CN113826496B - Automatic grafting method and device in vegetable grafting - Google Patents
Automatic grafting method and device in vegetable grafting Download PDFInfo
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- CN113826496B CN113826496B CN202111281745.6A CN202111281745A CN113826496B CN 113826496 B CN113826496 B CN 113826496B CN 202111281745 A CN202111281745 A CN 202111281745A CN 113826496 B CN113826496 B CN 113826496B
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- A—HUMAN NECESSITIES
- A01—AGRICULTURE; FORESTRY; ANIMAL HUSBANDRY; HUNTING; TRAPPING; FISHING
- A01G—HORTICULTURE; CULTIVATION OF VEGETABLES, FLOWERS, RICE, FRUIT, VINES, HOPS OR SEAWEED; FORESTRY; WATERING
- A01G2/00—Vegetative propagation
- A01G2/30—Grafting
- A01G2/38—Holding; Ligating
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- A—HUMAN NECESSITIES
- A01—AGRICULTURE; FORESTRY; ANIMAL HUSBANDRY; HUNTING; TRAPPING; FISHING
- A01G—HORTICULTURE; CULTIVATION OF VEGETABLES, FLOWERS, RICE, FRUIT, VINES, HOPS OR SEAWEED; FORESTRY; WATERING
- A01G2/00—Vegetative propagation
- A01G2/30—Grafting
- A01G2/32—Automatic apparatus therefor
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- A—HUMAN NECESSITIES
- A01—AGRICULTURE; FORESTRY; ANIMAL HUSBANDRY; HUNTING; TRAPPING; FISHING
- A01G—HORTICULTURE; CULTIVATION OF VEGETABLES, FLOWERS, RICE, FRUIT, VINES, HOPS OR SEAWEED; FORESTRY; WATERING
- A01G2/00—Vegetative propagation
- A01G2/30—Grafting
- A01G2/35—Cutting; Inserting
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
- Y02A40/00—Adaptation technologies in agriculture, forestry, livestock or agroalimentary production
- Y02A40/10—Adaptation technologies in agriculture, forestry, livestock or agroalimentary production in agriculture
- Y02A40/25—Greenhouse technology, e.g. cooling systems therefor
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Abstract
The invention discloses an automatic grafting method and device in vegetable grafting, and relates to the technical field of vegetable grafting. The invention comprises the following steps: step S1: the method comprises the following steps that a stock manipulator grabs a stock from a stock receiving station, rotates 90 degrees to reach a stock cutting station, and rotates 90 degrees to reach a binding station after cutting is completed; step S2: the ear seedling manipulator grabs the ear seedling from ear seedling material receiving station, rotates 90 and arrives ear seedling cutting station, and the rotation 90 arrives and wraps the station and carry out the alignment of two scarf after the cutting is accomplished, wraps after the alignment. According to the method, the position of a cutting point in the image is identified by shooting the cut pictures of the stock and the scion, the freedom degree of the stock in up-and-down motion is controlled by a stock manipulator, the scion manipulator is used for controlling the scion to stretch and retract, the two oblique planes are overlapped in the horizontal direction, and the cutting precision during grafting and the survival rate of the grafted scion are improved.
Description
Technical Field
The invention belongs to the technical field of vegetable grafting, and particularly relates to an automatic grafting method and device in vegetable grafting.
Background
In the grafting mode, the hypocotyls of the stock and the scion seedling are obliquely cut respectively, and finally the two obliquely cut surfaces are aligned and bound in space to realize the grafting process. When the two chamfer planes are aligned theoretically, the following 5 degrees of freedom are needed: the degree of freedom in the vertical direction, the degree of freedom in the horizontal direction, the degree of freedom in the offset direction, and the two-dimensional degree of freedom of the parallelism of the cut surface. The design of the 5 degrees of freedom is completely realized, theoretical parallel coincidence of two oblique cutting planes can be realized certainly, but in the engineering implementation process, the design can be simplified, the control of a part of degrees of freedom is realized, and finally the fitting of the two oblique cutting planes in the engineering is also realized.
