Second-order Image Research Articles

A fractional filter based efficient algorithm for retinal blood vessel segmentation

This paper presents a new fractional filter and an algorithm for retinal blood vessel segmentation. The proposed fractional filter is designed with the help of a weighted fractional derivative and an exponential weight factor. We have utilized the fractional filter and the eigenvalue maps of a local covariance matrix to develop the algorithm for retinal vessel segmentation. The local covariance matrix is formed by a second-order image moment. Experiments are performed on two well-studied evaluation databases named STARE and DRIVE. Experimental results show that the proposed method is computationally efficient, and the average accuracy of the vessel segmentation on STARE and DRIVE databases are 95.73% and 94.76%, respectively. The performance of the proposed method is compared with other existing methods. Simulation results show that the average performance of the proposed method is comparatively better than most of the discussed methods.

Learning-based deformable image registration: effect of statistical mismatch between train and test images.

Convolutional neural networks (CNNs) offer a promising means to achieve fast deformable image registration with accuracy comparable to conventional, physics-based methods. A persistent question with CNN methods, however, is whether they will be able to generalize to data outside of the training set. We investigated this question of mismatch between train and test data with respect to first- and second-order image statistics (e.g., spatial resolution, image noise, and power spectrum). A UNet-based architecture was built and trained on simulated CT images for various conditions of image noise (dose), spatial resolution, and deformation magnitude. Target registration error was measured as a function of the difference in statistical properties between the test and training data. Generally, registration error is minimized when the training data exactly match the statistics of the test data; however, networks trained with data exhibiting a diversity in statistical characteristics generalized well across the range of statistical conditions considered. Furthermore, networks trained on simulated image content with first- and second-order statistics selected to match that of real anatomical data were shown to provide reasonable registration performance on real anatomical content, offering potential new means for data augmentation. Characterizing the behavior of a CNN in the presence of statistical mismatch is an important step in understanding how these networks behave when deployed on new, unobserved data. Such characterization can inform decisions on whether retraining is necessary and can guide the data collection and/or augmentation process for training.

Optical Second-harmonic Observation of Stimulated Sacran Aggregates

Second-order nonlinear optical images of aggregates of the ampholytic megamolecular polysaccharide sacran under various stimuli were observed by optical second-harmonic generation (SHG) microscopy. SHG intensity microspots of several tens of micrometers in size are seen for sacran cotton-like lumps and fibers and they have very clear incident polarization dependence. In these microspots, the sacran molecules are oriented in concentric multilayers. We also observed SHG images of sacran prepared in a needle-ring electrode with applied voltage, where SHG was enhanced near the negatively biased needle electrode. We also observed SHG signals near the cast film edges of sacran. The appearance of the SHG image suggested a phase-separation structure in sacran aggregates. These results show that sacran molecules aggregate in several different ways.

Image Inpainting Based on Fractional-Order Nonlinear Diffusion for Image Reconstruction

Image inpainting, image deblurring, and noise removal are influential concepts in the field of digital image processing. Second-order diffusion-based image restoration models suffer from staircase effects and connectivity principle, while fourth-order models suffer from speckle artifacts. In this article, a robust image inpainting model using fractional-order nonlinear diffusion driven by difference curvature is proposed and fractional-order variational model is utilized to remove the noise and blur. Fractional-order derivatives can deal well with edges and attain good trade-off between edges preservation and elimination of staircase and speckle artifacts of an image. Difference curvature is a feature descriptor which can effectively characterize the intensity variations in the image. In this work, difference curvature-based a bi-weight, adaptive conductance coefficient is proposed to restore the image and fractional-order derivative is implemented by using discrete Fourier transform. Simulation results validate that the proposed model can adequately complete the damaged regions, solve the connectivity principle, and also avoid the staircase and speckle artifacts.

