Grayscale Gradient Research Articles

Quantum image sharpness estimation based on the Laplacian operator

In order to solve the high complexity of classical image processing, a quantum scheme for image sharpness estimation based on the Laplacian operator is proposed. The mean of grayscale gradients of all pixels is regarded as the sharpness estimation metric. A new quantum image representation model is presented by extending the Novel Enhanced Quantum Representation (NEQR) model, which is greatly useful for quantum image convolution. In quantum platforms, it has been shown that the mean calculation of numbers is rather difficult because the numbers are stored in a quantum superposition state. In order to solve this problem, we put forward an algorithm which essential idea is cyclically shifting the superposition state and iteratively calculating the mean of the new one and the original state. The mean can be obtained from the superposition state by only one quantum measurement. By analyzing the space complexity and time complexity, the scheme is far superior to classical ones in terms of resource consumption and execution speed. In addition, the results of simulation experiments show that for noiseless images, the performance of the scheme is consistent with subjective visual perception of images sharpness.

Anisotropic analysis of fibrous and woven materials part 1: Estimation of local orientation

In many material science applications mechanical and thermal properties are often locally anisotropic. As such, a common requirement for high fidelity computational modeling is the knowledge of the local property tensor. In fibrous or woven materials, the properties are known along the direction of the fibers, so it is necessary to know their orientation to correctly align the tensors. In this study, three techniques are investigated for estimating the direction in these microstructures, obtained on Cartesian grids using microtomography as grayscale values: a common image processing technique called structure tensor, a method based on artificial flux, and a novel ray-casting approach. All the methods start by identifying the fibers using a grayscale cutoff. The first technique estimates the fiber direction based on the eigenvector corresponding to the smallest eigenvalue obtained from the grayscale gradients. The second method estimates the orientation as the local steady-state flux vector in a heat transfer simulation with temperature gradients imposed in all three directions. In the third method, rays are created at the center of each solid voxel and travel until the first collision with a material boundary occurs. The local direction vector is estimated based on the travel distance of these rays. The performance of each method is studied by examining their predictions for artificially generated weaves and fibrous materials, whose true local fiber direction is known a priori. The last part of this paper contains fiber orientation simulations for different real world materials scanned with X-ray microtomography, and describes a new workflow for weaves.

Grayscale distribution of maize canopy based on HLS-SVM method

ABSTRACT It is a crucial step locating the maize plant or even its target location precisely during the intelligent agricultural equipment working in farmland. Therefore, the segmentation of plants from the background image is one of the important research contents of agricultural machine vision. Under the background of significant color difference, the current method can effectively complete maize canopy segmentation and plant location identification. However, under the background of no-significant color difference, there is no robust and high-precision method for maize canopy segmentation and plant location identification. In this study, it was found that the grayscale of maize canopy had gradient distribution trend along the radial direction. The Hue Saturation Value color space and Support Vector Machine method was used to segment 600 maize canopy images, then the polynomial regression method was used to find out the functional relationship between grayscale gradient and canopy diameter. The functional relationship gave identification results of canopy central region under different gray gradient distribution. The result provided a theoretical basis for accurate identification and rapid location of maize plant center at seedling stage, and provided accurate position coordinate and yaw information for field navigation of agricultural intelligent equipment such as plant protection UAV.

Automatic Detection of Dispersed Defects in Resin Eyeglass Based on Machine Vision Technology

This paper is concerned with detection of dispersed defects in the resin eyeglass. At present, manual detection is always used in industry, which inevitably causes impairing eyes and a high rate of false-negative detection. Statistics show that its average accuracy and the average detection time are about 85% and 10s, respectively. We for the first time propose an automatic approach to detection of dispersed defects in resin eyeglass, based on the machine vision technology. It is observed that the refractivity of the normal and the defective regions of an eyeglass are different, and thus the reflection image is also collected in our system in addition to the normal transmission image. Such an optical imaging system is modelled and its analysis shows the gray-scale gradient difference between the normal and defective regions in the acquired image is dramatically enhanced under the illumination of a point light source with our designed system. An image processing algorithm is then developed to reveal the above difference and detect dispersed defects in resin eyeglasses. Our simulation study verifies the proposed approach. Further, its experimental evaluation was carried out and the result was consistent with the simulation one, showing that its detection accuracy and the average detection time were 97.50% and 0.636s, respectively, which meet the requirements for online detection of dispersed defects.

