Automatic matching method of cross-modal neuron images

Abstract

The application provides an automatic matching method of cross-modal neuron images, which is used for matching corresponding neurons on a two-dimensional two-photon cell image and a three-dimensional fMOST cell image, and comprises the following steps: S1. fMOST cell image library construction; S2. two-photon cell image preprocessing; and S3. cell image matching. The automatic matching method of cross-modal neuron images is used for constructing a two-dimensional fMOST cell image library by using a three-dimensional fMOST cell image, and realizes automatic matching of a two-photon cell image and an fMOST cell image based on local cell image similarity, so that artificial intervention is not needed, human experience is not relied on, and human subjectivity is not influenced, and the accuracy is relatively high, and the method can be used for marking relatively dense brain image data.

Description

Technical Field

[0001] This invention relates to the field of image processing technology, and in particular to an automatic matching method for cross-modal neuronal images based on local cell image similarity. Background Technology

[0002] The brain is the highest center of the nervous system and the most important and complex organ in the human body. Like an incredibly sophisticated central processing unit, it controls all advanced human functions, including consciousness, emotion, learning, and memory. Hundreds of billions of neurons in the brain are interconnected to form extremely complex neural networks, enabling the brain to continuously receive, process, and transmit information.

[0003] To gain a more comprehensive and in-depth understanding of the brain and nervous system, it is necessary to grasp the functions, morphological structures, and interconnections of neurons. The key to this research lies in simultaneously acquiring functional information of neurons and complete structural information of the entire brain. By performing functional and structural imaging of neurons separately, and then confirming the correspondence between neurons in the two imaging methods, the goal of integrating structural and functional information can be achieved. This process requires matching the neuronal image data obtained from the two imaging methods.

[0004] The specific task of matching is to match corresponding neurons in a two-dimensional two-photon image with a three-dimensional fMOST image. Cross-modal neuron image matching is currently mainly achieved through manual matching methods. The general steps of this method are to use information such as blood vessels obtained from the two imaging methods to assist in image localization and orientation correction, and then perform manual matching based on the morphological characteristics and positional relationships of neurons. This method relies on manual judgment of neuron correspondences, which is highly subjective and requires a certain level of operator experience. Furthermore, manual searching becomes extremely difficult, time-consuming, and labor-intensive when data labels are dense. Summary of the Invention

[0005] Based on the aforementioned deficiencies of the existing technology, the present invention provides an automatic matching method for cross-modal neuron images that does not require human intervention, does not rely on human experience, is not affected by human subjectivity, has high accuracy, and can be used for data with dense neuron labels.

[0006] To achieve the above objectives, this invention provides an automatic matching method for cross-modal neuron images, used to match corresponding neurons in two-dimensional two-photon cell images with three-dimensional fMOST cell images, including:

[0007] Step S1. fMOST cell image library construction: Extract target image patches, cell body detection, edge detection, and image projection from the three-dimensional fMOST cell images to construct a two-dimensional fMOST cell image library;

[0008] Step S2. Two-photon cell image preprocessing: The two-dimensional two-photon cell image is enhanced with edge information, contrast is increased, parameters are standardized, and filtered to obtain the two-photon cell image to be matched;

[0009] Step S3. Cell Image Matching: Input the two-photon cell images to be matched into the fMOST cell image library, and use the "normalized correlation coefficient and normalized mutual information combination method" to calculate the cell image similarity for matching. Select the two-dimensional fMOST cell image with the highest similarity as the matching result. The "normalized correlation coefficient and normalized mutual information combination method" is a method of weighted summation of "normalized correlation coefficient" and "normalized mutual information".

[0010] In one embodiment, step S1 includes:

[0011] Step S11. Extract the target image patch: Present the three-dimensional fMOST cell image data in the visualization software Amira, and then extract the high-brightness image patch. This part of the data is the location of the marked neuron cell body.

[0012] Step S12. Cell body detection: Use the trained target detection model to identify each cell body in the image patch, and save the cell body position information in the form of three-dimensional coordinates as an SWC file, and output the SWC file that records the cell body coordinates;

[0013] Step S13. Edge detection: Use the Sobel edge detection operator to detect the edge information of the image;

[0014] Step S14. Image Projection: The cortical surface edge information is represented by edge points. The principal direction of the edge points is obtained by principal component analysis. Then, the direction perpendicular to the principal direction is used as the projection direction of the fMOST cell image. Each cell body in the three-dimensional fMOST cell image is projected according to the projection direction to obtain a two-dimensional fMOST cell image library of all cell bodies in this set of data.

