An effective processing method for biomedical images and the Fuzzy C-mean (FCM) algorithm based on the wavelet transform are investigated.By using hierarchical wavelet decomposition, an original image could be decompo...An effective processing method for biomedical images and the Fuzzy C-mean (FCM) algorithm based on the wavelet transform are investigated.By using hierarchical wavelet decomposition, an original image could be decomposed into one lower image and several detail images. The segmentation started at the lowest resolution with the FCM clustering algorithm and the texture feature extracted from various sub-bands. With the improvement of the FCM algorithm, FCM alternation frequency was decreased and the accuracy of segmentation was advanced.展开更多
The rapid development of data communication in modern era demands secure exchange of information. Steganography is an established method for hiding secret data from an unauthorized access into a cover object in such a...The rapid development of data communication in modern era demands secure exchange of information. Steganography is an established method for hiding secret data from an unauthorized access into a cover object in such a way that it is invisible to human eyes. The cover object can be image, text, audio,or video. This paper proposes a secure steganography algorithm that hides a bitstream of the secret text into the least significant bits(LSBs) of the approximation coefficients of the integer wavelet transform(IWT) of grayscale images as well as each component of color images to form stego-images. The embedding and extracting phases of the proposed steganography algorithms are performed using the MATLAB software. Invisibility, payload capacity, and security in terms of peak signal to noise ratio(PSNR) and robustness are the key challenges to steganography. The statistical distortion between the cover images and the stego-images is measured by using the mean square error(MSE) and the PSNR, while the degree of closeness between them is evaluated using the normalized cross correlation(NCC). The experimental results show that, the proposed algorithms can hide the secret text with a large payload capacity with a high level of security and a higher invisibility. Furthermore, the proposed technique is computationally efficient and better results for both PSNR and NCC are achieved compared with the previous algorithms.展开更多
A mixed scheme based on Wavelet Transformation (WT) is proposed for image edge detection. The scheme combines the wavelet transform and traditional Sobel and LoG (Laplacian of Gaussian) operator edge-detection algorit...A mixed scheme based on Wavelet Transformation (WT) is proposed for image edge detection. The scheme combines the wavelet transform and traditional Sobel and LoG (Laplacian of Gaussian) operator edge-detection algorithms. The precise theory analysis is given to show that the wavelet transformation has an advantage for signal processing. Simulation results show that the new scheme is better than only using the Sobel or LoG methods. Complexity analysis is also given and the conclusion is acceptable, therefore the proposed scheme is effective for edge detection.展开更多
We studied the variation of image entropy before and after wavelet decomposition, the optimal number of wavelet decomposition layers, and the effect of wavelet bases and image frequency components on entropy. Numerous...We studied the variation of image entropy before and after wavelet decomposition, the optimal number of wavelet decomposition layers, and the effect of wavelet bases and image frequency components on entropy. Numerous experiments were done on typical images to calculate (using Matlab) the entropy before and after wavelet transform. It was verified that, to obtain minimal entropy, a three-layer decomposition should be adopted rather than higher orders. The result achieved by using biorthogonal wavelet decomposition is better than that of the orthogonal wavelet decomposition. The results are not directly proportional to the vanishing moment, however.展开更多
For the image processing technology, technicians have been looking for a convenient and simple detection method for a long time, especially for the innovation research on image edge detection technology. Because there...For the image processing technology, technicians have been looking for a convenient and simple detection method for a long time, especially for the innovation research on image edge detection technology. Because there are a lot of original information at the edge during image processing, thus, we can get the real image data in terms of the data acquisition. The usage of edge is often in the case of some irregular geometric objects, and we determine the contour of the image by combining with signal transmitted data. At the present stage, there are different algorithms in image edge detection, however, different types of algorithms have divergent disadvantages so It is diffi cult to detect the image changes in a reasonable range. We try to use wavelet transformation in image edge detection, making full use of the wave with the high resolution characteristics, and combining multiple images, in order to improve the accuracy of image edge detection.展开更多
