CN114627056B - Real-time high-precision children auricle deformity detection method - Google Patents
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- 238000001514 detection method Methods 0.000 title claims abstract description 53
- 238000005070 sampling Methods 0.000 claims abstract description 21
- 210000005069 ears Anatomy 0.000 claims abstract description 9
- 238000000034 method Methods 0.000 claims abstract description 9
- 230000005484 gravity Effects 0.000 claims abstract description 8
- 239000011159 matrix material Substances 0.000 claims description 30
- 238000001914 filtration Methods 0.000 claims description 14
- 230000007797 corrosion Effects 0.000 claims description 12
- 238000005260 corrosion Methods 0.000 claims description 12
- 230000009466 transformation Effects 0.000 claims description 12
- 238000010586 diagram Methods 0.000 claims description 10
- CLOMYZFHNHFSIQ-UHFFFAOYSA-N clonixin Chemical compound CC1=C(Cl)C=CC=C1NC1=NC=CC=C1C(O)=O CLOMYZFHNHFSIQ-UHFFFAOYSA-N 0.000 claims description 6
- 238000012805 post-processing Methods 0.000 claims description 3
- 238000007781 pre-processing Methods 0.000 claims description 3
- 208000032170 Congenital Abnormalities Diseases 0.000 description 35
- 206010061619 Deformity Diseases 0.000 description 34
- 238000012217 deletion Methods 0.000 description 4
- 230000037430 deletion Effects 0.000 description 4
- 230000035772 mutation Effects 0.000 description 4
- 108090000623 proteins and genes Proteins 0.000 description 4
- 210000000624 ear auricle Anatomy 0.000 description 3
- 230000036244 malformation Effects 0.000 description 3
- 230000002159 abnormal effect Effects 0.000 description 2
- 230000006870 function Effects 0.000 description 2
- 206010010356 Congenital anomaly Diseases 0.000 description 1
- 206010058314 Dysplasia Diseases 0.000 description 1
- 208000016621 Hearing disease Diseases 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 210000000845 cartilage Anatomy 0.000 description 1
- 210000000959 ear middle Anatomy 0.000 description 1
- 238000005457 optimization Methods 0.000 description 1
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/0002—Inspection of images, e.g. flaw detection
- G06T7/0012—Biomedical image inspection
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B5/00—Measuring for diagnostic purposes; Identification of persons
- A61B5/72—Signal processing specially adapted for physiological signals or for diagnostic purposes
- A61B5/7235—Details of waveform analysis
- A61B5/725—Details of waveform analysis using specific filters therefor, e.g. Kalman or adaptive filters
-
- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B5/00—Measuring for diagnostic purposes; Identification of persons
- A61B5/72—Signal processing specially adapted for physiological signals or for diagnostic purposes
- A61B5/7235—Details of waveform analysis
- A61B5/7253—Details of waveform analysis characterised by using transforms
- A61B5/7257—Details of waveform analysis characterised by using transforms using Fourier transforms
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/10—Segmentation; Edge detection
- G06T7/194—Segmentation; Edge detection involving foreground-background segmentation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/60—Analysis of geometric attributes
-
- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B2503/00—Evaluating a particular growth phase or type of persons or animals
- A61B2503/06—Children, e.g. for attention deficit diagnosis
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/30—Subject of image; Context of image processing
- G06T2207/30004—Biomedical image processing
Abstract
The invention relates to a real-time high-precision children auricle deformity detection method, which solves the technical problems of low real-time and low accuracy, and comprises the steps of extracting images containing ears of children as target images by adopting multiple angles, separating and processing image backgrounds, wherein each angle corresponds to one image, and optionally determining one image; defining the top left corner vertex of the minimum circumscribed rectangle of the target image, intercepting an optimized image calculation center, calculating the center of gravity of the target image, translating the center of gravity of the target image to the optimized image center, and determining the center as a centroid point; the technical scheme that the distance from the sampling boundary point to the centroid point is calculated as the radius, the normalized radius sequence and the absolute value of the difference between the normalized radii of the adjacent 2 sampling boundary points is larger than a predefined threshold range is regarded as the possible deformity, so that the problem is well solved, and the method can be used for detecting the ear deformity of children.
