texture analysis

This paper presents a new approach to rotation invariant texture classification. The proposed approach benefits from the fact that most of the texture patterns either have directionality (anisotropic textures) or are not with a specific direction (isotropic textures). The wavelet energy features of the directional textures change significantly when the image is rotated. However, for the isotropic images, the wavelet features are not sensitive to rotation. Therefore, for the directional textures, it is essential to calculate the wavelet features along a specific direction. In the proposed approach, the Radon transform is first employed to detect the principal direction of the texture. Then, the texture is rotated to place its principal direction at 0 degrees. A wavelet transform is applied to the rotated image to extract texture features. This approach provides a features space with small intraclass variability and, therefore, good separation between different classes. The performance of the method is evaluated using three texture sets. Experimental results show the superiority of the proposed approach compared with some existing methods.