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* **Brightness** - | * **Brightness** - | ||
- | * **Correlation** - Correlation is a similarity measure between two data sets under an absolute scale between [-1,1]. It is calculated as showed by the next formula: | + | * **Correlation** - Correlation is a similarity measure between two data sets under an absolute scale between [-1,1]. It is calculated as shown by the next formula: |
{{ interimage:att_correlation.gif }} | {{ interimage:att_correlation.gif }} | ||
- | * **Covariance** - The covariance value represents the similarity degree between two data sets showing how correlated they are. Higher data correlation leads to higher covariance values. The calculus is showed by the following formula where N is the number of image elements for one given area. X(i) are the element values for each given index "i". | + | * **Covariance** - The covariance value represents the similarity degree between two data sets showing how correlated they are. Higher data correlation leads to higher covariance values. The calculus is shown by the following formula where N is the number of image elements for one given area. X(i) are the element values for each given index "i". |
{{ interimage:att_covariance.gif }} | {{ interimage:att_covariance.gif }} | ||
- | * **Entropy** - This is a randomness statistical measure that can be used to describe some texture features. Higher data randomness leads to higher entropy values. The calculus is done as showed by the next formula, where n is the number of distinct image element values and p(xi) is the occurrence frequence associated to that pixel value.: | + | * **Entropy** - This is a randomness statistical measure that can be used to describe some texture features. Higher data randomness leads to higher entropy values. The calculus is done as shown by the next formula, where n is the number of distinct image element values and p(xi) is the occurrence frequence associated to that pixel value.: |
{{ interimage:att_entropy.gif }} | {{ interimage:att_entropy.gif }} | ||
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* **MinPixelValue** - The minimum pixel value found inside one region for the given image band/channel. | * **MinPixelValue** - The minimum pixel value found inside one region for the given image band/channel. | ||
- | * **Mode** - Represents the most frequent value among a set of values. There are cases where mode value cannot exist and there are cases where its value it is not garanteed to be unique. Examples: | + | * **Mode** - Represents the most frequent value among a set of values. There are cases where a mode value cannot exist and there are cases where its value is not guaranteed to be unique. Examples: |
* 1,1,3,3,5,7,7,7,11,13 : Mode 7 | * 1,1,3,3,5,7,7,7,11,13 : Mode 7 | ||
- | * 3,5,8,11,13,18 : Mode value does not exists. | + | * 3,5,8,11,13,18 : Mode value does not exist. |
* 3,5,5,5,6,6,7,7,7,11,12 : Two mode values - 5 and 7 (bimodal). | * 3,5,5,5,6,6,7,7,7,11,12 : Two mode values - 5 and 7 (bimodal). | ||
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* **Ratio** - | * **Ratio** - | ||
- | * **StdDeviation** - The standart deviation represents the numerical data dispersion degree surrounding the mean. It is defined by: | + | * **StdDeviation** - The standard deviation represents the numerical data dispersion degree surrounding the mean. It is defined by: |
{{ interimage:att_stddev.gif }} | {{ interimage:att_stddev.gif }} | ||
- | * **SumPixelsValues** - Represents the sum of all elements values inside on area for one given image band/channel. | + | * **SumPixelsValues** - Represents the sum of all element values inside an area for one given image band/channel. |
- | * **Variance** - Like the standart deviation, the variance also represents the numerical data dispersion degree surrounding the mean but in the original data values scale. It is defined by: | + | a * **Variance** - Like the standard deviation, the variance also represents the numerical data dispersion degree surrounding the mean but in the original data value scale. It is defined by: |
{{ interimage:att_variance.gif }} | {{ interimage:att_variance.gif }} | ||
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===== Texture Attributes ===== | ===== Texture Attributes ===== | ||
- | The texture attributes are based on the co-occurence gray scale matrix (GLCM) described by the following references: | + | The texture attributes are based on the co-occurrence gray scale matrix (GLCM) described in the following references: |
