CN103020889A - Method and device for image gradient computation - Google Patents

Abstract

The invention discloses a method and a device for image gradient computation. The method comprises the steps of conducting buffering of the N*N window size on input image data; conducting rightward moving operation on all efficient points in a N*N window respectively, and dividing efficient points into M types; dividing the window into a left portion and a right portion, and conducting statistics on numbers of all types within M types in the left portion and the right portion of the window respectively; and according to the number of efficient points of each of the types in the left portion and the right portion of the window and according to the X2 histogram distribution, calculating a gradient value of the current efficient point. According to the method and the device, classification and X2 histogram computation can be conducted for efficient points in the window in parallel, so that the gradient value of the window which is represented by each of the input pixel points can be calculated accurately, and an accurate gradient image can be obtained.

Description

Image gradient computing method and device

[technical field]

The present invention relates to image processing field, particularly a kind of image gradient computing method and device.

[background technology]

Rim detection is the basic problem in image processing and the computer vision, and the purpose of rim detection is that brightness changes obvious point in the reference numbers image.The rim detection of image can realize by gradient operator, and its essence is namely asked its gradient image to piece image.Gradient calculation becomes the important step of Image Edge-Detection.

In the prior art, often adopt Roberts, sobel, the operators such as prewitt come the gradient of computed image.The Roberts operator is a kind of operator that utilizes local difference operator to seek the edge, and its bearing accuracy is high, but for noise sensitivity very; The sobel operator is a discreteness difference operator, is used for the approximate value of gradient of arithmograph image brightness function, and it can suppress the impact of noise, but the detection at edge is wider; The prewitt operator utilizes about the pixel, the gray scale difference of left and right sides adjoint point, reach the extreme value Edge detected in edge, remove the part pseudo-edge, noise had smoothing effect, but can cause the erroneous judgement of marginal point, because the gray-scale value of many noise spots is also very large, and for the less marginal point of amplitude, its edge has been lost on the contrary.

To sum up, all there is coarse shortcoming in existing image gradient computing method degree of accuracy.

[summary of the invention]

The object of the present invention is to provide a kind of image gradient computing method and device, described image gradient computing method and device can obtain gradient image more accurately.

According to an aspect of the present invention, provide a kind of image gradient computing method, described method comprises:

Input image data is carried out the buffer memory of N*N window size; Respectively each available point in the N*N window is carried out the right shift operation, available point is divided into the M class; Two parts about window is divided into are added up respectively the number that belongs to each class in the M class about described window in the part; The number and the χ that belong to each class according to each available point of part about in the described window ²Histogram distribution is calculated the Grad of current available point.

Further, the described buffer memory that input image data is carried out the N*N window size comprises:

Needs according to image buffer storage, the image buffer storage district adopts the rectangular window of N*N to come the view data of the capable N row of buffer memory N, here adopt FIFO ((First Input First Output, First Input First Output) as the hardware configuration of cache lines data, its bit wide is 8, the degree of depth is X, and wherein bit wide is consistent with the required maximum bit wide of view data, and the degree of depth equals the number of data line; The matrix that the right of FIFO is comprised of the register of N*N 8, view data enters uppermost FIFO and one group of register simultaneously by input end, wait for X all after date, the data that uppermost FIFO begins to read buffer memory are to second group of register, and second FIFO begins to write data; Wait for 2X all after date, second FIFO begins read data to the 3rd group of register, and the 3rd FIFO begins to write data simultaneously, and the rest may be inferred, waits until [X* (N-1)+N] individual all after dates, and the data buffer storage of the capable N row of image N is complete;

Wherein, X is the number of input picture data line, and N is the odd number more than or equal to 3.

Further, describedly respectively each available point in the N*N window is carried out right shift operation, available point is divided into the M class comprises:

Each available point in the N*N window is carried out the dextroposition operation, current available point is divided into the M class from small to large, the corresponding predetermined size of every class, described M is the integer greater than 0.

Further, describedly respectively each available point in the N*N window is carried out right shift operation, available point is divided into the M class also comprises:

Described M is 32, and the default value of the pixel of image is the number between 0～255, and it is divided into 32 classes, namely remove 8 computings for pixel, according to the shifting function of hardware configuration, with move to right 3 operation of each available point numerical value in the window, realize that 32 classes of available point are divided.