Study on optical imaging distortion of underwater thermal disturbance

In order to study the influence of underwater thermal disturbance environment on imaging distortion, such as optical imaging distortion or imaging blur, the level of distortion of target image in radial and axial directions was evaluated by using the gray scale distribution, structural similarity image measurement (SSIM), and normalized maximum gray-scale gradient definition evaluation function of underwater images. Furthermore, the laws of underwater thermal disturbance on optical imaging changes were obtained. Experimental results show that with the increase of the axial distance between the imaging system and the target, the level of image distortion and blurring becomes larger and larger. When the axial distance is equal to 500 mm, the SSIM is better than 0.7 and the normalized definition is better than 0.8. When the axial distance reaches 1500 mm, the SSIM is lower than 0.2 and the normalized definition is less than 0.6. In addition, when the axial distance equals 500 mm, the drift of the edges will be greater as the imaging area comes closer the heating source in the radial direction, that is, the imaging distortion is more serious. Finally, under the same axial and radial conditions, the conclusion that the SSIM and normalized definition values of the target images are different at different times can provide a reference for further underwater image restoration.

A Digital Analysis Approach for Estimating Decarburization Layer Depth of Carbon Steel via a Portable Device

Decarburization layer depth has great influence on the quality of metal forming process. For determining the depth value, the inspector progresses the measurement by manual nearly, which is subjective and inconsistency. This paper presents a digital analysis approach for measuring the decarburization depth automatically. Meanwhile, this analysis can be carried out by a portable device. For the digital analysis approach, the morphology image process is developed by comparing the variation of gray gradient of image from edge to core region. While the histogram of grayscale gradient falling down sharply, the distance from edge to the point was defined as the ferrite decarburization depth. Meanwhile, if the histogram keeps decreasing and stopping the decrease at one point, then the distance from edge to that point was defined as the totally decarburization depth. For the portable device, the analysis software is settled on a cloud-based calculating system. The analyst can capture the metallographic image shown in the monitor by smart glasses. Then, the analysis result is shown in smart glasses directly. All analysis and calculation process are progressed on a cloud-computing system. Finally, a digital metallographic analysis approach for estimating decarburization depth of carbon steel specimen by a portable device can be carried out.

GIS-based hillshade representation combined with relative relief as pseudo shade to enhance micro-topography

Abstract. Hillshade is a useful terrain representation that can express complicated topographic features on a map in 3D. However, the visual effects depend on the azimuth and the altitude of the light source corresponding to the target area. The purpose of this study is to provide a new method of GIS-based hillshade which can recognize various topographies in greater detail while reducing the dependency on the light source. The azimuth dependency of the light source can be traced back to the time of handwritten mapping, when cartographers combined multiple hillshades with differing azimuth settings.The authors of this study first tried to combine three types of hillshade (A, B and C, Figure1-3) that had not only different light sources but also different grayscale gradients. Hillshade A had a light source from the upper side of the map with the darkest grayscale gradient. Hillshade B had a light source from the left side with a medium grayscale gradient. Finally, Hillshade C’s light source was from the right side of the map with the brightest grayscale gradient. We confirmed that combining Hillshades A to C reproduces the same natural shading as that of a single light source from the upper left.The next purpose of the study was to enhance the topographic features of hillshade maps without overemphasizing the elevation factor in the GIS. We attempted to combine various topographic values through spatial analysis using a DEM in the GIS. Thus, we decided to combine a relative relief—a topographic value of maximum elevation change rate—as a pseudo shade (Figure4). However, because synthesizing the amount of relative relief in all directions overemphasizes the topography, we applied this only to downslope surfaces on the map created in the GIS. This pseudo shade works better for emphasizing micro-topography than does an upper light source in Hillshade A (Figure5).

Ionic Hydrogels with Biomimetic 4D‐Printed Mechanical Gradients: Models for Soft‐Bodied Aquatic Organisms

AbstractDirect‐ink writing (DIW), a rapidly growing and advancing form of additive manufacturing, provides capacities for on‐demand tailoring of materials to meet specific requirements for final designs. The penultimate challenge faced with the increasing demand of customization is to extend beyond modification of shape to create 4D structures, dynamic 3D structures that can respond to stimuli in the local environment. Patterning material gradients is foundational for assembly of 4D structures, however, there remains a general need for useful materials chemistries to generate gray scale gradients via DIW. Here, presented is a simple materials assembly paradigm using DIW to pattern ionotropic gradients in hydrogels. Using structures that architecturally mimic sea‐jelly organisms, the capabilities of spatial patterning are highlighted as exemplified by selectively programming the valency of the ion‐binding agents. Spatial gradients, when combined with geometry, allow for programming the flexibility and movement of iron oxide nanoparticle–loaded ionotropic hydrogels to generate 4D‐printed structures that actuate in the presence of local magnetic fields. This work highlights approaches to 4D design complexity that exploits 3D‐printed gray‐scale/gradient mechanics.