Robust detection of median filtering based on combined features of difference image

Median filtering is a widely used method for denoising and smoothing regions of an image; it has drawn much attention from researchers of image forensic. A new detection scheme of median filtering based on combined features of difference image (CFDI) is proposed in this paper. In the proposed scheme, the combined features consist of joint conditional probability density functions (JCPDFs) of first-order and second-order difference image (DI), the principal component analysis (PCA) is used to reduce the dimensionality of JCPDFs, and thus, the final features are obtained for the given threshold. A large number of experiments on single database and compound databases show that, the proposed scheme achieves superior performance on the uncompressed image datasets, and it also achieves better performance compared with state-of-the-art methods, especially for strong JPEG compression and low resolution images.

Predicting bird species richness and micro-habitat diversity using satellite data

Effective biodiversity management in forest ecosystems relies on the assessment of environmental indicators (surrogates) when attempting to measure total biodiversity. Bird species (BS) richness and micro-habitat (MH) diversity are two key features that are easily measured and can be utilized as biodiversity surrogates. Remote sensing technologies may be employed as a cost-efficient measure as well as accurately mapping diversity features across broad geographical areas. This study examined the possibilities of predicting BS richness and MH diversity using variables derived from satellite data in a brutian pine (Pinus brutia Ten.) forest ecosystem located in the Southwestern Mediterranean Region of Turkey. The study utilized 40 (90 × 90 m, 0.81 ha) sample plots. We used first, and second-order image texture measures calculated from RapidEye, SPOT-5 and Aster Normalized Difference Vegetation Index (NDVI) as explanatory variables for predicting these biodiversity surrogates at alpha (α) level. Stepwise linear regression analyses showed that BS richness and MH diversity can be estimated using image texture measures. According to the cross-validation test; BS richness was best predicted using standard deviation of Gray levels (STD) and Gray-Level Co-Occurrence Matrix (GLCM) Homogeneity of RapidEye NDVI (RCV2 = 0.73, STECV = 4.321), while MH diversity was best predicted using STD and GLCM Correlation of SPOT NDVI (RCV2 = 0.73, STECV = 0.148). In conclusion, the satellite-based diversity maps produced in this study can provide valuable data for forest managers and assist in formulating adaptive management plans for the ecologically sustainable management of brutian pine forest ecosystems.

Applying stochastic second-order entropy images to multi-modal image registration

Which metric to use for multi-modal image registration is still a nontrivial research problem. Recently, some methods have used structural representations of images to address this problem. Efficiency and optimization simplicity are the advantages of these algorithms; however, they have some limitations. First, structural representation based registrations often fail when there are intensity variations in the patch (local block) of the image. Second, structural representation based methods are not as accurate as mutual information based methods. In this article, the shortcomings of structural image representation are overcome by devising a new similarity metric called Stochastic Second-Order Entropy Image (SSOEI). We interpolate the neighbourhood intensity information of random pixels in each patch to estimate the histogram of the intensity distribution. Then, entropy of a patch can be computed by this joint histogram. An entropy image is a collection of the entropy value of every image patch. Then, the sum of squared difference from the entropy image can be utilized as the metric of the registration framework. The robustness and accuracy of SSOEI were tested on both synthetic and clinical data, and the results showed the advantages of SSOEI over the state-of-art methods.

On (L,M)-Double Fuzzy Filter Spaces

We give in this paper the definitions of (L,M)-double fuzzy filter base and (L,M)-double fuzzy filter structures where L and M are strictly two-sided commutative quantales, and we also investigate the relations between them. Moreover, we propose second-order image and preimage operators of (L,M)-double fuzzy filter base and study some of its fundamental properties. Finally, we handle the given structures in the categorical aspect. For instance, we show that the category (L,M)-DFIL of (L,M)-double fuzzy filter spaces and filter maps between these spaces is a topological category over the category SET.