In the fusion of image,how to measure the local character and clarity is called activity measurement. According to the problem,the traditional measurement is decided only by the high-frequency detail coefficients, whi...In the fusion of image,how to measure the local character and clarity is called activity measurement. According to the problem,the traditional measurement is decided only by the high-frequency detail coefficients, which will make the energy expression insufficient to reflect the local clarity. Therefore,in this paper,a novel construction method for activity measurement is proposed. Firstly,it uses the wavelet decomposition for the fusion resource image, and then utilizes the high and low frequency wavelet coefficients synthetically. Meantime,it takes the normalized variance as the weight of high-frequency energy. Secondly,it calculates the measurement by the weighted energy,which can be used to measure the local character. Finally,the fusion coefficients can be got. In order to illustrate the superiority of this new method,three kinds of assessing indicators are provided. The experiment results show that,comparing with the traditional methods,this new method weakens the fuzzy and promotes the indicator value. Therefore,it has much more advantages for practical application.展开更多
In this paper,we propose a new image fusion algorithm based on two-dimensional Scale-Mixing Complex Wavelet Transform(2D-SMCWT).The fusion of the detail 2D-SMCWT cofficients is performed via a Bayesian Maximum a Poste...In this paper,we propose a new image fusion algorithm based on two-dimensional Scale-Mixing Complex Wavelet Transform(2D-SMCWT).The fusion of the detail 2D-SMCWT cofficients is performed via a Bayesian Maximum a Posteriori(MAP)approach by considering a trivariate statistical model for the local neighboring of 2D-SMCWT coefficients.For the approx imation coefficients,a new fusion rule based on the Principal Component Analysis(PCA)is applied.We conduct several experiments using three different groups of multimodal medical images to evaluate the performance of the proposed method.The obt ained results prove the superiority of the proposed method over the state of the art fusion methods in terms of visual quality and several commonly used metrics.Robustness of the proposed method is further tested against different types of noise.The plots of fusion met rics establish the accuracy of the proposed fusion method.展开更多
This paper presents systematically a method for image compression/decompression via wavelet transform. It consists of filter, quantization and Huffman coding etc.. Different methods have been compared. Finally,some su...This paper presents systematically a method for image compression/decompression via wavelet transform. It consists of filter, quantization and Huffman coding etc.. Different methods have been compared. Finally,some suggestions for further studies are proposed. In fact,the paper is a summary of our recent research.展开更多
There are few applications of image processing technology for diagnosing andstate monitoring for internal combustion (IC) engines, which is discussed in detail in this paper.The time-frequency distribution images of c...There are few applications of image processing technology for diagnosing andstate monitoring for internal combustion (IC) engines, which is discussed in detail in this paper.The time-frequency distribution images of cylinder head vibration signals are obtained bydecomposing them with a wavelet packet algorithm. It is the first time that we look attime-frequency distribution images from the point of images. Based on this, a new method forapplying image processing technology for diagnosing and state monitoring for internal combustionengines is presented in this paper. A valve fault diagnosis model is set up by image matching, whichis realized on a four-stroke, six-cylinder diesel engine. At the same time, some notes arepresented in this paper. It has been proved that it is of no good effect to diagnose with histogramsof time-frequency images generated by cylinder head vibration signals that have been processed witha wavelet packet algorithm. The reason is given in this paper. Comparisons of diagnosing effect arecarried out between noise-added signals and original signals. It has little effect on diagnosingresults after signals have been added with noise. The results show that this method has a clearphysical meaning and is of good engineering practicability, feasibility, good precision and highspeed.展开更多
In this paper, an adaptive multiresolution speech enhancement algorithm based on wavelet transform is put forward. It can make adaptive filtering to noise speech both at scales and among scales. So that the noise part...In this paper, an adaptive multiresolution speech enhancement algorithm based on wavelet transform is put forward. It can make adaptive filtering to noise speech both at scales and among scales. So that the noise parts during the frequency intervals which decrease hearing quality mostly are reduced efficiently. Both the SNR and subject hearing quality of denoised speech are high and good.展开更多
Single-stripe laser was applied to acquire V-shape groove contour information. Most of arc light and splash noise was removed and stripe laser image was kept by wavelet transform. Half-threshold algorithm was used for...Single-stripe laser was applied to acquire V-shape groove contour information. Most of arc light and splash noise was removed and stripe laser image was kept by wavelet transform. Half-threshold algorithm was used for image segmentation and stripe laser image was gotten after refining. Weld seam center position was identified and extracted by extreme curvature corner detection method. The location of torch was detected to accord the frequency of computer program with robot program and serial communication program. The tracking experiments of sidelong, reflex and curve weld line show that the system can meet the demand of the tracking precision under normal welding conditions.展开更多