Research on Vision-Based Navigation for Plant Protection UAV under the Near Color Background

GPS (Global Positioning System) navigation in agriculture is facing many challenges, such as weak signals in orchards and the high cost for small plots of farmland. With the reduction of camera cost and the emergence of excellent visual algorithms, visual navigation can solve the above problems. Visual navigation is a navigation technology that uses cameras to sense environmental information as the basis of an aircraft flight. It is mainly divided into five parts: Image acquisition, landmark recognition, route planning, flight control, and obstacle avoidance. Here, landmarks are plant canopy, buildings, mountains, and rivers, with unique geographical characteristics in a place. During visual navigation, landmark location and route tracking are key links. When there are significant color-differences (for example, the differences among red, green, and blue) between a landmark and the background, the landmark can be recognized based on classical visual algorithms. However, in the case of non-significant color-differences (for example, the differences between dark green and vivid green) between a landmark and the background, there are no robust and high-precision methods for landmark identification. In view of the above problem, visual navigation in a maize field is studied. First, the block recognition method based on fine-tuned Inception-V3 is developed; then, the maize canopy landmark is recognized based on the above method; finally, local navigation lines are extracted from the landmarks based on the maize canopy grayscale gradient law. The results show that the accuracy is 0.9501. When the block number is 256, the block recognition method achieves the best segmentation. The average segmentation quality is 0.87, and time is 0.251 s. This study suggests that stable visual semantic navigation can be achieved under the near color background. It will be an important reference for the navigation of plant protection UAV (Unmanned Aerial Vehicle).

Bridge deck delamination segmentation based on aerial thermography through regularized grayscale morphological reconstruction and gradient statistics

Environmental and surface texture-induced temperature variation across the bridge deck is a major source of errors in delamination detection through thermography. This type of external noise poises a significant challenge for conventional quantitative methods such as global thresholding and k-means clustering. An iterative top-down approach is proposed for delamination segmentation based on grayscale morphological reconstruction. A weight-decay function was used to regularize the reconstruction for regional maxima extraction. The mean and coefficient of variation of temperature gradient estimated from delamination boundaries were used for discrimination. The proposed approach was tested on a lab experiment and an in-service bridge deck. The results demonstrated the improved capability of the framework to handle the non-uniform background, and thus eliminates the need of inferencing the background temperature which is often required by existing methods. That the results also suggested that the gradient statistics of the delamination boundary in the thermal image could be valid criterions to refine the segmentation under the proposed framework. Therefore, the authors concluded that the proposed method is a valid delamination segmentation approach for processing field concrete deck thermal images. The parameter selection and the limitation of this approach were also discussed. Further work will be carried out in more field cases to fine tune the parameter selection of the framework.

Classifier Adaptive Fusion: Deep Learning for Robust Outdoor Vehicle Visual Tracking

Deep auto-encoder (DAE) models have been successfully used in object tracking due to its strong capability of feature representation. However, single deep auto-encoder model would not be robust enough to represent the appearance model of outdoor vehicle for its harsh working environment, such as illumination variation, occlusion, cluttered background and so on. In this paper, a novel multiple-DAE-based tracking approach, that is, classifier adaptive fusion for robust outdoor vehicle visual tracking approach is proposed under particle filter framework. Firstly, two deep auto-encoders are offline trained by gray-scale image and gradient image of the raw training images, respectively to obtain the stronger feature representation of gray-scale image and gradient image. Secondly, two classifiers are constructed using the encoder of the two well-trained deep auto-encoders and the output of the each classifier is used to compute the confidence of the corresponding particles. Finally, the confidence output of the two classifiers is fused and applied in online tracking, where, the fusion weight of the each classifier is computed according to the distribution of particles represented by different classifier. Extensive tracking experiments conducted on visual tracking benchmark (VTB) show that the proposed tracking algorithm outperforms 9 popular tracking algorithms in the challenge scenes of outdoor vehicle tracking such as illumination variation, occlusion, cluttered background and scale variation.