Description
Technical Field
The invention relates to the field of detection of ear deformity of children, in particular to a real-time high-precision detection method of auricle deformity of children.
Background
The auricle malformation is congenital auricle developmental malformation, and the malformation degree can be greatly different. The most severe deformity appears as no ear, the lightest one presents a morphology approximating the auricle, but significantly less than normal. Both of these conditions are less common. Most small ear deformities are composed of small cartilage masses which shrink without auricular morphology, and earlobes which are more normal in shape but displaced forward and upward. Has no external auditory meatus or tympanic cavity, and has auditory osseous dysplasia, and hearing disorder.
The existing children ear deformity detection technology has the technical problems of low real-time performance and low accuracy. The invention provides a real-time high-precision detection method for auricle deformity of children, which aims to solve the technical problems.
Disclosure of Invention
The technical problems to be solved by the invention are the technical problems of low real-time performance and low accuracy in the prior art. The novel real-time high-precision children auricle deformity detection method has the characteristics of high real-time performance and high accuracy.
In order to solve the technical problems, the technical scheme adopted is as follows:
a real-time high-precision detection method for pinna deformity of children, the real-time high-precision detection method for pinna deformity of children comprising:
step S1, extracting images containing ears of children as target images at multiple angles, separating image backgrounds, wherein each angle corresponds to one image, and optionally determining one image to execute step S2;
step S2, defining (N, M) as the number of pixels of the abscissa of the minimum circumscribed rectangle of the target image;
s3, taking the top left corner vertex of the minimum circumscribed matrix of the target image, and taking the image size (L, L) as an optimized image;
r max k=max (N/2, m/2) for the maximum distance from the object boundary point to the center;
step S4, calculating the center of gravity of the target imageOptimizing the center of the image (x 0 ，y 0 ) According to a translation functionShifting the center of gravity of the target image to the optimized image center (x 0 ，y 0 ) Thereafter, the (x) 0 ，y 0 ) Determining as a centroid point;
step S5, determining sampling boundary points by taking the equal pixel spacing as a sampling step length, and calculating a kth sampling boundary point (x k ，y k ) To centroid point (x) 0 ，y 0 ) Is defined as the distance ofRadius:
step S6, calculating normalized radius sequence asCalculating the absolute value Deltar of the difference between the normalized radii of every two adjacent sampling boundary points n (m)＝|r n (k+1)-r n (k) I, m=0, 1..k-1, k is a positive integer greater than 1, determining Δr n The magnitude of (m), e.g. Deltar n (m) regarding a possible deformity greater than a predefined threshold range, defining each of the aforementioned 2 adjacent sampling boundary points as a possible point of deformity;
and S7, reselecting one image, returning to the step S2, until all the images are traversed, defining that the possible point of distortion is ear distortion, and otherwise, defining that the possible point of distortion is normal.
The working principle of the invention is as follows: the invention changes the existing gene detection and image contrast detection in children ear deformity detection, changes deformity detection into shape mutation or deletion detection, and improves detection efficiency and instantaneity. On the basis, the shape of the contour abrupt change is detected and defined as a possible distortion point by calculating the absolute value of the difference between the normalized radii of every adjacent 2 sampling boundary points. And further, through counting and calculating the number of possible distortion points, a threshold is preset, so that the detection accuracy is improved.
In the above scheme, for optimization, the method for detecting the ear deformity of the child further comprises:
and S8, calculating the possibility of deformity after all the patterns are detected, wherein the possibility of deformity is larger than a predefined threshold value, and the deformity is regarded as the deformity of the ears of the children.