Most grafting equipment in reality does not realize the control of any one degree of freedom in 5 degrees of freedom, and the fitting of two oblique cutting surfaces is realized, so that the spatial alignment of the two oblique cutting surfaces is completely ensured by means of mechanical assembly. The advantage of the design is that the cost is very low, but the disadvantage of the device is that the accuracy of the abutment is not high. The final result is that the survival rate of the grafted seedlings is not high.
Disclosure of Invention
The invention aims to provide an automatic grafting method and device in vegetable grafting, which realize the fitting of two oblique planes of grafting by a method with controllable two degrees of freedom and solve the problems of low precision and low survival rate of grafted seedlings in the conventional grafting.
In order to solve the technical problems, the invention is realized by the following technical scheme:
the invention relates to an automatic grafting method in vegetable grafting, which comprises the following steps:
step S1: the method comprises the following steps that a stock manipulator grabs a stock from a stock receiving station, rotates 90 degrees to reach a stock cutting station, and rotates 90 degrees to reach a binding station after cutting is completed;
step S2: the spike seedling manipulator grabs the spike seedlings from the spike seedling receiving station, rotates 90 degrees to reach a spike seedling cutting station, rotates 90 degrees to reach a binding station after cutting is finished, aligns two bevels, and binds after aligning;
the alignment process of the two oblique planes of the stock and the scion seedling is as follows:
step Q1: shooting a stock diagonal plane by a stock camera, and identifying a stock cutting upper point P0 and a stock cutting lower point P1 in the image;
step Q2: identifying the position of the P0 point on the y axis in the image;
and step Q3: shooting a bias cutting plane of the scion seedlings by a scion seedling camera, and identifying a cutting upper point R0 of the scion seedlings in the image;
and step Q4: identifying the Y-axis position of the R0 point in the spike seedling image;
and step Q5: determining the heights of the two oblique planes at the point P0 and the point R0, and controlling the freedom degree of the vertical movement of the stock manipulator to realize the superposition of the two oblique planes in the vertical direction;
step Q6: calculating the positions of the P0 point and the R0 point on the X axis in the image, controlling the telescopic motion of the spike seedling manipulator, and realizing the superposition of the two oblique planes in the horizontal direction;
step Q7: and after the two oblique planes of the stock and the scion seedling are aligned, binding treatment is carried out.
As a preferred technical scheme, in the step S1, before grafting, the stock receiving station, the wrapping station and the scion receiving station are adjusted to be on the same straight line.
As a preferred technical solution, in the step Q1, identifying a cut point in the image includes the following specific steps:
step P1: carrying out edge detection on the stock image by using a Canny algorithm to obtain right edge pixel points;
step P2: acquiring an edge pixel point chain code of a right edge position by a contour tracking method;
step P3: identifying an angular point through a chain code;
and step P4: identifying PO points by cutting size;
step P5: the same approach identifies the P1 and R0 points.
As a preferred technical solution, in the step P1, before performing edge detection on the rootstock image, the rootstock image needs to be preprocessed to obtain an edge image, and the preprocessing steps are as follows:
step Y1: inputting a stock image;
step Y2: carrying out noise reduction and smoothing treatment through a Gaussian filter;
step Y3: calculating the gradient amplitude and direction by adopting a differential method;
step Y4: carrying out non-maximum suppression on the smoothed image to obtain a single-edge image with accurate positioning;
step Y5: obtaining more boundary details by a hysteresis threshold through a Canny algorithm;
step Y6: an edge image is obtained.
As a preferred technical solution, in step P2, the edge pixel point chain code adopts an 8-adjacent chain code, and the specific steps are as follows:
step L1: searching in a sub-contour mode: finding a boundary contour point X at the leftmost upper corner of the image 0 Taking the point as a search starting point and taking the chain code value dir =0 as the initial search direction;
step L2: searching the next point of the starting point in the anticlockwise direction of the eight neighborhoods, and rotating the chain code value anticlockwise by 45 degrees once every time, namely dir +1;
step L3: if a new boundary point is found, the chain code value is assigned to the previous point X 1 1, taking the point as the central point of eight neighborhoods, and clockwise rotating the chain code value direction by 90 degrees, namely dir-2 is taken as the starting search direction of the point, and continuing searching;
step L4: repeating the steps L2 to L3 until the starting point X is searched 0 And finishing the whole contour search.