- | * Textural Features for Image Classification - Robert M. Haralick, K. Shanmugam, Its'hak Dinstein. Systems, Man and Cybernetics, IEEE Transactions on In Systems, Man and Cybernetics, IEEE Transactions on, Vol. 3, No. 6. (1973), pp. 610-621. | + | * Textural Features for Image Classification - Robert M. Haralick, K. Shanmugam, Its'hak Dinstein. Systems, Man and Cybernetics, IEEE Transactions on Systems, Man and Cybernetics, IEEE Transactions on, Vol. 3, No. 6. (1973), pp. 610-621. |
* Computer and Robot Vision - Robert M. Haralick - Addison-Wesley Publishing Company. | * Computer and Robot Vision - Robert M. Haralick - Addison-Wesley Publishing Company. | ||
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- | * **Angular2ndMomentGLCM (a.k.a. EnergyGLCM)** - Returns the square sum of image points pairs occurrences under one pre-defined direction. The returned values range is between [0,1]. For those images without variations the value will be 1. The calculus is showed on the next formula where "i" and "j" are adjacent image points values under one pre-defined direction. p(i,j) is the probability of that co-ocurrence over the image. | + | * **Angular2ndMomentGLCM (a.k.a. EnergyGLCM)** - Returns the square sum of image point pairs occurrences under one pre-defined direction. The returned value range is between [0,1]. For those images without variations the value will be 1. The calculus is shown on the next formula where "i" and "j" are adjacent image point values under one pre-defined direction. p(i,j) is the probability of that co-occurrence over the image. |
{{ interimage:att_angular2ndmomentglcm.gif }} | {{ interimage:att_angular2ndmomentglcm.gif }} | ||
- | * **ContrastGLCM** - Returns a contrast intensity measure between one image point and its neighborhood. For those images without variations the contrast value will be zero. The calculus is showed on the next formula where "i" and "j" are adjacent image points values under one pre-defined direction. p(i,j) is the probability of that co-ocurrence over the image. | + | * **ContrastGLCM** - Returns a contrast intensity measure between one image point and its neighborhood. For those images without variations the contrast value will be zero. The calculus is shown on the next formula where "i" and "j" are adjacent image point values under one pre-defined direction. p(i,j) is the probability of that co-ocurrence over the image. |
{{ interimage:att_contrastglcm.gif }} | {{ interimage:att_contrastglcm.gif }} | ||
- | * **DissimilarityGLCM** - Returns one intensity measure quite similar to contrast between one point and its neighborhood. But the difference it that this measure has linear increments. The calculus is showed on the next formula where "i" and "j" are adjacent image points values under one pre-defined direction. p(i,j) is the probability of that co-ocurrence over the image. | + | * **DissimilarityGLCM** - Returns one intensity measure quite similar to contrast between one point and its neighborhood. But the difference it that this measure has linear increments. The calculus is shown on the next formula where "i" and "j" are adjacent image point values under one pre-defined direction. p(i,j) is the probability of that co-ocurrence over the image. |
{{ interimage:att_dissimilarityglcm.gif }} | {{ interimage:att_dissimilarityglcm.gif }} | ||
- | * **EntropyGLCM** - Like the simple statistical entropy the GLCM entropy also is a statistical measure of image data randomness. The difference is that it uses frequencies of gray levels co-ocurrences instead of using point values frequencies. The co-ocurrences matrix is used and the calculus is showed by the next formula where "i" and "j" are adjacent image points values under one pre-defined direction. p(i,j) is the probability of that co-ocurrence over the image. | + | * **EntropyGLCM** - Like the simple statistical entropy the GLCM entropy also is a statistical measure of image data randomness. The difference is that it uses frequencies of gray level co-ocurrences instead of using point value frequencies. The co-ocurrence matrix is used and the calculus is shown by the next formula where "i" and "j" are adjacent image point values under one pre-defined direction. p(i,j) is the probability of that co-ocurrence over the image. |
{{ interimage:att_entropyglcm.gif }} | {{ interimage:att_entropyglcm.gif }} | ||
- | * **HomogeneityGLCM** - Returns a value representing the distance between the distribuition of co-ocurrence matrix elements and those diagonal elements. The returned values range is between [0,1]. For images with low values variation the returned value will be near to zero. The calculus is showed by the next formula where "i" and "j" are adjacent image points values under one pre-defined direction. p(i,j) is the probability of that co-ocurrence over the image. | + | * **HomogeneityGLCM** - Returns a value representing the distance between the distribution of co-ocurrence matrix elements and those diagonal elements. The returned value range is between [0,1]. For images with low value, variation the returned value will be near zero. The calculus is shown by the next formula where "i" and "j" are adjacent image point values under one pre-defined direction. p(i,j) is the probability of that co-ocurrence over the image. |