High entropy of edge orientations characterizes visual artworks from diverse cultural backgrounds

We asked whether “good composition” or “visual rightness” of artworks manifest themselves in a particular arrangement of basic image features, such as oriented luminance edges. Specifically, we analysed the layout of edge orientations in images from a collection of >1600 paintings of Western provenance by comparing pairwise the orientation of each edge in an image with the orientations of all other edges in the same image. From the resulting orientation histograms, we calculated Shannon entropy and parallelism (i.e., the degree to which lines are parallel in the image). For comparison, we analysed the same second-order image properties in photographs of diverse natural patterns and man-made objects and scenes. Results showed that Shannon entropy of relative orientations of edge pairs was high and parallelism was low for the paintings and some of the natural patterns, but differed from other sets of photographs, including other man-made stimuli. The differences were also observed when images were matched for image content. Moreover, high entropy of edge orientations was found in traditional artworks produced by different techniques, in artworks that represented different content matter and art genres, as well as in artworks from other cultural backgrounds (East Asian and Islamic). In conclusion, we found that high entropy of edge orientations characterizes diverse sets of traditional artworks from various cultural backgrounds.

Second-Order Regression-Based MR Image Upsampling

The spatial resolution of magnetic resonance imaging (MRI) is often limited due to several reasons, including a short data acquisition time. Several advanced interpolation-based image upsampling algorithms have been developed to increase the resolution of MR images. These methods estimate the voxel intensity in a high-resolution (HR) image by a weighted combination of voxels in the original low-resolution (LR) MR image. As these methods fall into the zero-order point estimation framework, they only include a local constant approximation of the image voxel and hence cannot fully represent the underlying image structure(s). To this end, we extend the existing zero-order point estimation to higher orders of regression, allowing us to approximate a mapping function between local LR-HR image patches by a polynomial function. Extensive experiments on open-access MR image datasets and actual clinical MR images demonstrate that our algorithm can maintain sharp edges and preserve fine details, while the current state-of-the-art algorithms remain prone to some visual artifacts such as blurring and staircasing artifacts.

BSD: Blind image quality assessment based on structural degradation

Research in biological vision and neurology has evidenced that there are separate mechanisms in human visual cortex to process the first- and second-order patterns. Image structures detected by a linear filter are the first-order patterns which describe luminance changes, while patterns that are invisible to linear filters are often referred as the second-order structures. In this paper, we propose a general-purpose blind image quality assessment (BIQA) method by taking account of both the first- and second-order image structures. Specifically, the Prewitt linear filters are used to extract first-order image structures and the local contrast normalization is employed to extract second-order image structures. Perceptual features are extracted from these two image structural maps and used as the input to a support vector regression to model the nonlinear relationship between feature space to human opinion score. Extensive experiments on five image databases manifest the outstanding performance of the proposed method compared to the relevant state-of-the-art BIQA methods.

Decomposition-based tensor learning regression for improved classification of multimedia

Existing vector-based multimedia classification often incurs loss of space-time information and requires generation of high-dimensional vectors. To explore a possible new solution for the problem, we propose a novel tensor-based logistic regression algorithm via Tucker decomposition to complete multimedia classification. In order to strengthen the classification process, ℓF-norm is used for regularization term. A logistic Tucker regression model is established to achieve effective extraction of principal components out of the tensors, and hence reduce the dimension of inputs to improve the efficiency of multimedia classification. To evaluate the proposed algorithm, we carried out extensive experiments on a number of data sets, including two second-order grayscale image datasets and one third-order video sequence dataset. All the results indicate that our proposed algorithm outperforms the existing state-of-the-arts in relevant areas.

Evaluating Abstract Art: Relation between Term Usage, Subjective Ratings, Image Properties and Personality Traits