As a preferred technical solution, in the step P3, the specific steps of identifying the corner point by the chain code are as follows:
step M1: according to the chain codes of the image contour points, calculating the chain code differences of all points of the contour;
step M2: performing chain code repair on the contour points at the convex or concave positions;
step M3: analyzing a plurality of chain codes around the point where the chain code changes;
if the chain code difference of the two points is 1, the included angle is an acute angle of 45 degrees; if the chain code difference of the two points is 2, the included angle is 90 degrees; if the chain code difference of the two points is 3, the included angle is 135 degrees, and the contour point is an angular point; if the chain code difference between the two points is 4, the included angle is 180 degrees.
The invention relates to an automatic grafting device in vegetable grafting, which comprises a stock cutting device, a scion seedling cutting device and a grafting clamp;
the rootstock cutting device comprises a rootstock manipulator, a rootstock camera and a rootstock cutter; the stock manipulator is used for clamping a stock to be grafted from a stock receiving station; the rootstock manipulator clamps a rootstock to be grafted and rotates 90 degrees to a rootstock cutting station, and a rootstock cutter cuts the rootstock; the method comprises the steps that a stock camera collects images of the oblique cuts of stocks, and after cutting points of the stocks are identified, a stock manipulator rotates 90 degrees to a binding station;
the ear seedling cutting device comprises an ear seedling manipulator, an ear seedling camera and an ear seedling cutter; the scion seedling manipulator is used for clamping scion seedlings to be grafted from the scion seedling receiving station; the scion seedling manipulator clamps scion seedlings to be grafted and rotates 90 degrees to a scion seedling cutting station, and a scion seedling cutter cuts the scion seedlings; the ear seedling camera collects oblique section images of the ear seedlings, and after cutting points of the ear seedlings are identified, the ear seedling manipulator rotates 90 degrees to a binding station;
the grafting clamp clamps and fixes the grafting stock and the scion seedling which are aligned in the two oblique section spaces.
As a preferred technical scheme, background plates are arranged right in front of the stock camera and the scion seedling camera; the background plate is used for shooting images of the rootstock and the scion.
The invention has the following beneficial effects:
according to the method, the position of a cutting point in the image is identified by shooting the cut pictures of the stock and the scion, the freedom degree of the stock in up-and-down motion is controlled by a stock manipulator, the scion manipulator is used for controlling the scion to stretch and retract, the two oblique planes are overlapped in the horizontal direction, and the cutting precision during grafting and the survival rate of the grafted scion are improved.
Of course, it is not necessary for any product in which the invention is practiced to achieve all of the above-described advantages at the same time.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the description below are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic structural view of an automatic grafting device in vegetable grafting;
FIG. 2 is a flow chart of an automatic grafting method in vegetable grafting;
FIG. 3 is a flow chart of aligning two oblique planes of a stock and a scion;
FIG. 4 is a flow chart of identifying cut points in an image;
FIG. 5 is a flow chart of image pre-processing;
FIG. 6 is a diagram of an 8-neighbor chain code of a partial outline according to the second embodiment.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The first embodiment is as follows:
referring to fig. 2, the present invention relates to an automatic grafting method in vegetable grafting, comprising the following steps:
step S1: the method comprises the following steps that a stock manipulator grabs a stock from a stock receiving station, rotates 90 degrees to reach a stock cutting station, and rotates 90 degrees to reach a binding station after cutting is completed;
step S2: the ear seedling manipulator grabs the ear seedlings from the ear seedling receiving station, rotates 90 degrees to reach the ear seedling cutting station, rotates 90 degrees to reach the binding station after cutting is finished, aligns the two bevels, and binds the two bevels after aligning;
in order to realize the parallelism of the two oblique planes of the binding station, the knife outlet surfaces of the two knives are ensured to be completely parallel by mechanical installation in the knife outlet directions of the stock knife and the scion seedling knife. The degree of freedom of the parallelism of the two chamfer planes is not controlled here but is ensured by the mechanical mounting.