Further, step S1 further includes performing image enhancement filtering on the image, including:
s11, use (-1) x+y Multiplying the input image F (x, y) by the central transformation to finish image preprocessing, and then calculating Fourier transformation to F (u, v);
s12, the filtering function H (u, v) is multiplied by F (u, v) to complete the filtering G (u, v) =h (u, v) ×f (u, v);
wherein D (u, v) is the distance from the origin of the Fourier transform, and sigma is the expansion coefficient of the Gaussian curve;
s13, performing Fourier inverse transformation;
s14, taking the real part of the Fourier inverse transformation, multiplying by (-1) x+y And finishing the image post-processing to obtain an enhanced image f' (x, y).
Further, step S6 further includes:
step S61, taking any possible distortion point as a midpoint, intercepting an image with the size of N multiplied by M to be defined as a fine image, dividing the fine image into blocks with the size of w multiplied by w, and calculating the pixel mean value avg_local and the mean square error local of each block;
bloc (i, j) refers to the pixel value of the pixel point (i, j), i is less than or equal to M, j is less than or equal to N;
step S62, comparing the mean square value local of each block with a predefined threshold value, defining k1 times of the maximum value of each block as the threshold value, taking the value 1 if the mean square value local is larger than the threshold value, otherwise taking the value 0, and traversing to obtain a logic matrix, wherein k1 is a constant;
step S63, defining a closed operation coefficient and a corrosion operation coefficient, and initially performing closed operation on the logic matrix and then performing corrosion operation;
step S64, calculating the number of non-0 points in the dot multiplication of the logic matrix after corrosion operation and the filtered image, and if the number of the non-0 points is more than or equal to a predefined threshold value, adjusting the closing operation coefficient and the corrosion operation coefficient, and returning to the step S63; when the number of the non-0 points is smaller than a predefined threshold value, recording the current position of the non-0 points and the gray value of the corresponding pixel points;
step S65, calculating the direction field of the fine image, and calculating the gradient of each pixel point (i, j) asCalculating the local direction FX (i, j) of each block, and combining the local directions of all blocks into a fine image direction field diagram;
step S66, finding out the area with the angle less than or equal to pi/2 in the fine image direction field diagram, setting the value of the position of the area to be 1, otherwise, setting the value to be 0, and obtaining a corresponding logic matrix;
step S67, calculating the boundary of a logic matrix corresponding to the fine image direction field diagram, performing point multiplication operation on the obtained matrix and the logic matrix at the pixel point position in the step S64 to obtain a new logic matrix, performing point multiplication operation on the new logic matrix and the image which accords with the filtering, calculating the position and gray value of the obtained maximum pixel point, and defining the point as an alternative shape point;
step S68, updating the angle to be pi/2+/-g multiplied by delta angel, repeating the steps S66-S67 to obtain an alternative shape point set, wherein delta angel is any angle number, and g is an integer;
step S69, classifying the candidate shape points according to the distance, calculating the average value of the candidate shape point positions in the classification with the point number larger than the predefined threshold value, and determining the largest candidate shape point in the class with the largest average value as the coordinate of the candidate shape point of the fine image
The invention has the beneficial effects that: the invention changes the existing gene detection and image contrast detection in children ear deformity detection, changes deformity detection into shape mutation or deletion detection, and improves detection efficiency and instantaneity. On the basis, the shape of the contour abrupt change is detected and defined as a possible distortion point by calculating the absolute value of the difference between the normalized radii of every adjacent 2 sampling boundary points. And further, through counting and calculating the number of possible distortion points, a threshold is preset, so that the detection accuracy is improved. And meanwhile, the image is subjected to image enhancement filtering, so that the image quality is improved, and the detection precision is increased. Finally, the detection of the children's abnormal ears with high precision is realized by accurately positioning, intercepting and re-detecting the possibly distorted region.
Drawings
The invention will be further described with reference to the drawings and examples.
FIG. 1 is a schematic diagram of a method for detecting ear deformity in children in example 1.