Further, described window is divided into about two parts, add up respectively about described window the number that belongs to each class in the M class in the part and comprise:

With the rectangular window of buffer memory pixel according to first direction, second direction, third direction and four directions two parts about be divided into; For each direction, about the part respectively have Number belongs to respectively the number of the number of each class of 32 classes the inside in two parts about the statistics; For about part, the respectively cumulative sum1～sum32 that obtains.

Further, described number and the χ that belongs to each class according to each available point of part about in the described window ²The Grad that histogram distribution is calculated current available point comprises:

Calculate the Grad of current available point according to following formula:

${\mathrm{\χ}}^2=\frac{1}{2}\underset{i}{\mathrm{\Σ}}\frac{{(g_i-h_i)}^2}{g_i+h_i}$

Wherein, g _i, h _iPart belongs to the number of of a sort number about being respectively in the N*N size windows centered by current available point, and i is the class number of dividing, and the value of i is 32 here.

According to a further aspect in the invention, the present invention also provides a kind of image gradient calculation element, and described image gradient calculation element comprises: the view data cache module, for the buffer memory that input image data is carried out the N*N window size; Sort module is used for each available point in the N*N window is carried out the right shift operation, and available point is divided into the M class; The left-half statistical module is used for adding up the number that belongs to each class of M class in the described window left-half; The right half part statistical module is used for adding up the number that belongs to each class of M class in the described window right half part; The image gradient computing module is used for belonging to according to each available point of part about in the described window number and the χ of each class ²Histogram distribution is calculated the Grad of current available point.

Further, described view data cache module, the concrete rectangular window that is used for employing N*N comes the view data of the capable N row of buffer memory N, adopt FIFO ((First Input First Output, First Input First Output) as the hardware configuration of cache lines data, its bit wide is 8, and the degree of depth is X, wherein bit wide is consistent with the required maximum bit wide of view data, and the degree of depth equals the number of data line; The matrix that the right of described FIFO is comprised of the register of N*N 8, view data enters uppermost FIFO and one group of register simultaneously by input end, wait for X all after date, the data that uppermost FIFO begins to read buffer memory are to second group of register, and second FIFO begins to write data; Wait for that 2X sings all after dates, second FIFO begins read data to the 3rd group of register, and the 3rd FIFO begins to write data simultaneously, and the rest may be inferred, waits until [X* (N-1)+N] individual all after dates, and the data buffer storage of the capable N row of image N is complete;

Wherein, X is the number of input picture data line, and N is the odd number more than or equal to 3.

Further, described sort module, concrete being used for carried out the dextroposition operation to each available point in the N*N window, and current available point is divided into the M class from small to large, the corresponding predetermined size of every class, described M is the integer greater than 0.

Described M is 32, and the default value of the pixel of image is the number between 0～255, and it is divided into 32 classes, namely remove 8 computings for pixel, according to the shifting function of hardware configuration, with move to right 3 operation of each available point numerical value in the window, realize that 32 classes of available point are divided.

Further, described left-half statistical module, concrete being used for the rectangular window of buffer memory pixel according to first direction, second direction, third direction and four directions two parts about be divided into; For each direction, left-half has

Number, the number of adding up the number that belongs to each class of 32 classes the inside in the left-half; For left-half, the cumulative sum1～sum32 that obtains.

Further, described right half part statistical module, concrete being used for the rectangular window of buffer memory pixel according to first direction, second direction, third direction and four directions two parts about be divided into; For each direction, right half part has

Number, the number of adding up the number that belongs to each class of 32 classes the inside in the right half part; For right half part, the cumulative sum1～sum32 that obtains.

Further, described image gradient computing module, the concrete Grad that is used for calculating according to following formula current available point:

${\mathrm{\χ}}^2=\frac{1}{2}\underset{i}{\mathrm{\Σ}}\frac{{(g_i-h_i)}^2}{g_i+h_i}$

Wherein, g _i, h _iPart belongs to the number of of a sort number about being respectively in the N*N size windows centered by current available point, and i is the class number of dividing, and the value of i is 32 here.