Referring to fig. 3, the alignment procedure of the two oblique cuts of the stock and the scion is as follows:
step Q1: shooting a stock diagonal plane by a stock camera, and identifying a stock cutting upper point P0 and a stock cutting lower point P1 in an image;
step Q2: identifying the position of the P0 point on the y axis in the image;
and step Q3: shooting a bias cutting plane of the scion seedlings by a scion seedling camera, and identifying a cutting upper point R0 of the scion seedlings in the image;
step Q4: identifying the Y-axis position of the R0 point in the spike seedling image;
step Q5: determining the heights of the two oblique planes at the point P0 and the point R0, and controlling the freedom degree of the vertical movement of the stock manipulator to realize the superposition of the two oblique planes in the vertical direction;
step Q6: calculating the positions of the P0 point and the R0 point on the X axis in the image, controlling the telescopic motion of the spike seedling manipulator, and realizing the superposition of the two oblique planes in the horizontal direction;
step Q7: and after the two oblique planes of the stock and the scion seedling are aligned, binding treatment is carried out.
In order to realize the superposition of the two bevels in the horizontal direction, the positions of the P0 and R0 points on the X axis in the image are calculated, so that the telescopic motion of the spike manipulator is controlled, and the superposition of the two bevels in the horizontal direction is realized. In order to realize the superposition of the two oblique cutting planes in the staggered direction, three red points of the lower drawing are ensured to be on the same straight line when the equipment is installed. Therefore, after the rootstock manipulator and the scion seedling manipulator rotate 180 degrees, the staggered directions are overlapped in the mechanical space. The superposition requirement of theoretical 5-dimensional freedom degrees is guaranteed by the above 5 designs, the superposition requirement comprises 2-dimensional controllable freedom degrees and 3-dimensional fixed freedom degrees, the control target of the 2-dimensional controllable freedom degrees is to realize the space superposition of an upper cutting point, finally the space alignment of two oblique cutting planes of the grafting stock and the scion seedling is realized, and after the spaces of the two oblique cutting planes of the grafting stock and the scion seedling are aligned, the grafting clamp discharging device clamps the position of the spatial alignment of the oblique cutting planes through the grafting clamp.
Example two:
referring to fig. 4, in step S1, before grafting, the stock receiving station, the wrapping station, and the scion receiving station are adjusted to be on the same straight line.
In step Q1, identifying a cut point in the image, specifically including the following steps:
step P1: carrying out edge detection on the stock image by using a Canny algorithm to obtain right edge pixel points;
step P2: acquiring an edge pixel point chain code at the right edge position by a contour tracking method;
and step P3: identifying an angular point through a chain code;
step P4: identifying PO points by cutting size;
step P5: the same approach identifies the P1 and R0 points.
Referring to fig. 5, in step P1, before performing edge detection on the rootstock image, the rootstock image needs to be preprocessed to obtain an edge image, and the preprocessing steps are as follows:
step Y1: inputting a stock image;
step Y2: carrying out noise reduction and smoothing treatment through a Gaussian filter;
step Y3: calculating the gradient amplitude and direction by adopting a differential method;
step Y4: carrying out non-maximum suppression on the smoothed image to obtain a single-edge image with accurate positioning;
step Y5: obtaining more boundary details by a hysteresis threshold through a Canny algorithm;
step Y6: an edge image is obtained.