[0015] In one embodiment, in step S11,

[0016] The voxel resolution of the three-dimensional fMOST cell image is 0.325×0.325×1μm3, and the voxel resolution of the image patch is set to 0.65×0.65×2μm3. The voxel resolution of the image patch is converted to an isotropic 0.65×0.65×0.65μm3 using the Resample tool in Amira software.

[0017] In one embodiment, step S13 includes: first converting the grayscale image into a binary image, then cleaning and smoothing the image through morphological opening and closing operations, repairing it with hole filling operations, and finally using the Sobel edge detection operator to detect the edge information of the binary image.

[0018] In one embodiment, step S2 includes:

[0019] Step S21. Two-photon cell image edge enhancement: The two-photon cell image is enhanced using the DeepCAD plugin in Fiji;

[0020] Step S22. Two-photon cell image contrast enhancement: The contrast of the two-photon cell image is enhanced using the principle of fuzzy sets;

[0021] Step S23. Two-photon cell image parameter standardization: Adjust the parameters of the two-photon cell image to be consistent with the two-dimensional fMOST cell image;

[0022] Step S24. Two-photon cell image screening: The two-photon cell images are screened according to quality standards. Those that meet the quality standards are retained, and those that do not meet the quality standards are removed. The quality standard is "the edge information of the cell body in the two-photon image is clear and regular".

[0023] In one embodiment, step S21 includes:

[0024] The DeepCAD plugin in Fiji is used to enhance the two-photon cell image. The enhanced two-photon cell image can be obtained by projecting the enhanced two-photon cell image.

[0025] In one embodiment, in step S22, the pixel grayscale value of the final output image is:

[0026]

[0027] Where v0 represents the pixel grayscale value of the output image, μ d (p0), μ g (p0), μ b (p0) represents the membership degree of the original pixel p0 to the three sets of dark, gray, and light, respectively. d The value of v is set to 0. g The value is set to 128, v b The value is set to 255.

[0028] In one embodiment, the parameters in step S23 include the image orientation, resolution, size, and bit depth. The image orientation is verified and adjusted by combining the vascular planar image of the cranial window in two-photon cell images and the vascular image of the cortical surface in fMOST cell images. For two-photon cell images with a resolution lower than that of fMOST cell images, the resolution is improved by linear interpolation.

[0029] In one embodiment, in step S3, the "normalized correlation coefficient" is used to evaluate the correlation between two images, and the formula is as follows:

[0030]

[0031] Where X and Y represent two images to be matched, n represents the number of pixels in the image, and x i and y i These represent the values ​​of the i-th pixel in images X and Y, respectively. and represents the average pixel value in images X and Y, respectively; the normalized correlation coefficient NCC(X,Y) of the two images ranges from [-1,1]. When the value is 1, it means that the two images are completely correlated, and when the value is -1, it means that they are completely uncorrelated. Therefore, the larger the value, the greater the similarity between the images.

[0032] In one embodiment, in step S3, the "normalized mutual information" is a method for calculating the similarity between images using the principles of information theory, as shown in the following formula:

[0033]

[0034] M and N represent two images to be matched, and I(M,N) is the mutual information between the two images, representing the correlation between the images, as shown in the following formula:

[0035]

[0036] H(M) and H(N) are the entropies of images M and N, respectively, representing the amount of information in the images, as shown in the following formulas:

[0037] H(M)=-∑ m∈M p(m)log p(m);

[0038] H(N)=-∑ n∈N p(n)log p(n);

[0039] p(m,n) is the joint probability distribution of M and N taking values ​​m and n simultaneously, while p(m) and p(n) are the marginal probability distributions of M and N, respectively; where p(m) is the probability distribution of pixel value m in image M; the normalized mutual information NMI(M,N) of two images ranges from [0,1]. The larger the value, the greater the amount of information shared between the images, the higher the correlation, and the greater the similarity between the images.