Detailed Description
The present invention will be described in further detail with reference to the following examples in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Example 1
The embodiment provides a real-time high-precision children auricle deformity detection method, which is characterized in that: the real-time high-precision children auricle deformity detection method comprises the following steps:
step S1, extracting images containing ears of children as target images at multiple angles, separating image backgrounds, wherein each angle corresponds to one image, and optionally determining one image to execute step S2;
step S2, defining (N, M) as the number of pixels of the abscissa of the minimum circumscribed rectangle of the target image;
s3, taking the top left corner vertex of the minimum circumscribed matrix of the target image, and taking the image size (L, L) as an optimized image;
r max k=max (N/2, m/2) for the maximum distance from the object boundary point to the center;
step S4, calculating the center of gravity of the target imageOptimizing the center of the image (x 0 ，y 0 ) According to a translation functionShifting the center of gravity of the target image to the optimized image center (x 0 ，y 0 ) Thereafter, the (x) 0 ，y 0 ) Determining as a centroid point;
step S5, determining sampling boundary points by taking the equal pixel spacing as a sampling step length, and calculating a kth sampling boundary point (x k ，y k ) To centroid point (x) 0 ，y 0 ) Is defined as the radius:
step S6, calculating normalized radius sequence asCalculating the absolute value Deltar of the difference between the normalized radii of every two adjacent sampling boundary points n (m)＝|r n (k+1)-r n (k) I, m=0, 1..k-1, k is a positive integer greater than 1, determining Δr n The magnitude of (m), e.g. Deltar n (m) regarding a possible deformity greater than a predefined threshold range, defining each of the aforementioned 2 adjacent sampling boundary points as a possible point of deformity;
and S7, reselecting one image, returning to the step S2, until all the images are traversed, defining that the possible point of distortion is ear distortion, and otherwise, defining that the possible point of distortion is normal.
The embodiment changes the existing gene detection and image contrast detection in the detection of the ear deformity of children, changes the deformity detection into the shape mutation or deletion detection, and improves the detection efficiency and the instantaneity. On the basis, the shape of the contour abrupt change is detected and defined as a possible distortion point by calculating the absolute value of the difference between the normalized radii of every adjacent 2 sampling boundary points. And further, through counting and calculating the number of possible distortion points, a threshold is preset, so that the detection accuracy is improved.
Preferably, in order to improve detection accuracy, the method for detecting ear deformity of a child preferably further includes:
and S8, calculating the possibility of deformity after all the patterns are detected, wherein the possibility of deformity is larger than a predefined threshold value, and the deformity is regarded as the deformity of the ears of the children.
In order to improve the image quality, submitting the detection precision, preferably, the step S1 further includes performing image enhancement filtering on the image, including:
s11, use (-1) x+y Multiplying the input image F (x, y) by the central transformation to finish image preprocessing, and then calculating Fourier transformation to F (u, v);
s12, the filtering function H (u, v) is multiplied by F (u, v) to complete the filtering G (u, v) =h (u, v) ×f (u, v);
wherein D (u, v) is the distance from the origin of the Fourier transform, and sigma is the expansion coefficient of the Gaussian curve;
s13, performing Fourier inverse transformation;
s14, taking the real part of the Fourier inverse transformation, multiplying by (-1) x+y And finishing the image post-processing to obtain an enhanced image f' (x, y).