Aiming at the problem,i.e.infrared images own the characters of bad contrast ratio and fuzzy edges,a method to enhance the contrast of infrared image is given,which is based on stationary wavelet transform.After makin...Aiming at the problem,i.e.infrared images own the characters of bad contrast ratio and fuzzy edges,a method to enhance the contrast of infrared image is given,which is based on stationary wavelet transform.After making stationary wavelet transform to an infrared image,denoising is done by the proposed method of double-threshold shrinkage in detail coefficient matrixes that have high noisy intensity.For the approximation coefficient matrix with low noisy intensity,enhancement is done by the proposed method based on histogram.The enhanced image can be got by wavelet coefficient reconstruction.Furthermore,an evaluation criterion of enhancement performance is introduced.The results show that this algorithm ensures target enhancement and restrains additive Gauss white noise effectively.At the same time,its amount of calculation is small and operation speed is fast.展开更多
The paper describes a texture-based fast text location scheme which operates directly in the Discrete Wavelet Transform (DWT) domain. By the distinguishing texture characteristics encoded in wavelet transform domain, ...The paper describes a texture-based fast text location scheme which operates directly in the Discrete Wavelet Transform (DWT) domain. By the distinguishing texture characteristics encoded in wavelet transform domain, the text is fast detected from complex background images stored in the compressed format such as JPEG2000 without full decompress. Compared with some traditional character location methods, the proposed scheme has the advantages of low computational cost, robust to size and font of characters and high accuracy. Preliminary experimental results show that the proposed scheme is efficient and effective.展开更多
A novel approach using shift invariant wavelet transform is presented for the contrast enhancement of radiographs. By exploiting cross-scale correlation among wavelet coefficients, edge information of radiographic ima...A novel approach using shift invariant wavelet transform is presented for the contrast enhancement of radiographs. By exploiting cross-scale correlation among wavelet coefficients, edge information of radiographic images is extracted and protected, while noise is smoothed out in the wavelet domain. Radiographs are then reconstructed from the transform coefficients modified at multi-scales by nonlinear enhancement operator. The method can achieve effectively contrast enhancement and edge-preserved denoising simultaneously, yet it is capable of giving visually distinct images and offering considerable benefits in medical diagnosis.展开更多
This paper first reviews the application research works of wavelet transform on the fluid mechanics. Then the theories of continuous wavelet transform and multi-dimensional orthogonal(discrete) wavelet transform, incl...This paper first reviews the application research works of wavelet transform on the fluid mechanics. Then the theories of continuous wavelet transform and multi-dimensional orthogonal(discrete) wavelet transform, including wavelet multiresolution analysis, are introduced. At last the applications of wavelet transform on 2 D and 3 D turbulent wakes and turbulent boundary layer flows are described based on the hot-wire, 2 D particle image velocimetry(PIV) and 3 D tomographic PIV.展开更多
To develop a quick, accurate and antinoise automated image registration technique for infrared images, the wavelet analysis technique was used to extract the feature points in two images followed by the compensation f...To develop a quick, accurate and antinoise automated image registration technique for infrared images, the wavelet analysis technique was used to extract the feature points in two images followed by the compensation for input image with angle difference between them. A hi erarchical feature matching algorithm was adopted to get the final transform parameters between the two images. The simulation results for two infrared images show that the method can effectively, quickly and accurately register images and be antinoise to some extent.展开更多
The construction of basic wavelet was discussed and many basic analyzing wavelets was compared. Acomplex analyzing wavelet which is continuous, smoothing, orthogonal and exponential decreasing was presented, andit was...The construction of basic wavelet was discussed and many basic analyzing wavelets was compared. Acomplex analyzing wavelet which is continuous, smoothing, orthogonal and exponential decreasing was presented, andit was used to decompose two blasting seismic signals with the continuous wavelet transforms (CWT). The resultshows that wavelet analysis is the better method to help us determine the essential factors which create damage effectsthan Fourier analysis.展开更多
A muitisensor image fusion algorithm is described using 2-dimensional nonseparable wavelet frame (NWF) transform. The source muitisensor images are first decomposed by the NWF transform. Then, the NWF transform coef...A muitisensor image fusion algorithm is described using 2-dimensional nonseparable wavelet frame (NWF) transform. The source muitisensor images are first decomposed by the NWF transform. Then, the NWF transform coefficients of the source images are combined into the composite NWF transform coefficients. Inverse NWF transform is performed on the composite NWF transform coefficients in order to obtain the intermediate fused image. Finally, intensity adjustment is applied to the intermediate fused image in order to maintain the dynamic intensity range. Experiment resuits using real data show that the proposed algorithm works well in muitisensor image fusion.展开更多