[0040] This invention provides an automatic matching method for cross-modal neuronal images. It utilizes three-dimensional fMOST cell images to construct a two-dimensional fMOST cell image library. Based on local cell image similarity, it achieves automatic matching between two-photon cell images and fMOST cell images. This method does not require human intervention, does not rely on human experience, and is not affected by human subjectivity. Moreover, it has high accuracy and can be used for densely labeled brain image data. Attached Figure Description

[0041] The accompanying drawings described herein are for illustrative purposes only and are not intended to limit the scope of the invention in any way. Furthermore, the shapes and proportions of the components in the drawings are merely illustrative to aid in understanding the invention and are not intended to specifically limit the shapes and proportions of the components. Those skilled in the art, guided by the teachings of this invention, can select various possible shapes and proportions to implement the invention according to specific circumstances. In the drawings:

[0042] Figure 1 A flowchart illustrating an automatic matching method for cross-modal neuron images provided in the first embodiment of the present invention;

[0043] Figure 2 for Figure 1 Detailed flowchart of step S1;

[0044] Figure 3 for Figure 1 Detailed flowchart of step S2;

[0045] Figure 4 for Figure 2 A detailed flowchart illustrating step S1.

[0046] Figure 5 for Figure 3 A schematic diagram showing the comparison effect of step S21;

[0047] Figure 6 for Figure 3 A diagram illustrating the demonstration and comparison of steps S22. Detailed Implementation

[0048] To enable those skilled in the art to better understand the technical solutions of this invention, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this invention.

[0049] Please see Figure 1 As shown, the first embodiment of the present invention provides an automatic matching method for cross-modal neuron images, used to match corresponding neurons on two-dimensional two-photon cell images with three-dimensional fMOST cell images, including:

[0050] Step S1. fMOST cell image library construction: Extract target image patches, cell body detection, edge detection, and image projection from the three-dimensional fMOST cell images to construct a two-dimensional fMOST cell image library;

[0051] Step S2. Two-photon cell image preprocessing: The two-dimensional two-photon cell image is enhanced with edge information, contrast is increased, parameters are standardized, and filtered to obtain the two-photon cell image to be matched;

[0052] Step S3. Cell Image Matching: Input the two-photon cell images to be matched into the fMOST cell image library, and use the "normalized correlation coefficient and normalized mutual information combination method" to calculate the cell image similarity for matching. Select the two-dimensional fMOST cell image with the highest similarity as the matching result. The "normalized correlation coefficient and normalized mutual information combination method" is a method of weighted summation of "normalized correlation coefficient" and "normalized mutual information".

[0053] Please refer to the following: Figure 2 , Figure 4 As shown, in one embodiment, step S1 specifically includes:

[0054] Step S11. Extract the target image patch: Present the three-dimensional fMOST cell image data in the visualization software Amira, and then extract the high-brightness image patch. This part of the data is the location of the marked neuron cell body.

[0055] Step S12. Cell body detection: Use the trained target detection model to identify each cell body in the image patch, and save the cell body position information in the form of three-dimensional coordinates as an SWC file, and output the SWC file that records the cell body coordinates;

[0056] Step S13. Edge detection: Use the Sobel edge detection operator to detect the edge information of the image;

[0057] Step S14. Image Projection: The cortical surface edge information is represented by edge points. The principal direction of the edge points is obtained by principal component analysis. Then, the direction perpendicular to the principal direction is used as the projection direction of the fMOST cell image. Each cell body in the three-dimensional fMOST cell image is projected according to the projection direction to obtain a two-dimensional fMOST cell image library of all cell bodies in this set of data.

[0058] In one embodiment, in step S11,

[0059] The voxel resolution of the three-dimensional fMOST cell image is 0.325×0.325×1μm3. In order to reduce memory and video memory overhead in subsequent steps and speed up processing, the voxel resolution of the image block is set to 0.65×0.65×2μm3. The voxel resolution of the image block is converted to an isotropic 0.65×0.65×0.65μm3 using the Resample tool in Amira software. The principle of this tool to improve axial resolution is linear interpolation.

[0060] In one embodiment, step S13 includes: first converting the grayscale image into a binary image, then cleaning and smoothing the image through morphological opening and closing operations, repairing it with hole filling operations, and finally using the Sobel edge detection operator to detect the edge information of the binary image.

[0061] The two-dimensional fMOST cell image library obtained in step S14 consists of multiple two-dimensional fMOST cell images.