Preferably, in order to improve the detection accuracy, further accurate detection is performed on the possible distortion points, and step S6 further includes:
step S61, taking any possible distortion point as a midpoint, intercepting an image with the size of N multiplied by M to be defined as a fine image, dividing the fine image into blocks with the size of w multiplied by w, and calculating the pixel mean value avg_local and the mean square error local of each block;
bloc (i, j) refers to the pixel value of the pixel point (i, j), i is less than or equal to M, j is less than or equal to N;
step S62, comparing the mean square value local of each block with a predefined threshold value, defining k1 times of the maximum value of each block as the threshold value, taking the value 1 if the mean square value local is larger than the threshold value, otherwise taking the value 0, and traversing to obtain a logic matrix, wherein k1 is a constant;
step S63, defining a closed operation coefficient and a corrosion operation coefficient, and initially performing closed operation on the logic matrix and then performing corrosion operation;
step S64, calculating the number of non-0 points in the dot multiplication of the logic matrix after corrosion operation and the filtered image, and if the number of the non-0 points is more than or equal to a predefined threshold value, adjusting the closing operation coefficient and the corrosion operation coefficient, and returning to the step S63; when the number of the non-0 points is smaller than a predefined threshold value, recording the current position of the non-0 points and the gray value of the corresponding pixel points;
step S65, calculating the direction field of the fine image, and calculating the gradient of each pixel point (i, j) asCalculating the local direction FX (i, j) of each block, and combining the local directions of all blocks into a fine image direction field diagram;
step S66, finding out the area with the angle less than or equal to pi/2 in the fine image direction field diagram, setting the value of the position of the area to be 1, otherwise, setting the value to be 0, and obtaining a corresponding logic matrix;
step S67, calculating the boundary of a logic matrix corresponding to the fine image direction field diagram, performing point multiplication operation on the obtained matrix and the logic matrix at the pixel point position in the step S64 to obtain a new logic matrix, performing point multiplication operation on the new logic matrix and the image which accords with the filtering, calculating the position and gray value of the obtained maximum pixel point, and defining the point as an alternative shape point;
step S68, updating the angle to be pi/2+/-g multiplied by delta angel, repeating the steps S66-S67 to obtain an alternative shape point set, wherein delta angel is any angle number, and g is an integer;
step S69, classifying the candidate shape points according to the distance, calculating the average value of the candidate shape point positions in the classification with the point number larger than the predefined threshold value, and determining the largest candidate shape point in the class with the largest average value as the coordinate of the candidate shape point of the fine image
The embodiment changes the existing gene detection and image contrast detection in the detection of the ear deformity of children, changes the deformity detection into the shape mutation or deletion detection, and improves the detection efficiency and the instantaneity. On the basis, the shape of the contour abrupt change is detected and defined as a possible distortion point by calculating the absolute value of the difference between the normalized radii of every adjacent 2 sampling boundary points. And further, through counting and calculating the number of possible distortion points, a threshold is preset, so that the detection accuracy is improved. And meanwhile, the image is subjected to image enhancement filtering, so that the image quality is improved, and the detection precision is increased. Finally, the detection of the children's abnormal ears with high precision is realized by accurately positioning, intercepting and re-detecting the possibly distorted region.
While the foregoing describes the illustrative embodiments of the present invention so that those skilled in the art may understand the present invention, the present invention is not limited to the specific embodiments, and all inventive innovations utilizing the inventive concepts are herein within the scope of the present invention as defined and defined by the appended claims, as long as the various changes are within the spirit and scope of the present invention.
Claims (4)
1. A real-time high-precision children auricle deformity detection method is characterized in that: the real-time high-precision children auricle deformity detection method comprises the following steps:
step S1, extracting images containing ears of children as target images at multiple angles, separating image backgrounds, wherein each angle corresponds to one image, and optionally determining one image to execute step S2;
step S2, defining (N, M) as the number of pixels of the abscissa of the minimum circumscribed rectangle of the target image;
s3, taking the top left corner vertex of the minimum circumscribed matrix of the target image, and taking the image size (L, L) as an optimized image;
r max k=max (N/2, m/2) for the maximum distance from the object boundary point to the center;
step S4, calculating the center of gravity of the target imageOptimizing the center of the image (x 0 ，y 0 ) According to a translation functionShifting the center of gravity of the target image to the optimized image center (x 0 ，y 0 ) Thereafter, the (x) 0 ，y 0 ) Determining as a centroid point;
step S5, determining sampling boundary points by taking the equal pixel spacing as a sampling step length, and calculating a kth sampling boundary point (x k ，y k ) To centroid point (x) 0 ，y 0 ) Is defined as the radius:
step S6, calculating normalized radius sequence asCalculating the absolute value Deltar of the difference between the normalized radii of every two adjacent sampling boundary points n (m)＝|r n (k+1)-r n (k) I, m=0, 1..k-1, k is a positive integer greater than 1, determining Δr n The magnitude of (m), e.g. Deltar n (m) regarding a possible deformity greater than a predefined threshold range, defining each of the aforementioned 2 adjacent sampling boundary points as a possible point of deformity;
and S7, reselecting one image, returning to the step S2, until all the images are traversed, defining that the possible point of distortion is ear distortion, and otherwise, defining that the possible point of distortion is normal.