Referring to fig. 6, in step P2, the edge pixel point chain code adopts an 8-adjacent chain code, and the specific steps are as follows:
step L1: searching in a sub-outline mode: finding a boundary contour point X at the leftmost upper corner of the image 0 Taking the point as a search starting point and taking a chain code value dir =0 as the initial search direction;
step L2: searching the next point of the starting point in the anticlockwise direction of the eight neighborhoods, and rotating the chain code value anticlockwise by 45 degrees once every time, namely dir +1;
step L3: if a new boundary point is found, the chain code value is assigned to the previous point X 1 1, taking the point as the central point of eight neighborhoods, and clockwise rotating the chain code value direction by 90 degrees, namely dir-2 is taken as the starting search direction of the point, and continuing searching;
FIG. 6 (a) is a schematic diagram of 4-adjacent codes; FIG. 6 (b) is a schematic diagram of an 8-neighbor code; FIG. 6 (c) is a diagram of 8-adjacent chain codes of a certain section of outline, and in FIG. 6 (c), the chain code is 6- >0- >0- >0- >0- >1- >2- >4- >3.
Step L4: repeating the steps L2 to L3 until the starting point X is searched 0 The whole contour search is completed.
In step P3, the specific steps of identifying the corner point by the chain code are as follows:
step M1: according to the chain codes of the image contour points, calculating the chain code differences of all points of the contour;
step M2: performing chain code repair on the contour points at the convex or concave positions;
step M3: analyzing a plurality of chain codes around the point where the chain code changes;
if the chain code difference of the two points is 1, the included angle is an acute angle of 45 degrees; if the chain code difference of the two points is 2, the included angle is 90 degrees; if the chain code difference of the two points is 3, the included angle is 135 degrees, and the contour point is an angular point; if the chain code difference between the two points is 4, the included angle is 180 degrees.
Example three:
referring to fig. 1, the present invention relates to an automatic grafting device for vegetable grafting, which comprises a stock cutting device, a scion cutting device and a grafting clip;
the stock cutting device comprises a stock manipulator, a stock camera and a stock cutter; the stock manipulator is used for clamping the stocks to be grafted from the stock receiving station; the method comprises the following steps that a stock manipulator clamps a stock to be grafted and rotates 90 degrees to a stock cutting station, and a stock cutter cuts the stock; the method comprises the steps that a stock camera collects images of diagonal cuts of stocks, and after cutting points of the stocks are identified, a stock manipulator rotates 90 degrees to a binding station;
the scion seedling cutting device comprises a scion seedling manipulator, a scion seedling camera and a scion seedling cutter; the scion seedling manipulator is used for clamping scion seedlings to be grafted from a scion seedling receiving station; the scion seedling manipulator clamps the scion seedlings to be grafted and rotates 90 degrees to a scion seedling cutting station, and a scion seedling cutter cuts the scion seedlings; the scion seedling camera collects images of oblique planes of the scion seedlings, and after cutting points of the scion seedlings are identified, the scion seedling manipulator rotates by 90 degrees to a binding station;
the grafting clamp clamps and fixes the grafting stock and the scion seedling which are aligned in the two oblique section spaces.
Background plates are arranged right in front of the stock camera and the scion seedling camera; the background plate is used for shooting the images of the stocks and the scions, and the shot images only have the images of the stocks and the scions due to the fact that the background plate is only in one color, so that the background can be conveniently removed to process the images, and the accuracy and the recognition efficiency of image recognition are improved.
Example four:
the positioning method adopted in the above embodiment is an upper cutting point positioning method, but the positioning method of the device using automatic attachment in this document includes, but is not limited to: upper cutting point location, lower cutting point location, cutting surface center point location, or other reference point location.
It should be noted that, in the above system embodiment, each included unit is only divided according to functional logic, but is not limited to the above division as long as the corresponding function can be implemented; in addition, the specific names of the functional units are only for the convenience of distinguishing from each other, and are not used for limiting the protection scope of the present invention.
In addition, it is understood by those skilled in the art that all or part of the steps in the method for implementing the embodiments described above may be implemented by a program instructing associated hardware, and the corresponding program may be stored in a computer-readable storage medium.
The preferred embodiments of the invention disclosed above are intended to be illustrative only. The preferred embodiments are not intended to be exhaustive or to limit the invention to the precise embodiments disclosed. Obviously, many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the invention and the practical application, to thereby enable others skilled in the art to best understand the invention for and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.