[0062] Please see Figure 3 As shown, in one embodiment, step S2 specifically includes:

[0063] Step S21. Two-photon cell image edge enhancement: The two-photon cell image is enhanced using the DeepCAD plugin in Fiji;

[0064] Step S22. Two-photon cell image contrast enhancement: The contrast of the two-photon cell image is enhanced using the principle of fuzzy sets;

[0065] Step S23. Two-photon cell image parameter standardization: Adjust the parameters of the two-photon cell image to be consistent with the two-dimensional fMOST cell image;

[0066] Step S24. Two-photon cell image screening: The two-photon cell images are screened according to quality standards. Those that meet the quality standards are retained, and those that do not meet the quality standards are removed. The quality standard is "the edge information of the cell body in the two-photon image is clear and regular".

[0067] Please refer to the following: Figure 5 As shown, in one embodiment, step S21 specifically includes:

[0068] Two-photon cell images are enhanced using the DeepCAD plugin in Fiji. Projecting the enhanced two-photon cell image yields a two-dimensional enhanced two-photon cell image. In one specific embodiment, the DeepCAD plugin in Fiji is used to enhance a three-dimensional xyt two-photon cell image. Projecting the enhanced three-dimensional two-photon cell image yields a two-dimensional enhanced two-photon cell image. Since two-photon cell images are spatially two-dimensional, the three-dimensional xyt two-photon cell image here represents the change of the image at the same location over time. It is only used for image enhancement; the projected enhanced image remains two-dimensional, and the image used for matching is also two-dimensional. Figure 5 (A) is the cell image before edge enhancement. Figure 5 (B) is the cell image after edge information enhancement.

[0069] Please refer to the following: Figure 6 As shown, in one embodiment, in step S22, the pixel grayscale value of the final output image is:

[0070]

[0071] Where v0 represents the pixel grayscale value of the output image, μ d (p0), μ g (p0), μ b (p0) represents the membership degree of the original pixel p0 to the three sets of dark, gray, and light, respectively. d The value of v is set to 0. g The value is set to 128, v b The value is set to 255. Figure 6 (A) is the cell image before contrast enhancement. Figure 6 (B) is a cell image with enhanced contrast.

[0072] In one embodiment, step S23 includes parameters such as image orientation, resolution, size, and bit depth. The image orientation is verified and adjusted by combining a vascular planar image of the cranial window from a two-photon cell image with a vascular image of the cortical surface from an fMOST cell image. For two-photon cell images with a resolution lower than that of fMOST cell images, linear interpolation is used to improve the resolution. Because the imaging orientations of the two imaging methods are generally roughly the same, the image orientation can be verified and adjusted by combining a vascular planar image of the cranial window from a two-photon cell image with a vascular image of the cortical surface from an fMOST cell image.

[0073] In one embodiment, in step S3, the "normalized correlation coefficient" is used to evaluate the correlation between two images, and the formula is as follows:

[0074]

[0075] Where X and Y represent two images to be matched, n represents the number of pixels in the image, and x i and y i These represent the values ​​of the i-th pixel in images X and Y, respectively. and represents the average pixel value in images X and Y, respectively; the normalized correlation coefficient NCC(X,Y) of the two images ranges from [-1,1]. When the value is 1, it means that the two images are completely correlated, and when the value is -1, it means that they are completely uncorrelated. Therefore, the larger the value, the greater the similarity between the images.

[0076] In one embodiment, in step S3, the "normalized mutual information" is a method for calculating the similarity between images using the principles of information theory, as shown in the following formula:

[0077]

[0078] M and N represent two images to be matched, and I(M,N) is the mutual information between the two images, representing the correlation between the images, as shown in the following formula:

[0079]

[0080] H(M) and H(N) are the entropies of images M and N, respectively, representing the amount of information in the images, as shown in the following formulas:

[0081] H(M)=-∑ m∈M p(m)log p(m);

[0082] H(N)=-∑ n∈N p(n)log p(n);

[0083] p(m,n) is the joint probability distribution of M and N taking values ​​m and n simultaneously, while p(m) and p(n) are the marginal probability distributions of M and N, respectively; where p(m) is the probability distribution of pixel value m in image M; the normalized mutual information NMI(M,N) of two images ranges from [0,1]. The larger the value, the greater the amount of information shared between the images, the higher the correlation, and the greater the similarity between the images.

