CN109215046B - Laplacian operator edge detection method based on image interpolation operation - Google Patents
Laplacian operator edge detection method based on image interpolation operation Download PDFInfo
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Abstract
The invention provides a Laplace operator edge detection method based on image interpolation operation, which comprises the following steps of 1: inputting an original image H, inserting an average value between two adjacent pixel values in each row of the original image, and inserting an average value between two adjacent pixel values in each column on the image subjected to row interpolation to obtain an interpolated extended image H'; step 2: expanding the 3 x 3 laplace template L to obtain a 5 x 5 laplace template L'; and step 3: the resulting image H "was obtained by convolving the extended image H 'with a 5 x 5 laplacian template L'. The method has the advantages that the influence of noise on edge detection is reduced by carrying out interpolation on the original image, and the edge detection effect is improved by expanding the Laplace template.
Description
Technical Field
The invention relates to an image edge detection method, in particular to a Laplace operator edge detection method based on image interpolation operation.
Background
The digital image contains rich visual information, especially edge information in the image, such as edge information of rivers in the image, edge information of human bones in medical CT images, edge information of various zebra crossings in road traffic images, and the like. The extraction of the edge information is widely applied to modern life, such as medical auxiliary diagnosis, face recognition, target tracking, remote sensing monitoring and other different fields, and the edge information has very important significance for the recognition and detection of the target in the image. The second partial derivatives of the digital image element g (x, y) in the x-axis and y-axis directions are defined as:
the Laplace edge detection operator is an edge detection operator based on the zero crossing point of the second derivative on the edge, and has detection effect on isolated points and line endsThe fruit is better.
The 3 x 3 laplacian template L is a common laplacian edge detector template, and is characterized in that the coefficient of the element g (i, j) in the center position is negative, the coefficient of the element in the edge direction is positive, and the sum of the coefficients of all the elements is zero, i.e., the template is a common laplacian edge detector template
The template has the advantages of rotation invariance and displacement invariance, but has certain defects, such as the possibility of losing edge direction information in the edge detection process and the possibility of intensifying the adverse effect of noise on the edge detection result.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a method for detecting the edge of the laplacian operator, which can reduce the influence of noise on the edge detection effect and improve the edge detection effect.
In order to solve the technical problem, the invention is realized by the following technical scheme, and the method for detecting the edge of the laplacian operator based on the image interpolation operation comprises the following steps:
step 1: inputting an original image H, inserting the average value between two adjacent pixel values in each line of the original image, inserting the average value between two adjacent pixel values in each column on the image after line interpolation to obtain an interpolated expanded image H',
step 2: expanding the 3 × 3 laplacian template to obtain a 5 × 5 laplacian template L ', wherein the value of the central element of the 5 × 5 laplacian template is the opposite number of the sum of the 24 neighborhood elements, the value of the 5 × 5 laplacian template L ' is centrosymmetric with respect to the central element g (i, j), and the value of the element closer to the central element is larger than the value of the element farther away and is the same as the value of the element at the same distance from the central element, and L ' satisfies the formula:
and step 3: convolving the extended image H 'with a 5 x 5 Laplace template L' to obtain a result image H ",
further, in step 2, the laplace template L' is:
the method has the advantages that the influence of noise on edge detection is reduced by performing interpolation operation on the original image in two directions of rows and columns, the edge detection effect is improved by expanding the 3 x 3 Laplace template to the 5 x 5 Laplace template and endowing different proportion coefficients to elements in all directions.
Drawings
The following detailed description of embodiments of the invention is provided in conjunction with the appended drawings, in which:
FIG. 1 is a flow chart of an embodiment of the present invention;
FIG. 2 is an original image H according to the present invention;
FIG. 3 is an expanded image H' of the present invention;
fig. 4 is a result image of 3 × 3 laplacian template L processing;
fig. 5 is a resulting image H "of the L' processing of the laplace template used in the present invention.