A Coverless Information Hiding Algorithm Based on Grayscale Gradient Co-occurrence Matrix

ABSTRACTIn this paper, a coverless information hiding algorithm is introduced. In which, the grayscale gradient co-occurrence matrix is used to encode images and the mapping relationship between the images and the random numbers is used to express the payload information. There are three steps for this algorithm. Firstly, the grayscale gradient co-occurrence matrix of cover image is calculated, in accordance with which a descriptor is introduced. Secondly, the descriptor is quantized into a binary sequence to construct a mapping relationship between the cover image and the binary random numbers. Finally, the binary secret information sequence is divided into many segments, and the correct images corresponding to those segments are selected from the image database according to the mapping relationship. Moreover, the secret information is encrypted by Turbo encoder to improve the security. The experimental results show that the proposed algorithm has a good tolerance towards JPEG compression attack and low-pass filter attack. This promising algorithm which can be applied into remote sensing satellites leads an applied value in covert communication with high-security.

Research on maize canopy center recognition based on nonsignificant color difference segmentation.

Weed control is a substantial challenge in field management. A better weed control method at an earlier growth stage is important for increasing yields. As a promising weed control technique, intelligent weeding based on machine vision can avoid the harm of chemical weeding. For machine vision, it is critical to extract and segment crops from their background. However, there is still no optimal solution for object tracking with occlusion under a similar color background. In this study, it was found that the gray distribution of a maize canopy follows the gradient law. Therefore, the recognition method based on the HLS-SVM (HLS color space and Support Vector Machine) and on the grayscale gradient was developed. First, the HLS color space was used to detect the maize canopy. Second, the SVM method was used to segment the central region of the maize canopy. Finally, the maize canopy center was identified according to the gradient law. The results showed that the average segmentation time was 0.49 s, the average segmentation quality was 87.25%, and the standard deviation of the segmentation was 3.57%. The average recognition rate of the center position was 93.33%. This study provided a machine vision method for intelligent weeding agricultural equipment as well as a theoretical reference for further agricultural machine vision research.

Research on feature extraction and segmentation of rover wheel imprint

The wheel imprint photograph of the rover contains important information such as wheel motion parameters, soil characteristic parameters and movement status of the rover. Segmenting the wheel imprint area from the photograph is an important prerequisite for feature extraction and parameter identification. Traditional image segmentation cannot take both speed and precision into account because they are based on a wide range of image object attributes, such as grayscale threshold, color, texture, gradient, contrast, shape and size. This paper presents an image segmentation method based on the wheel imprint feature. Compared to other common graphics segmentation methods, the morphological characteristics and frequency domain characteristics of the wheel imprint are found out by analyzing the mechanism of the wheel–terrain interaction process, and the eigenvector is also constructed. In the wheel trace feature space, the clustering algorithm is used to divide the image into the trace area and the non-trace area. The segmentation accuracy and processing speed were used to evaluate the algorithm. The experimental results show that the developed algorithm based on the characteristics of wheel imprint formation mechanism is more accurate and efficient than the traditional method.

Research on Vehicle Detection Algorithms in Surveillance Video Images

Intelligent traffic video surveillance system, including vehicle inspection, vehicle tracking and license plate recognition module. The video vehicle detection in this paper is divided into four steps: video image pre-processing, background modeling and updating, foreground detection and adhesion vehicle area segmentation. After the collected video sequence is subjected to mean-value down-sampling and gray-scale conversion preprocessing, the background model is built using a mixture of Gaussian models. A sliding window is set on the time axis, and the grayscale video frame image in the sliding window is median-filtered to output a background gradient map. By merging the results of the spatial background difference between the color space and the grayscale gradient, the foreground image detected by the vehicle is obtained. Finally, the background difference is obtained in the gradient domain to obtain the foreground image to achieve vehicle detection.

