CN111986117A - System and method for correcting arithmetic operation - Google Patents
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Abstract
The invention discloses an arithmetic operation correcting system and a method, wherein the system comprises: the device comprises an image preprocessing and segmenting module, a character recognition module and a calculation and verification module; the image preprocessing and dividing module carries out preprocessing such as denoising and binarization on the original image and then divides the original image into single numbers or symbols; the character recognition module recognizes the segmented single character by using a convolutional neural network; the calculation and verification module recombines the recognized characters into arithmetic and calculates the correctness of the verification answer. The invention realizes the shooting and identification of the homework through the common intelligent electronic equipment such as a smart phone and the like, can run locally to finish the automatic correction of arithmetic homework, is suitable for the correction of the mathematical calculation homework of the lower grades of primary schools, and helps teachers improve the teaching efficiency.
Description
Technical Field
The invention belongs to the technical field of picture processing and character recognition, and particularly relates to an automatic arithmetic operation correction system and method capable of being shot based on a smart phone and running locally.
Background
Homework has long played an important role in student education. For teachers, the knowledge mastering conditions of students can be further known by correcting homework of the students; on the other hand, it is helpful for students to wholesale homework to further master their knowledge. However, correcting homework is a very time-consuming task, especially for those tasks with simple and clear titles but large number of titles, such as: the four fundamental operational problems of primary school. Therefore, it is necessary to help the teacher reduce the burden of homework correction by technical means.
At present, the technology for the four fundamental operational problems of primary schools mainly takes pictures through mobile intelligent equipment (smart phones, tablets and the like), sends the pictures to a server through a network for processing and identification, and returns identification results to the mobile intelligent equipment through the network. Such a way of working relies on network connectivity and uploading user data may risk privacy disclosure.
Disclosure of Invention
In view of the above-mentioned deficiencies of the prior art, the present invention provides an arithmetic job modification system and method, so as to solve the problems that the method for modifying home jobs in the prior art depends on network connection and privacy disclosure may occur in uploading user data.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
the invention provides an arithmetic operation correcting system, comprising: the device comprises an image preprocessing and segmenting module, a character recognition module and a calculation and verification module; wherein the content of the first and second substances,
the image preprocessing and dividing module is used for carrying out graying, noise reduction and binarization processing on an input image initially containing operation content to convert the image into a binary image, cutting the binary image into a plurality of line images by using a horizontal projection method, wherein each line image contains one or a plurality of four arithmetic operation formulas, then dividing each line image into the image containing a single arithmetic formula by using a vertical projection method, and dividing each four arithmetic operation formulas into the image containing a single character by using a vertical projection method;
the character recognition module is used for recognizing the picture containing the single character through a convolutional neural network model;
and the calculation verification module is used for finishing the calculation of the calculation formula on the left side of the arithmetic formula equal sign by a dividing and conquering method, comparing the calculation result with the result on the right side of the arithmetic formula equal sign and outputting a comparison result.
Further, the image preprocessing and segmenting module preprocessing the input picture specifically includes:
(11) setting the RGB components of each pixel of the input picture to be the same value to finish graying the picture;
(12) and (3) performing noise reduction on the grayed picture by using bilateral filtering, wherein a bilateral filtering formula is expressed as follows:
where i, j represents the other pixel coordinates of the template window, k, l represents the center coordinate of the template window, σd，σrRepresents the standard deviation of the gaussian function, and f (i, j) and f (k, l) represent the pixel values at coordinates (i, j) and (k, l), respectively;
(13) and processing the processed picture by using an adaptive threshold method, wherein the pixel value is higher than the threshold value and is set to be 1, and the pixel value is lower than the threshold value and is set to be 0, so that a binary image is obtained.
Further, the process of segmenting the binary image by the image preprocessing and segmenting module specifically includes:
(21) horizontally projecting the obtained binary image, counting the number of black pixel points of each line of the image, recording the number in an array P, expressing the number of black pixel points of the ith line by P [ i ], and then segmenting the part of the binary image corresponding to each interval [ i, j ] which meets the following conditions and is stored in the array P:
thereby obtaining row diagrams, wherein each row diagram has one or more equations in the horizontal direction;
(22) vertically projecting the obtained line graph, and recording the sum SumLength of the lengths of the continuous blank columns and the number Num of the continuous blank columns; when the length L of a continuous blank column is more than 4 SumLength/Num, the continuous blank column is taken as a partition boundary, so that each line graph is finally divided into column graphs showing a single formula;
(23) vertically projecting the obtained histogram, counting the number of black pixels in each row of the histogram, recording the number of black pixels in an array Q, expressing the number of black pixels in the ith row by Q [ i ], and then segmenting the portion of the histogram corresponding to each interval [ i, j ] which meets the following conditions and is stored in the array Q:
thereby obtaining the picture of a single character in each nomogram.