The scientific satellite SST (Space Solar Telescope) is an important research project strongly supported by the Chinese Academy of Sciences. Every day, SST acquires 50 GB of data (after processing) but only 10GB can b...The scientific satellite SST (Space Solar Telescope) is an important research project strongly supported by the Chinese Academy of Sciences. Every day, SST acquires 50 GB of data (after processing) but only 10GB can be transmitted to the ground because of limited time of satellite passage and limited channel volume. Therefore, the data must be compressed before transmission. Wavelets analysis is a new technique developed over the last 10 years, with great potential of application. We start with a brief introduction to the essential principles of wavelet analysis, and then describe the main idea of embedded zerotree wavelet coding, used for compressing the SST images. The results show that this coding is adequate for the job.展开更多
文摘An effective processing method for biomedical images and the Fuzzy C-mean (FCM) algorithm based on the wavelet transform are investigated.By using hierarchical wavelet decomposition, an original image could be decomposed into one lower image and several detail images. The segmentation started at the lowest resolution with the FCM clustering algorithm and the texture feature extracted from various sub-bands. With the improvement of the FCM algorithm, FCM alternation frequency was decreased and the accuracy of segmentation was advanced.
文摘The rapid development of data communication in modern era demands secure exchange of information. Steganography is an established method for hiding secret data from an unauthorized access into a cover object in such a way that it is invisible to human eyes. The cover object can be image, text, audio,or video. This paper proposes a secure steganography algorithm that hides a bitstream of the secret text into the least significant bits(LSBs) of the approximation coefficients of the integer wavelet transform(IWT) of grayscale images as well as each component of color images to form stego-images. The embedding and extracting phases of the proposed steganography algorithms are performed using the MATLAB software. Invisibility, payload capacity, and security in terms of peak signal to noise ratio(PSNR) and robustness are the key challenges to steganography. The statistical distortion between the cover images and the stego-images is measured by using the mean square error(MSE) and the PSNR, while the degree of closeness between them is evaluated using the normalized cross correlation(NCC). The experimental results show that, the proposed algorithms can hide the secret text with a large payload capacity with a high level of security and a higher invisibility. Furthermore, the proposed technique is computationally efficient and better results for both PSNR and NCC are achieved compared with the previous algorithms.
基金Supported by the National Defence 973 project(2002HS0604,2002HS0634)
文摘A mixed scheme based on Wavelet Transformation (WT) is proposed for image edge detection. The scheme combines the wavelet transform and traditional Sobel and LoG (Laplacian of Gaussian) operator edge-detection algorithms. The precise theory analysis is given to show that the wavelet transformation has an advantage for signal processing. Simulation results show that the new scheme is better than only using the Sobel or LoG methods. Complexity analysis is also given and the conclusion is acceptable, therefore the proposed scheme is effective for edge detection.
基金the Natural Science Foundation of China (No. 60472037).
文摘We studied the variation of image entropy before and after wavelet decomposition, the optimal number of wavelet decomposition layers, and the effect of wavelet bases and image frequency components on entropy. Numerous experiments were done on typical images to calculate (using Matlab) the entropy before and after wavelet transform. It was verified that, to obtain minimal entropy, a three-layer decomposition should be adopted rather than higher orders. The result achieved by using biorthogonal wavelet decomposition is better than that of the orthogonal wavelet decomposition. The results are not directly proportional to the vanishing moment, however.
文摘For the image processing technology, technicians have been looking for a convenient and simple detection method for a long time, especially for the innovation research on image edge detection technology. Because there are a lot of original information at the edge during image processing, thus, we can get the real image data in terms of the data acquisition. The usage of edge is often in the case of some irregular geometric objects, and we determine the contour of the image by combining with signal transmitted data. At the present stage, there are different algorithms in image edge detection, however, different types of algorithms have divergent disadvantages so It is diffi cult to detect the image changes in a reasonable range. We try to use wavelet transformation in image edge detection, making full use of the wave with the high resolution characteristics, and combining multiple images, in order to improve the accuracy of image edge detection.