[0084] The fMOST cell image with the highest similarity is selected as the matching result, and the cell image and its corresponding cell body coordinates are output. The cell body coordinates can be used to find the position of the cell in the 3D fMOST cell image, and the image features can be manually compared for verification.

[0085] The inventors applied the method of this invention to 12 sets of mouse brain data for matching tests, and the matching results are shown in Table 1 below.

[0086] Table 1. Basic Data Information and Matching Test Results

[0087]

[0088]

[0089] The accuracy rate of matching all two-photon cell images was above 70%, mainly ranging from 70% to 90%. A total of 205 two-photon cell images were matched, with 159 accurate matches, resulting in an overall accuracy rate of 77.6%.

[0090] This invention provides an automatic matching method for cross-modal neuronal images. It utilizes three-dimensional fMOST cell images to construct a two-dimensional fMOST cell image library. Based on local cell image similarity, it achieves automatic matching between two-photon cell images and fMOST cell images. This method requires no manual intervention, is independent of human experience, and is unaffected by human subjectivity. Furthermore, it boasts high accuracy and can be used for densely labeled brain image data. Its main advantages are as follows:

[0091] 1. This invention significantly improves the accuracy of the matching method by using two-photon cell image enhancement as a preprocessing step for cell image matching for the first time.

[0092] 2. This invention proposes a strategy of combining matching methods with accuracy as a weight, which improves the accuracy of the combined matching methods compared to the single matching methods.

[0093] 3. This invention solves some key problems existing in previous manual neuron matching methods. Since the matching process is automatic, it solves the difficulty of manually searching for dense data, and therefore can be used for labeling relatively dense neuron data.

[0094] 4. This invention utilizes the similarity of cell images as a quantitative indicator for automatic neuron matching, which greatly improves the matching efficiency and eliminates the influence of subjective factors on the matching results.

[0095] It should be understood that the above description is for illustrative purposes and not for limitation. Many embodiments and applications beyond the provided examples will be apparent to those skilled in the art upon reading the above description. Therefore, the scope of this teaching should not be determined by reference to the above description, but rather by reference to the foregoing claims and the full scope of their equivalents. For purposes of completeness, all articles and references, including patent applications and publications, are incorporated herein by reference. The omission of any aspect of the subject matter disclosed herein in the foregoing claims is not intended as a waiver of that subject matter, nor should it be construed as an indication that the applicant has not considered that subject matter as part of the disclosed application subject matter.

Claims

1. An automatic matching method for cross-modal neuron images, used to match corresponding neurons in two-dimensional two-photon cell images with three-dimensional fMOST cell images, characterized in that, include: Step S1. fMOST cell image library construction: Extract target image patches, cell body detection, edge detection, and image projection from the three-dimensional fMOST cell images to construct a two-dimensional fMOST cell image library; Step S2. Two-photon cell image preprocessing: The two-dimensional two-photon cell image is enhanced with edge information, contrast is increased, parameters are standardized, and filtered to obtain the two-photon cell image to be matched; Step S3. Cell Image Matching: Input the two-photon cell images to be matched into the fMOST cell image library, and use the "normalized correlation coefficient and normalized mutual information combination method" to calculate the cell image similarity for matching. Select the two-dimensional fMOST cell image with the highest similarity as the matching result. The "normalized correlation coefficient and normalized mutual information combination method" is a method of weighted summation of "normalized correlation coefficient" and "normalized mutual information".

2. The automatic matching method for cross-modal neuron images as described in claim 1, characterized in that, Step S1 includes: Step S11. Extract the target image patch: Present the three-dimensional fMOST cell image data in the visualization software Amira, and then extract the high-brightness image patch. This part of the data is the location of the marked neuron cell body. Step S12. Cell body detection: Use the trained target detection model to identify each cell body in the image patch, and save the cell body position information in the form of three-dimensional coordinates as an SWC file, and output the SWC file that records the cell body coordinates; Step S13. Edge detection: Use the Sobel edge detection operator to detect the edge information of the image; Step S14. Image Projection: The cortical surface edge information is represented by edge points. The principal direction of the edge points is obtained by principal component analysis. Then, the direction perpendicular to the principal direction is used as the projection direction of the fMOST cell image. Each cell body in the three-dimensional fMOST cell image is projected according to the projection direction to obtain a two-dimensional fMOST cell image library of all cell bodies in this set of data.