Further, the character recognition module respectively performs printing character recognition and handwriting character recognition by using two convolutional neural network models with the same structure but different parameters.
Further, before inputting the picture data into the convolutional neural network model, the character recognition module needs to perform boundary expansion and scaling on the single character picture to change the size of the single character picture into a standard size (print volume characters 28 × 28, handwriting characters 56 × 56).
Further, the convolutional neural network model is specifically as follows:
(31) the first layer of the convolutional neural network model is the convolutional layer, the convolutional kernel size is 3 × 3, 32 convolutional kernels are received, the received input size is (56,56,1), and the activation function uses the relu function, which is expressed by the formula:
f(x)＝max(0，wTx+b)；
(32) the second layer of the convolutional neural network model is a pooling layer, the maximum pooling operation is carried out on the output of the first layer, the size of a pooling window is 2 x 2, and the step length is 2;
(33) the third layer of the convolutional neural network model is a convolutional layer, the size of a convolutional kernel is 3 x 3, 64 convolutional kernels are used in total, and a relu function is used as an activation function;
(34) the fourth layer of the convolutional neural network is a pooling layer, the output of the third layer is subjected to maximum pooling operation, the size of a pooling window is 2 x 2, and the step length is 2;
(35) the fifth layer of the convolutional neural network is a convolutional layer, the size of the convolutional kernel is 3 x 3, 128 convolutional kernels are used in total, and the relu function is used as an activation function;
(36) the sixth layer of the convolutional neural network is a Flatten layer and is used for flattening the output of the fifth layer to a one-dimensional space;
(37) the seventh layer and the eighth layer of the convolutional neural network are all fully connected layers, the output scale of the seventh layer is 32 × 1, the activation function is a relu function, the output scale of the eighth layer is 10 × 1, the activation function is softmax, and the formula is as follows:
further, the convolutional neural network model identifies the input scale of the print volume character as (28,28,1), and the output scale as 15 × 1.
Further, the character recognition module performs character recognition on each formula by using a print body recognition model until a sign is recognized, and then the recognition process is changed to recognize the rest characters of the formula by using a handwriting recognition model.
Furthermore, the calculation and verification module combines the characters identified by the character identification module to form a formula form of four arithmetic operations which can be stored in a computer.
Further, the division and treatment method of the calculation and verification module specifically comprises the following steps:
(41) searching a sign in an operational expression, and dividing the whole operational expression into a left calculation part and a right result part;
(42) for the left part calculation part, repeatedly searching an operator with the lowest priority in the formula, splitting the original formula into two sub-formulas until the sub-formulas only contain a single operand, continuously backtracking the values of the sub-formulas, and finally obtaining the result of the left part calculation;
(43) and comparing the result calculated on the left side with the result calculated on the right side, and returning the result to the user.
The invention discloses an arithmetic operation correction method, which comprises the following steps:
1) acquiring picture data containing job content;
2) preprocessing the acquired picture to convert the preprocessed picture into a binary image;
3) dividing the binary image to obtain the content of each formula, and further dividing each formula to obtain a picture containing a single character;
4) performing boundary expansion and scaling on pictures containing single characters to change the size of the pictures into a specified size (print characters 28 x 28 and handwriting characters 56 x 56);
5) identifying the character picture by using a convolutional neural network model;
6) combining the recognized characters by taking the arithmetic as a unit to obtain each arithmetic;
7) aiming at each formula, searching a sign to divide the formula into a left calculation part and a right result part;
8) for the left calculation part, calculating by using a divide-and-conquer method to obtain a result;
9) and comparing the calculated result with the result of the right result part, and outputting a comparison result.
The invention has the beneficial effects that:
the invention can finish the correction of the operation by taking pictures through common electronic equipment such as a smart phone and the like, has simple operation and can improve the correction efficiency of teachers to a great extent.
The invention can quickly finish the correction of the operation without network connection, and can well protect the privacy of the user
Drawings
FIG. 1 is a block diagram of a system according to the present invention.
FIG. 2 is a schematic diagram of a picture preprocessing and segmentation module according to the present invention.
FIG. 3 is a schematic diagram of a convolutional neural network model according to the present invention.
FIG. 4 is a schematic diagram of a character recognition process according to the present invention.
FIG. 5 is a schematic diagram of a computing verification module according to an embodiment of the present invention.