Claims (2)
1. An automatic grafting method in vegetable grafting is characterized by comprising the following steps:
step S1: the method comprises the following steps that a stock manipulator grabs a stock from a stock receiving station, rotates 90 degrees to reach a stock cutting station, and rotates 90 degrees to reach a binding station after cutting is completed;
step S2: the ear seedling manipulator grabs the ear seedlings from the ear seedling receiving station, rotates 90 degrees to reach the ear seedling cutting station, rotates 90 degrees to reach the binding station after cutting is finished, aligns the two bevels, and binds the two bevels after aligning;
the alignment process of the two oblique planes of the stock and the scion seedling is as follows:
step Q1: shooting a stock diagonal plane by a stock camera, and identifying a stock cutting upper point P0 and a stock cutting lower point P1 in the image;
step Q2: identifying the position of the P0 point on the y axis in the image;
and step Q3: shooting a bias cutting plane of the scion seedlings by a scion seedling camera, and identifying a cutting upper point R0 of the scion seedlings in the image;
step Q4: identifying the Y-axis position of the R0 point in the spike seedling image;
step Q5: determining the heights of the two oblique planes at the point P0 and the point R0, and controlling the freedom degree of the vertical movement of the stock manipulator to realize the superposition of the two oblique planes in the vertical direction;
step Q6: calculating the positions of the P0 point and the R0 point on the X axis in the image, controlling the telescopic motion of the spike seedling manipulator, and realizing the superposition of the two oblique planes in the horizontal direction;
step Q7: binding after aligning the two oblique planes of the stock and the scion seedling;
in the step Q1, identifying a cut point in the image includes the following specific steps:
step P1: carrying out edge detection on the stock image by using a Canny algorithm to obtain right edge pixel points;
step P2: acquiring an edge pixel point chain code of a right edge position by a contour tracking method;
step P3: identifying an angular point through a chain code;
step P4: identifying PO points by cutting size;
step P5: identifying P1 and R0 points by the same method;
in the step P1, before performing edge detection on the stock image, the stock image needs to be preprocessed to obtain an edge image, and the preprocessing steps are as follows:
step Y1: inputting a stock image;
step Y2: carrying out noise reduction and smoothing treatment through a Gaussian filter;
step Y3: calculating the gradient amplitude and direction by adopting a differential method;
step Y4: carrying out non-maximum suppression on the smoothed image to obtain a single-edge image with accurate positioning;
step Y5: obtaining more boundary details by a hysteresis threshold through a Canny algorithm;
step Y6: obtaining an edge image;
in step P2, the edge pixel point chain code adopts an 8-adjacent chain code, and the specific steps are as follows:
step L1: searching in a sub-outline mode: finding a boundary contour point X at the leftmost upper corner of the image 0 Taking the point as a search starting point and taking a chain code value dir =0 as the initial search direction;
step L2: searching the next point of the starting point in the anticlockwise direction of the eight neighborhoods, and rotating the chain code value anticlockwise by 45 degrees once every time, namely dir +1;
step L3: if a new boundary point is found, the chain code value is assigned to the previous point X 1 1, taking the point as the central point of eight neighborhoods, and clockwise rotating the chain code value direction by 90 degrees, namely dir-2 is taken as the starting search direction of the point, and continuing searching;
step L4: repeating the steps L2 to L3 until the starting point X is searched 0 Finishing the whole contour search;
in the step P3, the specific steps of identifying the corner point through the chain code are as follows:
step M1: according to the chain codes of the image contour points, calculating the chain code differences of all points of the contour;
step M2: performing chain code repair on the contour points at the convex or concave positions;
step M3: analyzing a plurality of chain codes around the point where the chain code changes;
if the chain code difference of the two points is 1, the included angle is an acute angle of 45 degrees; if the chain code difference of the two points is 2, the included angle is 90 degrees; if the chain code difference of the two points is 3, the included angle is 135 degrees, and the contour point is an angular point; if the chain code difference of the two points is 4, the included angle is 180 degrees.
2. The automatic grafting method in vegetable grafting according to claim 1, wherein in the step S1, before grafting, the stock receiving station, the wrapping station and the scion receiving station are adjusted to be on the same straight line.
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