Detailed Description
The invention will be further illustrated with reference to specific embodiments. Referring to fig. 1 to 5, the present invention provides a laplacian edge detection method based on image interpolation operation.
The Laplace operator is a second derivative operator, and is an edge detection operator defined based on second partial derivatives in two coordinate axis directions of the image. The second partial derivatives of the digital image element g (x, y) in the x-axis and y-axis directions are defined as:
the edge part of the image is often a part with large gray scale change and jump, so the first-order partial derivative corresponding to the edge part is often a local extreme value, and therefore the edge area of the image corresponds to the corresponding position when the second-order partial derivative crosses the zero point, and the edge of the image can be detected through the zero point of the second-order partial derivative of the image. In the application field of the laplacian, a commonly used laplacian can be defined as:
i.e. laplace operator
In order to reduce the influence of noise on the edge detection effect and improve the edge detection effect, the following operations are performed:
s1: inputting an original image H, inserting the average value between two adjacent pixel values in each line of the original image, and inserting the average value between two adjacent pixel values in each column on the image after line interpolation to obtain an expanded image H'.
In H ', g1, g2, g3, g4, g5, g6, g7, g8, g9 … … gn, gm, gt respectively represent pixel values in the original image H, and k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, k15, k16 … … are pixel values in an extended image H' obtained by extension interpolation of the original image H.
The MATLAB code of the interpolation operation is:
s2: expanding the 3 x 3 Laplace template L to obtain 5 x 5 Laplace template L',
l' satisfies the formula:
the value of the central element of the 5 x 5 laplacian template is the opposite of the sum of the 24 neighborhood elements, the value of the 5 x 5 laplacian template L' is centrosymmetric with respect to the central element g (i, j), and the value of the element closer to the central element is larger than the value of the element farther away, and is the same as the value of the element at the same distance from the central element.
S3: and (5) convolving the extended image with a 5 by 5 Laplace template to obtain a result image H'.
The 3 × 3 laplacian template L before improvement only considers the horizontal direction and the vertical direction, the 5 × 5 laplacian template L ' after improvement can detect edge information in more directions, different weights are distributed to edges in different directions, the weight of the edge in the direction closer to the center point of the template is larger, the edge of the image H ' after interpolation is detected by using the template L ', a result image H ″ is obtained, and the comparison between the attached diagram 4 and the attached diagram 5 shows that the edge detection effect is improved.
The above examples only show one embodiment of the present invention, and the description thereof is more specific and detailed, but should not be construed as limiting the scope of the invention. It will be apparent to those skilled in the art that various changes and modifications can be made without departing from the spirit and scope of the invention. Therefore, the protection scope of the present patent shall be subject to the claims.
Claims (2)
1. A Laplacian edge detection method based on image interpolation operation is characterized by comprising the following steps:
step 1: inputting an original image H, inserting the average value between two adjacent pixel values in each line of the original image, inserting the average value between two adjacent pixel values in each column on the image after line interpolation to obtain an interpolated expanded image H',
g1, g2, g3, g4, g5, g6, g7, g8, g9 … … gn, gm, gt in H 'respectively represent pixel values in the original image H, and k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, k15, k16 … … are pixel values in an extended image H' obtained by extension interpolation of the original image H;
step 2: expanding the 3 × 3 laplacian template to obtain a 5 × 5 laplacian template L ', wherein the value of the central element of the 5 × 5 laplacian template is the opposite number of the sum of the 24 neighborhood elements, the values on the 5 × 5 laplacian template L ' are centrosymmetric with respect to the central element g (i, j), and the value of the element closer to the central element is larger than the value of the element farther from the central element and is the same as the value of the element with the same distance from the central element, and L ' satisfies the formula:
and step 3: convolving the extended image H 'with a 5 x 5 Laplace template L' to obtain a result image H ",
2. the method for detecting the edge of the laplacian based on the image interpolation operation as claimed in claim 1, wherein: in the step 2, the Laplace template L' is:
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