3. The automatic matching method for cross-modal neuron images as described in claim 2, characterized in that, In step S11 The voxel resolution of the three-dimensional fMOST cell image is 0.325×0.325×1μm3, and the voxel resolution of the image patch is set to 0.65×0.65×2μm3. The voxel resolution of the image patch is converted to an isotropic 0.65×0.65×0.65μm3 using the Resample tool in Amira software.

4. The automatic matching method for cross-modal neuron images as described in claim 2, characterized in that, Step S13 includes: first converting the grayscale image into a binary image, then cleaning and smoothing the image through morphological opening and closing operations, repairing it with hole filling operations, and finally using the Sobel edge detection operator to detect the edge information of the binary image.

5. The automatic matching method for cross-modal neuron images as described in claim 1, characterized in that, Step S2 includes: Step S21. Two-photon cell image edge enhancement: The two-photon cell image is enhanced using the DeepCAD plugin in Fiji; Step S22. Two-photon cell image contrast enhancement: The contrast of the two-photon cell image is enhanced using the principle of fuzzy sets; Step S23. Two-photon cell image parameter standardization: Adjust the parameters of the two-photon cell image to be consistent with the two-dimensional fMOST cell image; Step S24. Two-photon cell image screening: The two-photon cell images are screened according to quality standards. Those that meet the quality standards are retained, and those that do not meet the quality standards are removed. The quality standard is "the edge information of the cell body in the two-photon image is clear and regular".

6. The automatic matching method for cross-modal neuron images as described in claim 5, characterized in that, Step S21 includes: The DeepCAD plugin in Fiji is used to enhance the two-photon cell image. The enhanced two-photon cell image can be obtained by projecting the enhanced two-photon cell image.

7. The automatic matching method for cross-modal neuron images as described in claim 5, characterized in that, In step S22, the pixel grayscale values ​​of the final output image are: Where v0 represents the pixel grayscale value of the output image, μ d (p0), μ g (p0), μ b (p0) represents the membership degree of the original pixel p0 to the three sets of dark, gray, and light, respectively. d The value of v is set to 0. g The value is set to 128, v b The value is set to 255.

8. The automatic matching method for cross-modal neuron images as described in claim 5, characterized in that, In step S23, the parameters include the image orientation, resolution, size, and bit depth. The image orientation is verified and adjusted by combining the vascular planar image of the cranial window in two-photon cell images and the vascular image of the cortical surface in fMOST cell images. For two-photon cell images with a resolution lower than that of fMOST cell images, the resolution is improved by linear interpolation.

9. The automatic matching method for cross-modal neuron images as described in claim 1, characterized in that, In step S3, the "normalized correlation coefficient" is used to evaluate the correlation between two images, and the formula is as follows: Where X and Y represent two images to be matched, n represents the number of pixels in the image, and x i and y i These represent the values ​​of the i-th pixel in images X and Y, respectively. and represents the average pixel value in images X and Y, respectively; the normalized correlation coefficient NCC(X,Y) of the two images ranges from [-1,1]. When the value is 1, it means that the two images are completely correlated, and when the value is -1, it means that they are completely uncorrelated. Therefore, the larger the value, the greater the similarity between the images.

10. The automatic matching method for cross-modal neuron images as described in claim 1, characterized in that, In step S3, the "normalized mutual information" is a method for calculating the similarity between images using the principles of information theory, as shown in the following formula: M and N represent two images to be matched, and i(M,N) is the mutual information between the two images, representing the correlation between the images, as shown in the following formula: H(M) and H(N) are the entropies of images M and N, respectively, representing the amount of information in the images, as shown in the following formulas: H(M)=-∑ m∈M p(m)log p(m); H(N)=-∑ n∈N p(n)log p(n); p(m,n) is the joint probability distribution of M and N taking values ​​m and m, respectively, while p(m) and p(n) are the marginal probability distributions of M and N, respectively; where p(m) is the probability distribution of pixel value m in image M; the normalized mutual information NMI(M,N) of two images ranges from [0,1]. The larger the value, the greater the amount of information shared between the images, the higher the correlation, and the greater the similarity between the images.

Images