基金Sponsored by the Nation Nature Science Foundation of China(Grant No.61275010,61201237)the Fundamental Research Funds for the Central Universities(Grant No.HEUCFZ1129,No.HEUCF120805)
文摘In the fusion of image,how to measure the local character and clarity is called activity measurement. According to the problem,the traditional measurement is decided only by the high-frequency detail coefficients, which will make the energy expression insufficient to reflect the local clarity. Therefore,in this paper,a novel construction method for activity measurement is proposed. Firstly,it uses the wavelet decomposition for the fusion resource image, and then utilizes the high and low frequency wavelet coefficients synthetically. Meantime,it takes the normalized variance as the weight of high-frequency energy. Secondly,it calculates the measurement by the weighted energy,which can be used to measure the local character. Finally,the fusion coefficients can be got. In order to illustrate the superiority of this new method,three kinds of assessing indicators are provided. The experiment results show that,comparing with the traditional methods,this new method weakens the fuzzy and promotes the indicator value. Therefore,it has much more advantages for practical application.
文摘In this paper,we propose a new image fusion algorithm based on two-dimensional Scale-Mixing Complex Wavelet Transform(2D-SMCWT).The fusion of the detail 2D-SMCWT cofficients is performed via a Bayesian Maximum a Posteriori(MAP)approach by considering a trivariate statistical model for the local neighboring of 2D-SMCWT coefficients.For the approx imation coefficients,a new fusion rule based on the Principal Component Analysis(PCA)is applied.We conduct several experiments using three different groups of multimodal medical images to evaluate the performance of the proposed method.The obt ained results prove the superiority of the proposed method over the state of the art fusion methods in terms of visual quality and several commonly used metrics.Robustness of the proposed method is further tested against different types of noise.The plots of fusion met rics establish the accuracy of the proposed fusion method.
文摘This paper presents systematically a method for image compression/decompression via wavelet transform. It consists of filter, quantization and Huffman coding etc.. Different methods have been compared. Finally,some suggestions for further studies are proposed. In fact,the paper is a summary of our recent research.
文摘There are few applications of image processing technology for diagnosing andstate monitoring for internal combustion (IC) engines, which is discussed in detail in this paper.The time-frequency distribution images of cylinder head vibration signals are obtained bydecomposing them with a wavelet packet algorithm. It is the first time that we look attime-frequency distribution images from the point of images. Based on this, a new method forapplying image processing technology for diagnosing and state monitoring for internal combustionengines is presented in this paper. A valve fault diagnosis model is set up by image matching, whichis realized on a four-stroke, six-cylinder diesel engine. At the same time, some notes arepresented in this paper. It has been proved that it is of no good effect to diagnose with histogramsof time-frequency images generated by cylinder head vibration signals that have been processed witha wavelet packet algorithm. The reason is given in this paper. Comparisons of diagnosing effect arecarried out between noise-added signals and original signals. It has little effect on diagnosingresults after signals have been added with noise. The results show that this method has a clearphysical meaning and is of good engineering practicability, feasibility, good precision and highspeed.
文摘In this paper, an adaptive multiresolution speech enhancement algorithm based on wavelet transform is put forward. It can make adaptive filtering to noise speech both at scales and among scales. So that the noise parts during the frequency intervals which decrease hearing quality mostly are reduced efficiently. Both the SNR and subject hearing quality of denoised speech are high and good.
基金supported by National Natural Science Foundation of China No. 50705030Guangdong Province Foundation of No.0133002
文摘Single-stripe laser was applied to acquire V-shape groove contour information. Most of arc light and splash noise was removed and stripe laser image was kept by wavelet transform. Half-threshold algorithm was used for image segmentation and stripe laser image was gotten after refining. Weld seam center position was identified and extracted by extreme curvature corner detection method. The location of torch was detected to accord the frequency of computer program with robot program and serial communication program. The tracking experiments of sidelong, reflex and curve weld line show that the system can meet the demand of the tracking precision under normal welding conditions.