Detailed Description
In order to facilitate understanding of those skilled in the art, the present invention will be further described with reference to the following examples and drawings, which are not intended to limit the present invention.
Referring to fig. 1, an arithmetic job modification system according to the present invention includes: the device comprises an image preprocessing and segmenting module, a character recognition module and a calculation and verification module; wherein the content of the first and second substances,
the image preprocessing and dividing module is used for carrying out graying, noise reduction and binarization processing on an input image initially containing operation content to convert the image into a binary image, cutting the binary image into a plurality of line images by using a horizontal projection method, wherein each line image contains one or a plurality of four arithmetic operation formulas, then dividing each line image into the image containing a single arithmetic formula by using a vertical projection method, and dividing each arithmetic formula into the image containing a single character by using a vertical projection method;
referring to fig. 2, the preprocessing the input picture by the image preprocessing and segmenting module specifically includes:
(11) setting the RGB components of each pixel of the input picture to be the same value to finish graying the picture;
(12) and (3) performing noise reduction on the grayed picture by using bilateral filtering, wherein a bilateral filtering formula is expressed as follows:
where i, j represents the other pixel coordinates of the template window, k, l represents the center coordinate of the template window, σd，σrRepresents the standard deviation of the gaussian function, and f (i, j) and f (k, l) represent the pixel values at coordinates (i, j) and (k, l), respectively;
(13) and processing the processed picture by using an adaptive threshold method, wherein the pixel value is higher than the threshold value and is set to be 1, and the pixel value is lower than the threshold value and is set to be 0, so that a binary image is obtained.
The process of segmenting the binary image by the image preprocessing and segmenting module specifically comprises the following steps:
(21) horizontally projecting the obtained binary image, counting the number of black pixel points of each line of the image, recording the number in an array P, expressing the number of black pixel points of the ith line by P [ i ], and then segmenting the part of the binary image corresponding to each interval [ i, j ] which meets the following conditions and is stored in the array P:
thereby obtaining row diagrams, wherein each row diagram has one or more equations in the horizontal direction;
(22) vertically projecting the obtained line graph, and recording the sum SumLength of the lengths of the continuous blank columns and the number Num of the continuous blank columns; when the length L of a continuous blank column is more than 4 SumLength/Num, the continuous blank column is taken as a partition boundary, so that each line graph is finally divided into column graphs showing a single formula;
(23) vertically projecting the obtained histogram, counting the number of black pixels in each row of the histogram, recording the number of black pixels in an array Q, expressing the number of black pixels in the ith row by Q [ i ], and then segmenting the portion of the histogram corresponding to each interval [ i, j ] which meets the following conditions and is stored in the array Q:
thereby obtaining the picture of a single character in each nomogram.
The character recognition module is used for recognizing the picture containing the single character through a convolutional neural network model;
the character recognition module respectively performs printing character recognition and handwriting character recognition by using two convolutional neural network models with the same structure but different parameters.
Before inputting the picture data into the convolutional neural network model, the character recognition module needs to perform boundary expansion and scaling on the single character picture to change the size of the single character picture into a standard size (print volume characters 28 × 28, handwriting volume characters 56 × 56).
Referring to fig. 3, the convolutional neural network model is specifically as follows:
(31) the first layer of the convolutional neural network model is the convolutional layer, the convolutional kernel size is 3 × 3, 32 convolutional kernels are received, the received input size is (56,56,1), and the activation function uses the relu function, which is expressed by the formula:
f(x)＝max(0，wTx+b)；
(32) the second layer of the convolutional neural network model is a pooling layer, the maximum pooling operation is carried out on the output of the first layer, the size of a pooling window is 2 x 2, and the step length is 2;
(33) the third layer of the convolutional neural network model is a convolutional layer, the size of a convolutional kernel is 3 x 3, 64 convolutional kernels are used in total, and a relu function is used as an activation function;
(34) the fourth layer of the convolutional neural network is a pooling layer, the output of the third layer is subjected to maximum pooling operation, the size of a pooling window is 2 x 2, and the step length is 2;
(35) the fifth layer of the convolutional neural network is a convolutional layer, the size of the convolutional kernel is 3 x 3, 128 convolutional kernels are used in total, and the relu function is used as an activation function;
(36) the sixth layer of the convolutional neural network is a Flatten layer and is used for flattening the output of the fifth layer to a one-dimensional space;
(37) the seventh layer and the eighth layer of the convolutional neural network are all fully connected layers, the output scale of the seventh layer is 32 × 1, the activation function is a relu function, the output scale of the eighth layer is 10 × 1, the activation function is softmax, and the formula is as follows:
the convolutional neural network model identifies the input scale of the print volume character as (28,28,1) and the output scale as 15 x 1.