One of the major challenges in experimental aesthetics is the uncertainty of the terminology used in experiments. In this study, we recorded terms that are spontaneously used by participants to describe abstract artworks and studied their relation to the second-order statistical image properties of the same artworks (Experiment 1). We found that the usage frequency of some structure-describing terms correlates with statistical image properties, such as PHOG Self-Similarity, Anisotropy and Complexity. Additionally, emotion-associated terms correlate with measured color values. Next, based on the most frequently used terms, we created five different rating scales (Experiment 2) and obtained ratings of participants for the abstract paintings on these scales. We found significant correlations between descriptive score ratings (e.g., between structure and subjective complexity), between evaluative and descriptive score ratings (e.g., between preference and subjective complexity/interest) and between descriptive score ratings and statistical image properties (e.g., between interest and PHOG Self-Similarity, Complexity and Anisotropy). Additionally, we determined the participants’ personality traits as described in the ‘Big Five Inventory’ (Goldberg, 1990; Rammstedt and John, 2005) and correlated them with the ratings and preferences of individual participants. Participants with higher scores for Neuroticism showed preferences for objectively more complex images, as well as a different notion of the term complex when compared with participants with lower scores for Neuroticism. In conclusion, this study demonstrates an association between objectively measured image properties and the subjective terms that participants use to describe or evaluate abstract artworks. Moreover, our results suggest that the description of abstract artworks, their evaluation and the preference of participants for their low-level statistical properties are linked to personality traits.

Deficient Binocular Combination of Second-Order Stimuli in Amblyopia.

Sensory imbalances in humans with amblyopia have been well documented using luminance-modulated (first-order) stimuli. However, little is known regarding whether there is a deficient binocular combination in amblyopes for stimuli defined by modulations in contrast (second-order stimuli). To address this, we asked two questions: Does a sensory imbalance also exist in the binocular combination of second-order stimuli, and if so, is it more severe than that expected on the basis of the imbalance for first-order stimuli? The sensory imbalances of 14 adult amblyopes (mean age: 30.5 ± 11.5 years; 5 with strabismus and 9 without) were measured using a dichoptic phase combination task. Three types of second-order dichoptic stimulus pairs were used in the study, where the carriers in the two eyes were either correlated, anticorrelated, or uncorrelated. Results were compared with those obtained using first-order stimuli in all observers. We found that second-order binocular combination in amblyopes was not affected by the interocular carrier correlations. The amblyopic eye's contribution to the binocularly fused percept was much less than that of the nonamblyopic eye. The resulting sensory imbalance in binocular combination for second-order images was comparable to that for first-order images in 8 of the observers but was more severe in the other 6 amblyopes. These results indicate that amblyopia does not disrupt the normal architecture of binocular combination for second-order signals; however, there is an additional deficit in binocular combination of second-order image in some amblyopes that cannot be fully accounted for by the known first-order sensory imbalance.

Mathematical Analysis of a Inf-Convolution Model for Image Processing

We deal with a second-order image decomposition model to perform denoising and texture extraction that was previously presented. We look for the decomposition of an image as the summation of three different order terms. For highly textured images, the model gives a two-scale texture decomposition: The first-order term can be viewed as a macro-texture (larger scale) which oscillations are not too large, and the zero-order term is the micro-texture (very oscillating) that contains the noise. Here, we perform mathematical analysis of the model and give qualitative properties of solutions using the dual problem and inf-convolution formulation.

A Probabilistic WKL Rule for Incremental Feature Learning and Pattern Recognition

Recent advances in machine learning and computer vision have led to the development of several sophisticated learning schemes for object recognition by convolutional networks. One relatively simple learning rule, the Winner-Kill-Loser (WKL), was shown to be efficient at learning higher-order features in the neocognitron model when used in a written digit classification task. The WKL rule is one variant of incremental clustering procedures that adapt the number of cluster components to the input data. The WKL rule seeks to provide a complete, yet minimally redundant, covering of the input distribution. It is difficult to apply this approach directly to high-dimensional spaces since it leads to a dramatic explosion in the number of clustering components. In this work, a small generalization of the WKL rule is proposed to learn from high-dimensional data. We first show that the learning rule leads mostly to V1-like oriented cells when applied to natural images, suggesting that it captures second-order image statistics not unlike variants of Hebbian learning. We further embed the proposed learning rule into a convolutional network, specifically, the Neocognitron, and show its usefulness on a standard written digit recognition benchmark. Although the new learning rule leads to a small reduction in overall accuracy, this small reduction is accompanied by a major reduction in the number of coding nodes in the network. This in turn confirms that by learning statistical regularities rather than covering an entire input space, it may be possible to incrementally learn and retain most of the useful structure in the input distribution.