{{ interimage:att_homogeneityglcm.gif }} | {{ interimage:att_homogeneityglcm.gif }} | ||
- | * **MeanGLCM** - The GLCM mean value is expressed in function of the frequency of co-ocorrence of image elements related to their neighborhood under one pre-defined direction. The calculus is showed by the next formula where "i" and "j" are adjacent image points values under one pre-defined direction. p(i,j) is the probability of that co-ocurrence over the image. | + | * **MeanGLCM** - The GLCM mean value is expressed in function of the frequency of co-occurrence of image elements related to their neighborhood under one pre-defined direction. The calculus is showed by the next formula where "i" and "j" are adjacent image points values under one pre-defined direction. p(i,j) is the probability of that co-ocurrence over the image. |
{{ interimage:att_meanglcm.gif }} | {{ interimage:att_meanglcm.gif }} | ||
- | * **QuiSquareGLCM** - This metric can be understood as a form of energy normalization expressed in function of the linear dependency gray levels for image elements. The calculus is showed by the next formulas where "i" and "j" are adjacent image points values under one pre-defined direction. p(i,j) is the probability of that co-ocurrence over the image. Pj is the marginal probability for that co-ocurrence. | + | * **QuiSquareGLCM** - This metric can be understood as a form of energy normalization expressed in function of the linear dependency gray levels for image elements. The calculus is shown by the next formulas where "i" and "j" are adjacent image point values under one pre-defined direction. p(i,j) is the probability of that co-ocurrence over the image. Pj is the marginal probability for that co-ocurrence. |
{{ interimage:att_quisquareglcm_1.gif }} | {{ interimage:att_quisquareglcm_1.gif }} | ||
{{ interimage:att_quisquareglcm_2.gif }} | {{ interimage:att_quisquareglcm_2.gif }} | ||
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- | * **StdDeviationGLCM** - The standart deviation is a measure that represents the values dispersion around a GLCM mean value. The GLCM standart deviation calcule differs from the simple standart deviation because the use of co-ocurrence frequencies. The calculus is showed by the next formula where "i" and "j" are adjacent image points values under one pre-defined direction. p(i,j) is the probability of that co-ocurrence over the image. | + | * **StdDeviationGLCM** - The standard deviation is a measure that represents the value dispersion around a GLCM mean value. The GLCM standard deviation calculus differs from the simple standard deviation because the use of co-occurrence frequencies. The calculus is shown by the next formula where "i" and "j" are adjacent image point values under one pre-defined direction. p(i,j) is the probability of that co-ocurrence over the image. |
{{ interimage:att_stddeviationglcm.gif }} | {{ interimage:att_stddeviationglcm.gif }} | ||
===== Neighborhood Attributes ===== | ===== Neighborhood Attributes ===== | ||
- | * **existenceOf** - existence of an neighbor object belonging to the selected class **C** in a certain range **R** (in pixels) around the image object. If at least one object is found the value is 1 (true), othewise it would be 0 (false). The distance between the image object and its neighbors is calculated considering their centroids. If (**R**=0) only direct neighbors will be considered. | + | * **existenceOf** - existence of an neighbor object belonging to the selected class **C** in a certain range **R** (in pixels) around the image object. If at least one object is found the value is 1 (true), otherwise it would be 0 (false). The distance between the image object and its neighbors is calculated considering their centroids. If (**R**=0) only direct neighbors will be considered. |
* **numberOf** - number of neighbor objects belonging to the selected class **C** in a certain range **R** (in pixels) around the image object. The distance between the image object and its neighbors is calculated considering their centroids. If (**R**=0) only direct neighbors will be considered. | * **numberOf** - number of neighbor objects belonging to the selected class **C** in a certain range **R** (in pixels) around the image object. The distance between the image object and its neighbors is calculated considering their centroids. If (**R**=0) only direct neighbors will be considered. |