Referring to fig. 4, the recognition process of the character recognition module is that for each formula, character recognition is performed by using a print body recognition model until a sign is recognized, and then the recognition process is changed to recognize the rest characters of the formula by using a handwriting recognition model.
The calculation verification module is used for finishing the calculation of the left calculation formula of the arithmetic equal sign by a dividing and conquering method, comparing the calculation result with the right result of the arithmetic equal sign and outputting a comparison result;
the calculation and verification module combines the characters identified by the character identification module to form a formula form of four arithmetic operations which can be stored in a computer.
Referring to fig. 5, the divide and conquer method specifically includes:
(41) searching a sign in an operational expression, and dividing the whole operational expression into a left calculation part and a right result part;
(42) for the left part calculation part, repeatedly searching an operator with the lowest priority in the formula, splitting the original formula into two sub-formulas until the sub-formulas only contain a single operand, continuously backtracking the values of the sub-formulas, and finally obtaining the result of the left part calculation; operator priorities are as follows:
(43) and comparing the result calculated on the left side with the result calculated on the right side, and returning the result to the user.
The invention discloses an arithmetic operation correction method, which comprises the following steps:
1) acquiring picture data containing job content;
2) preprocessing the acquired picture to convert the preprocessed picture into a binary image;
3) dividing the binary image to obtain the content of each formula, and further dividing each formula to obtain a picture containing a single character;
4) performing boundary expansion and scaling on pictures containing single characters to change the size of the pictures into a specified size (print characters 28 x 28 and handwriting characters 56 x 56);
5) identifying the character picture by using a convolutional neural network model;
6) combining the recognized characters by taking the arithmetic as a unit to obtain each arithmetic;
7) aiming at each formula, searching a sign to divide the formula into a left calculation part and a right result part;
8) for the left calculation part, calculating by using a divide-and-conquer method to obtain a result;
9) and comparing the calculated result with the result of the right result part, and outputting a comparison result.
While the invention has been described in terms of its preferred embodiments, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention.
Claims (10)
1. An arithmetic job modification system, comprising: the device comprises an image preprocessing and segmenting module, a character recognition module and a calculation and verification module; wherein the content of the first and second substances,
the image preprocessing and dividing module is used for carrying out graying, noise reduction and binarization processing on an input image initially containing operation content to convert the image into a binary image, cutting the binary image into a plurality of line images by using a horizontal projection method, wherein each line image contains one or a plurality of four arithmetic operation formulas, then dividing each line image into the image containing a single arithmetic formula by using a vertical projection method, and dividing each arithmetic formula into the image containing a single character by using a vertical projection method;
the character recognition module is used for recognizing the picture containing the single character through a convolutional neural network model;
and the calculation verification module is used for finishing the calculation of the calculation formula on the left side of the arithmetic formula equal sign through a dividing and conquering method, comparing the calculation result with the calculation formula equal sign result on the right side, and outputting a comparison result.
2. The arithmetic job modification system according to claim 1, wherein the image preprocessing and segmentation module preprocessing the input picture specifically comprises:
(11) setting the RGB components of each pixel of the input picture to be the same value to finish graying the picture;
(12) and (3) performing noise reduction on the grayed picture by using bilateral filtering, wherein a bilateral filtering formula is expressed as follows:
where i, j represents the other pixel coordinates of the template window, k, l represents the center coordinate of the template window, σd，σrRepresents the standard deviation of the gaussian function, and f (i, j) and f (k, l) represent the pixel values at coordinates (i, j) and (k, l), respectively;
(13) and processing the processed picture by using an adaptive threshold method, wherein the pixel value is higher than the threshold value and is set to be 1, and the pixel value is lower than the threshold value and is set to be 0, so that a binary image is obtained.
3. The arithmetic job modification system according to claim 2, wherein the process of segmenting the binary image by the image preprocessing and segmentation module specifically comprises:
(21) horizontally projecting the obtained binary image, counting the number of black pixel points of each line of the image, recording the number in an array P, expressing the number of black pixel points of the ith line by P [ i ], and then segmenting the part of the binary image corresponding to each interval [ i, j ] which meets the following conditions and is stored in the array P:
thereby obtaining row graphs, wherein each row graph has one or more equations in the horizontal direction;
(22) vertically projecting the obtained line graph, and recording the sum SumLength of the lengths of the continuous blank columns and the number Num of the continuous blank columns; when the length L of a continuous blank column is more than 4 SumLength/Num, the continuous blank column is taken as a partition boundary, so that each line graph is finally divided into column graphs showing a single formula;
(23) vertically projecting the obtained histogram, counting the number of black pixels in each row of the histogram, recording the number of black pixels in an array Q, expressing the number of black pixels in the ith row by Q [ i ], and then segmenting the portion of the histogram corresponding to each interval [ i, j ] which meets the following conditions and is stored in the array Q:
thereby obtaining the picture of a single character in each nomogram.