Patterns and Sources of Spatial Heterogeneity in Soil Matrix From Contrasting Long Term Management Practices

With the advent of computed microtomography (μCT), in situ 3D visualization of soil at micron scale became easily achievable. However, most μCT-based research has focused on visualization and quantification of soil pores, roots, and particulate organic matter (POM), while little effort was been put in exploring the soil matrix itself. This study aims to characterize spatial heterogeneity of soil matrix in macroaggregates from three differing long term managements: conventionally managed and biologically based row-crop agricultural systems and primary successional unmanaged system and explore the utility of using grayscale gradients as a proxy of soil organic matter (SOM). To determine spatial characteristics of the soil matrix, we completed a geostatistical analysis of the aggregate matrix. It demonstrated that, while the treatments had the same range of spatial correlation, there was much greater overall variability in soil from the biologically based system. Since soil from both managements has the same mineralogy and texture, we hypothesized that greater variability is due to differences in SOM distributions, driven by spatial distribution patterns of soil pores. To test this hypothesis, we applied osmium (Os) staining to intact micro-cores from the biologically based management, and examined Os staining gradients every 4 μm from 26 to 213 µm from pores of biological or non-biological origin. Biological pores had the highest SOM levels adjacent to the pore, which receded to background levels at distances of 100-130 μm. Non-biological pores had lower SOM levels adjacent to the pores and returned to background levels at distances of 30-50 μm. This indicates that some of the spatial heterogeneity within the soil matrix can be ascribed to SOM distribution patterns as controlled by pore origins and distributions. Lastly, to determine if the grayscale values could be used as a proxy for SOM levels, gradients of grayscale values from biological and non-biological pores were compared with the Os gradients. Grayscale gradients matched Os gradients for biological pores, but not non-biological pores due to an image processing artifact. Grayscale gradients would, therefore, be a good proxy for SOM gradients near biological origin pores, while use for non-biological pores should be used with caution.

SEMANTIC INFORMATION EXTRACTION OF LANES BASED ON ONBOARD CAMERA VIDEOS

Abstract. In the field of autonomous driving, semantic information of lanes is very important. This paper proposes a method of automatic detection of lanes and extraction of semantic information from onboard camera videos. The proposed method firstly detects the edges of lanes by the grayscale gradient direction, and improves the Probabilistic Hough transform to fit them; then, it uses the vanishing point principle to calculate the lane geometrical position, and uses lane characteristics to extract lane semantic information by the classification of decision trees. In the experiment, 216 road video images captured by a camera mounted onboard a moving vehicle were used to detect lanes and extract lane semantic information. The results show that the proposed method can accurately identify lane semantics from video images.

Application of Color Transformation Techniques in Pediatric Spinal Cord MR Images: Typically Developing and Spinal Cord Injury Population.

The purpose of this study was to evaluate an improved and reliable visualization method for pediatric spinal cord MR images in healthy subjects and patients with spinal cord injury (SCI). A total of 15 pediatric volunteers (10 healthy subjects and 5 subjects with cervical SCI) with a mean age of 11.41years (range 8-16years) were recruited and scanned using a 3.0T Siemens Verio MR scanner. T2-weighted axial images were acquired covering entire cervical spinal cord level C1 to C7. These gray-scale images were then converted to color images by using five different techniques including hue-saturation-value (HSV), rainbow, red-green-blue (RGB), and two enhanced RGB techniques using automated contrast stretching and intensity inhomogeneity correction. Performance of these techniques was scored visually by two neuroradiologists within three selected cervical spinal cord intervertebral disk levels (C2-C3, C4-C5, and C6-C7) and quantified using signal to noise ratio (SNR) and contrast to noise ratio (CNR). Qualitative and quantitative evaluation of the color images shows consistent improvement across all the healthy and SCI subjects over conventional gray-scale T2-weighted gradient echo (GRE) images. Inter-observer reliability test showed moderate to strong intra-class correlation (ICC) coefficients in the proposed techniques (ICC > 0.73). The results suggest that the color images could be used for quantification and enhanced visualization of the spinal cord structures in addition to the conventional gray-scale images. This would immensely help towards improved delineation of the gray/white and CSF structures and further aid towards accurate manual or automatic drawings of region of interests (ROIs).

Latent Fingerprint Segmentation Based on Ridge Density and Orientation Consistency

Latent fingerprints are captured from the fingerprint impressions left unintentionally at the surfaces of the crime scene. They are often used as an important evidence to identify criminals in law enforcement agencies. Different from the widely used plain and rolled fingerprints, the latent fingerprints are usually of poor quality consisting of complex background with a lot of nonfingerprint patterns and various noises. Latent fingerprint segmentation is an important image processing step to separate fingerprint foreground from background for more accurate and efficient feature extraction and matching. Traditional methods are usually based on the local features such as gray scale variance and gradients, which are sensitive to noise and cannot work well for latent images. This paper proposes a latent fingerprint segmentation method based on combination of ridge density and orientation consistency, which are global and local features of fingerprints, respectively. First, a texture image is obtained by decomposition of latent image with a total variation model. Second, we propose to detect the ridge segments from the texture image, and then compute the density of ridge segments and ridge orientation consistency to characterize the global and local fingerprint patterns. Finally, fingerprint segmentation is performed by combining the ridge density and orientation consistency for latent images. The proposed method has been evaluated on NIST SD27 latent fingerprint database. Experimental results and comparison demonstrate the promising performance of the proposed method.