基金the Aeronautics Science Foundation of China(20070153005)Astronautics Science Technology Innovation Foundation of China(05C53005)
文摘Aiming at the problem,i.e.infrared images own the characters of bad contrast ratio and fuzzy edges,a method to enhance the contrast of infrared image is given,which is based on stationary wavelet transform.After making stationary wavelet transform to an infrared image,denoising is done by the proposed method of double-threshold shrinkage in detail coefficient matrixes that have high noisy intensity.For the approximation coefficient matrix with low noisy intensity,enhancement is done by the proposed method based on histogram.The enhanced image can be got by wavelet coefficient reconstruction.Furthermore,an evaluation criterion of enhancement performance is introduced.The results show that this algorithm ensures target enhancement and restrains additive Gauss white noise effectively.At the same time,its amount of calculation is small and operation speed is fast.
基金Supported by the National Natural Science Foundation of China(No.60402036)the Natural Science Foundation of Beijing(No.4042008).
文摘The paper describes a texture-based fast text location scheme which operates directly in the Discrete Wavelet Transform (DWT) domain. By the distinguishing texture characteristics encoded in wavelet transform domain, the text is fast detected from complex background images stored in the compressed format such as JPEG2000 without full decompress. Compared with some traditional character location methods, the proposed scheme has the advantages of low computational cost, robust to size and font of characters and high accuracy. Preliminary experimental results show that the proposed scheme is efficient and effective.
文摘A novel approach using shift invariant wavelet transform is presented for the contrast enhancement of radiographs. By exploiting cross-scale correlation among wavelet coefficients, edge information of radiographic images is extracted and protected, while noise is smoothed out in the wavelet domain. Radiographs are then reconstructed from the transform coefficients modified at multi-scales by nonlinear enhancement operator. The method can achieve effectively contrast enhancement and edge-preserved denoising simultaneously, yet it is capable of giving visually distinct images and offering considerable benefits in medical diagnosis.
基金the National Natural Science Foundation of China(Nos.11721202 and 11772035)support from JSPS Research Fellowships for Young Scientists(2019~2022)。
文摘This paper first reviews the application research works of wavelet transform on the fluid mechanics. Then the theories of continuous wavelet transform and multi-dimensional orthogonal(discrete) wavelet transform, including wavelet multiresolution analysis, are introduced. At last the applications of wavelet transform on 2 D and 3 D turbulent wakes and turbulent boundary layer flows are described based on the hot-wire, 2 D particle image velocimetry(PIV) and 3 D tomographic PIV.
文摘To develop a quick, accurate and antinoise automated image registration technique for infrared images, the wavelet analysis technique was used to extract the feature points in two images followed by the compensation for input image with angle difference between them. A hi erarchical feature matching algorithm was adopted to get the final transform parameters between the two images. The simulation results for two infrared images show that the method can effectively, quickly and accurately register images and be antinoise to some extent.
文摘The construction of basic wavelet was discussed and many basic analyzing wavelets was compared. Acomplex analyzing wavelet which is continuous, smoothing, orthogonal and exponential decreasing was presented, andit was used to decompose two blasting seismic signals with the continuous wavelet transforms (CWT). The resultshows that wavelet analysis is the better method to help us determine the essential factors which create damage effectsthan Fourier analysis.
文摘A muitisensor image fusion algorithm is described using 2-dimensional nonseparable wavelet frame (NWF) transform. The source muitisensor images are first decomposed by the NWF transform. Then, the NWF transform coefficients of the source images are combined into the composite NWF transform coefficients. Inverse NWF transform is performed on the composite NWF transform coefficients in order to obtain the intermediate fused image. Finally, intensity adjustment is applied to the intermediate fused image in order to maintain the dynamic intensity range. Experiment resuits using real data show that the proposed algorithm works well in muitisensor image fusion.
基金supported by the National 863 Foundation under grant 863-2.5.1.25.
文摘The scientific satellite SST (Space Solar Telescope) is an important research project strongly supported by the Chinese Academy of Sciences. Every day, SST acquires 50 GB of data (after processing) but only 10GB can be transmitted to the ground because of limited time of satellite passage and limited channel volume. Therefore, the data must be compressed before transmission. Wavelets analysis is a new technique developed over the last 10 years, with great potential of application. We start with a brief introduction to the essential principles of wavelet analysis, and then describe the main idea of embedded zerotree wavelet coding, used for compressing the SST images. The results show that this coding is adequate for the job.