Characterization and correction of eddy-current artifacts in unipolar and bipolar diffusion sequences using magnetic field monitoring

Diffusion tensor imaging (DTI) of moving organs is gaining increasing attention but robust performance requires sequence modifications and dedicated correction methods to account for system imperfections. In this study, eddy currents in the “unipolar” Stejskal-Tanner and the velocity-compensated “bipolar” spin-echo diffusion sequences were investigated and corrected for using a magnetic field monitoring approach in combination with higher-order image reconstruction. From the field-camera measurements, increased levels of second-order eddy currents were quantified in the unipolar sequence relative to the bipolar diffusion sequence while zeroth and linear orders were found to be similar between both sequences. Second-order image reconstruction based on field-monitoring data resulted in reduced spatial misalignment artifacts and residual displacements of less than 0.43mm and 0.29mm (in the unipolar and bipolar sequences, respectively) after second-order eddy-current correction. Results demonstrate the need for second-order correction in unipolar encoding schemes but also show that bipolar sequences benefit from second-order reconstruction to correct for incomplete intrinsic cancellation of eddy-currents.

A new formula for bivariate Hermite interpolation on variable step grids and its application to image interpolation.

In this paper, we present a novel formula of the bivariate Hermite interpolating (BHI) polynomial in the case of support points arranged on a grid with variable step. This expression is applicable when interpolation of a bivariate function is required, given its value and the values of its partial derivatives of arbitrarily high order, at the support points. The proposed formula is a generalization of an existing formula for the bivariate Hermite polynomial. It is also algebraically much simpler, thus can be computed more efficiently. In order to apply Hermite interpolation to image interpolation, we simplify the proposed (BHI) to handle support points on a regular unit-step grid. The values of image partial derivatives are arithmetically approximated using compact finite differences. The proposed method is being assessed in a number of image interpolation experiments that include a synthetic image, for which the values of the partial derivatives are computed analytically, as well as a collection of images from different medical modalities. The proposed BHI with up to second-order image partial derivatives, outperforms the convolution-based interpolation methods, as well as generalized interpolation methods with the same number of support points that was compared with, in the majority of image interpolation experiments. The computational load of the proposed BHI is calculated and its behaviour with respect to its controlling parameters is investigated.

HEp-2 cell classification using shape index histograms with donut-shaped spatial pooling.

We present a new method for automatic classification of indirect immunoflourescence images of HEp-2 cells into different staining pattern classes. Our method is based on a new texture measure called shape index histograms that captures second-order image structure at multiple scales. Moreover, we introduce a spatial decomposition scheme which is radially symmetric and suitable for cell images. The spatial decomposition is performed using donut-shaped pooling regions of varying sizes when gathering histogram contributions. We evaluate our method using both the ICIP 2013 and the ICPR 2012 competition datasets. Our results show that shape index histograms are superior to other popular texture descriptors for HEp-2 cell classification. Moreover, when comparing to other automated systems for HEp-2 cell classification we show that shape index histograms are very competitive; especially considering the relatively low complexity of the method.

An ADMM algorithm for second-order TV-based MR image reconstruction

In this paper, we propose a new model for MR image reconstruction based on second order total variation ( TV 2 $\text {TV}^{2}$ ) regularization and wavelet, which can be considered as requiring the image to be sparse in both the spatial finite differences and wavelet transforms. Furthermore, by applying the variable splitting technique twice, augmented Lagrangian method and the Barzilai-Borwein step size selection scheme, an ADMM algorithm is designed to solve the proposed model. It reduces the reconstruction problem to several unconstrained minimization subproblems, which can be solved by shrinking operators and alternating minimization algorithms. The proposed algorithm needs not to solve a fourth-order PDE but to solve several second-order PDEs so as to improve calculation efficiency. Numerical results demonstrate the effectiveness of the presented algorithm and illustrate that the proposed model outperforms some reconstruction models in the quality of reconstructed images.