Corrigendum: Empirical analysis of the relationship between CC and SLOC in a large corpus of Java methods and C functions published on 9 December 2015

INTRODUCTION During the preparation of the corresponding chapter in Davy Landman's PhD thesis, some minor graphical and statistical discrepancies were found in the paper “Empirical analysis of the relationship between CC and SLOC in a large corpus of Java methods and C functions.” To support future reproduction and use of this work, we prepared the current erratum, containing several updated figures, a diagnosis of the cause of the errors, and an explanation of the effect on the original paper. None of the issues reported in this erratum influence the conclusions of the original paper. ISSUES DISCOVERED The hexagonal scatter plots in Figure lack a more prominent line at CC = 0. This was caused by a bug *reported and confirmed: https://github.com/tidyverse/ggplot2/issues/2061in ggplot, which would filter out data around the limits. The R 2 values in the Tables B and B of the C corpus were off by a maximum of 0.01 from the actual result. The cause was that this table was not re-calculated after fixing a bug in the “remove out-of-scope code” phase. Note that the impact of this error is scattered throughout the paper, as the correlations of Tables and are often repeated for clarity in the remaining sections (for example, the R 2 of the linear model for all the C functions is 0.43 instead of 0.44). Our R code calculating the log-transformed linear fit contained an error. The dashed lines in Figures, and are impacted and the shape of the residual plot in 11. The biggest impact is in Figure, where the original fit seemed to miss the data almost entirely. We misinterpreted this phenomenon in the last sentence of the second paragraph of section 4.4.2; it is not caused by the skewness of the distributions of the two metrics, but rather by the current bug. The custom implementation of the log-scaled y-axis of the residual plots in Figure contained two errors: ∘ The labels on the y-axis were off by a factor 10 ∘For the negative side of the residual plot, we took the absolute, calculated the log10 value, and made it negative again. However, values between 0 and 1 (the values close to the linear fit) turn into a negative value (as log10(1) equals 0). This caused strange outliers in the original plots that were not scrutinized. The fixed residual plots do not have this outliers and look much more like the data in Figure. We republished the data sets related to the current paper on Zenodo to increase their availability: ∘ Landman, Davy. (2015). A Curated Corpus of Java Source Code based on Sourcerer (2015) [Data set]. Zenodo. http://doi.org/10.5281/zenodo.208213 ∘Landman, Davy. (2015). A Large Corpus of C Source Code based on Gentoo packages [Data set]. Zenodo. http://doi.org/10.5281/zenodo.208215 ∘Davy Landman. (2015, February 26). cwi-swat/jsep-sloc-versus-cc. Zenodo. http://doi.org/10.5281/zenodo.293795 NEW IMAGES The remaining part of this erratum contains updated tables and figures as replacements for the original paper. 8 (Figure presented.) Scatter plots of SLOC vs CC zoomed in on the bottom left quadrant. The solid and dashed lines are the linear regression before and after the log transform. The grayscale gradient of the hexagons is logarithmic 4 Correlations for part of the tail of the independent variable SLOC. All correlations have a high significance level p≤1×10 −16.(b) C functions (Table presented.) 5 Correlations for part of the tail of the independent variable SLOC removed. All correlations have a high significance level p≤1×10 −16.(b) C functions (Table presented.) 9 (Figure presented.) Scatter plots of SLOC vs CC on a log-log scale. The solid and dashed lines are the linear regression before and after the log transform. The grayscale gradient of the hexagons is logarithmic 11 (Figure presented.) Residual plot of the linear regressions after the log transform, both axis are on a log scale. The grayscale gradient of the hexagons is logarithmic 12 (Figure presented.) Scatter plots of SLOC vs CC for Java and C files. The solid and dashed lines are the linear regression before and after the log transform. The grayscale gradient of the hexagons is logarithmic.