4. The arithmetic job correction system according to claim 1, wherein the character recognition module performs print character recognition and handwritten character recognition, respectively, using two convolutional neural network models having the same architecture but different parameters.
5. The arithmetic job modification system of claim 1, wherein the character recognition module performs boundary expansion and scaling of the single character pictures to a standard size before inputting the picture data into the convolutional neural network model.
6. The arithmetic job modification system of claim 1, wherein the convolutional neural network model is specifically as follows:
(31) the first layer of the convolutional neural network model is the convolutional layer, the convolutional kernel size is 3 × 3, 32 convolutional kernels are received, the received input size is (56,56,1), and the activation function uses the relu function, which is expressed by the formula:
f(x)＝max(0，wTx+b)；
(32) the second layer of the convolutional neural network model is a pooling layer, the maximum pooling operation is carried out on the output of the first layer, the size of a pooling window is 2 x 2, and the step length is 2;
(33) the third layer of the convolutional neural network model is a convolutional layer, the size of a convolutional kernel is 3 x 3, 64 convolutional kernels are used in total, and a relu function is used as an activation function;
(34) the fourth layer of the convolutional neural network is a pooling layer, the output of the third layer is subjected to maximum pooling operation, the size of a pooling window is 2 x 2, and the step length is 2;
(35) the fifth layer of the convolutional neural network is a convolutional layer, the size of the convolutional kernel is 3 x 3, 128 convolutional kernels are used in total, and the relu function is used as an activation function;
(36) the sixth layer of the convolutional neural network is a Flatten layer and is used for flattening the output of the fifth layer to a one-dimensional space;
(37) the seventh layer and the eighth layer of the convolutional neural network are all fully connected layers, the output scale of the seventh layer is 32 × 1, the activation function is a relu function, the output scale of the eighth layer is 10 × 1, the activation function is softmax, and the formula is as follows:
7. the arithmetic job modification system of claim 6, wherein the convolutional neural network model identifies a print volume character with an input size of (28,28,1) and an output size of 15 x 1.
8. The arithmetic job correction system according to claim 1, wherein the character recognition module performs character recognition using a print recognition model until a sign is recognized for each formula, and then changes to recognize the remaining characters of the formula using a handwriting recognition model.
9. The arithmetic job modification system according to claim 1, wherein the division method of the calculation and verification module is specifically as follows:
(41) searching a sign in an operational expression, and dividing the whole operational expression into a left calculation part and a right result part;
(42) for the left part calculation part, repeatedly searching an operator with the lowest priority in the formula, splitting the original formula into two sub-formulas until the sub-formulas only contain a single operand, continuously backtracking the values of the sub-formulas, and finally obtaining the result of the left part calculation;
(43) and comparing the result calculated on the left side with the result calculated on the right side, and returning the result to the user.
10. A method for modifying arithmetic operations, comprising the steps of:
1) acquiring picture data containing job content;
2) preprocessing the acquired picture to convert the preprocessed picture into a binary image;
3) dividing the binary image to obtain the content of each formula, and further dividing each formula to obtain a picture containing a single character;
4) carrying out boundary expansion and scaling on pictures containing single characters to change the scale of the pictures into a specified size;
5) identifying the character picture by using a convolutional neural network model;
6) combining the recognized characters by taking the arithmetic as a unit to obtain each arithmetic;
7) aiming at each formula, searching a sign to divide the formula into a left calculation part and a right result part;
8) for the left calculation part, calculating by using a divide-and-conquer method to obtain a result;
9) and comparing the calculated result with the result of the right result part, and outputting a comparison result.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112906559A (en) * | 2021-02-10 | 2021-06-04 | 网易有道信息技术（北京）有限公司 | Machine-implemented method for correcting formulas and related product |
| CN113435441A (en) * | 2021-07-22 | 2021-09-24 | 广州华腾教育科技股份有限公司 | Bi-LSTM mechanism-based four-fundamental operation formula image intelligent batch modification method |
| CN113596418A (en) * | 2021-07-06 | 2021-11-02 | 作业帮教育科技（北京）有限公司 | Correction-assisted projection method, device, system and computer program product |
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