2. The real-time high-precision children auricle deformity detection method according to claim 1, wherein the method comprises the following steps of: the method for detecting the ear deformity of the child further comprises the following steps:
and S8, calculating the possibility of deformity after all the patterns are detected, wherein the possibility of deformity is larger than a predefined threshold value, and the deformity is regarded as the deformity of the ears of the children.
3. The real-time high-precision children auricle deformity detection method according to claim 1, wherein the method comprises the following steps of: step S1 further includes performing image enhancement filtering on the image, including:
s11, use (-1) x+y Multiplying the input image F (x, y) by the central transformation to finish image preprocessing, and then calculating Fourier transformation to F (u, v);
s12, the filtering function H (u, v) is multiplied by F (u, v) to complete the filtering G (u, v) =h (u, v) ×f (u, v);
where D (u, v) is the distance from the origin of the Fourier transform and σ isGaussian curve expansion coefficient;
s13, performing Fourier inverse transformation;
s14, taking the real part of the Fourier inverse transformation, multiplying by (-1) x+y And finishing the image post-processing to obtain an enhanced image f' (x, y).
4. The real-time high-precision children auricle deformity detection method according to claim 3, wherein the method comprises the following steps of: step S6 further includes:
step S61, taking any possible distortion point as a midpoint, intercepting an image with the size of N multiplied by M to be defined as a fine image, dividing the fine image into blocks with the size of w multiplied by w, and calculating the pixel mean value avg_local and the mean square error local of each block;
bloc (i, j) refers to the pixel value of the pixel point (i, j), i is less than or equal to M, j is less than or equal to N;
step S62, comparing the mean square value local of each block with a predefined threshold value, defining k1 times of the maximum value of each block as the threshold value, taking the value 1 if the mean square value local is larger than the threshold value, otherwise taking the value 0, and traversing to obtain a logic matrix, wherein k1 is a constant;
step S63, defining a closed operation coefficient and a corrosion operation coefficient, and initially performing closed operation on the logic matrix and then performing corrosion operation;
step S64, calculating the number of non-0 points in the dot multiplication of the logic matrix after corrosion operation and the filtered image, and if the number of the non-0 points is more than or equal to a predefined threshold value, adjusting the closing operation coefficient and the corrosion operation coefficient, and returning to the step S63; when the number of the non-0 points is smaller than a predefined threshold value, recording the current position of the non-0 points and the gray value of the corresponding pixel points;
in step S65 of the process of the present invention,calculating the direction field of the fine image, and calculating the gradient of each pixel point (i, j) asCalculating the local direction FX (i, j) of each block, and combining the local directions of all blocks into a fine image direction field diagram;
step S66, finding out the area with the angle less than or equal to pi/2 in the fine image direction field diagram, setting the value of the position of the area to be 1, otherwise, setting the value to be 0, and obtaining a corresponding logic matrix;
step S67, calculating the boundary of a logic matrix corresponding to the fine image direction field diagram, performing point multiplication operation on the obtained matrix and the logic matrix at the pixel point position in the step S64 to obtain a new logic matrix, performing point multiplication operation on the new logic matrix and the image which accords with the filtering, calculating the position and gray value of the obtained maximum pixel point, and defining the point as an alternative shape point;
step S68, updating the angle to be pi/2+/-g multiplied by delta angel, repeating the steps S66-S67 to obtain an alternative shape point set, wherein delta angel is any angle number, and g is an integer;
and step S69, classifying the candidate shape points according to the distance, calculating the average value of the candidate shape point positions in the classification with the point number larger than a predefined threshold value, and determining the largest candidate shape point in the class with the largest average value as the coordinate of the fine image shape point.
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