Compared with prior art, the image gradient computing method that the embodiment of the invention provides based on gradient orientation histogram, are a kind of computing method of new image gradient, can the noise reduction impact and guarantee the degree of accuracy of gradient image.

[description of drawings]

In conjunction with reaching with reference to the accompanying drawings ensuing detailed description, the present invention will be more readily understood, structure member corresponding to same Reference numeral wherein, wherein:

Fig. 1 is the image gradient computing method method flow diagram in one embodiment among the present invention;

Fig. 2 is the image gradient calculation element block diagram in one embodiment among the present invention.

[embodiment]

For above-mentioned purpose of the present invention, feature and advantage can be become apparent more, the present invention is further detailed explanation below in conjunction with the drawings and specific embodiments.

Histograms of oriented gradients (Histogram of Oriented Gradient, HOG) feature is a kind of Feature Descriptor that is used for carrying out object detection in computer vision and image processing.The method has been used the gradient direction feature of image own, be similar to the edge orientation histogram method, but it is characterized in that it calculates at an intensive big or small unified grid unit of grid, and used the normalized method of overlapping local contrast in order to improve degree of accuracy.Compare with other character description method, histograms of oriented gradients (HOG) descriptor has many good qualities, and it can both keep good unchangeability to image geometry with deformation optics.Therefore the image gradient computing method that the embodiment of the invention provides based on gradient orientation histogram, propose a kind of computing method of new image gradient, thus noise reduction impact and guarantee the degree of accuracy of gradient image.

The embodiment of the invention provides a kind of image gradient computing method and device, described image gradient computing method and device can be processed the image that is gathered by image capture device, when described image gradient computing method and device processing one frame input picture, finally can obtain the Grad of other pixel except the part edge pixel in this input picture, wherein the Grad of each pixel has represented the gradient information of the window of a pre-sizing centered by this pixel.

Please refer to Fig. 1, it shows the method flow diagram of image gradient computing method in an embodiment 100 among the present invention.Described image gradient computing method comprise:

Step 102 is carried out the buffer memory of N*N window size to input image data;

The image of image capture device collection normally has the image of certain resolution, is the gray level image of 1024*768 such as resolution.When these images are processed, need to be to each two field picture difference compute gradient value, therefore description hereinafter is also to process a two field picture as example, hereby explanation.After receiving a frame input picture, at first input image data is carried out the buffer memory of N*N window size; Can adopt FIFO as the buffer memory of the capable data of view data during implementation, realize the N*N window size with N*N register.

Such as in a specific embodiment, needs according to image buffer storage, the image buffer storage district adopts the rectangular window of N*N to come the view data of the capable N row of buffer memory N, adopt FIFO as the hardware configuration of cache lines data, its bit wide is 8, the degree of depth is X, and wherein bit wide is consistent with the required maximum bit wide of view data, and the degree of depth equals the number of data line; The matrix that the right of described FIFO is comprised of the register of N*N 8, view data enters uppermost FIFO and one group of register simultaneously by input end, wait for X all after date, the data that uppermost FIFO begins to read buffer memory are to second group of register, and second FIFO begins to write data; Wait for 2X all after date, second FIFO begins read data to the 3rd group of register, and the 3rd FIFO begins to write data simultaneously, and the rest may be inferred, waits until [X* (N-1)+N] individual all after dates, and the data buffer storage of the capable N row of image N is complete;

Wherein, X is the number of input picture data line, and N is the odd number more than or equal to 3.

Because what the present invention taked is the 7*7 windows cache, therefore upper and lower, left and right respectively have 3 row, 3 row not process, but the image outline that the edge part branch of a two field picture can represent is less, during processing, image also often the information of the pixel of marginal portion is given up, because the processing details of edge pixel point does not affect invention essence of the present invention, therefore this paper does not add detailed description, should not limit the present invention with the processing details of edge pixel point yet.

Step 104 is carried out the right shift operation to each available point in the N*N window respectively, and available point is divided into the M class;

Each available point in the described step 104 pair N*N window carries out the dextroposition operation, and current available point is divided into the M class from small to large, the corresponding predetermined size of every class, and described M is the integer greater than 0.

Such as in a specific embodiment, described M is 32, the default value of the pixel of image is the number between 0～255, it is divided into 32 classes, namely remove 8 computings for pixel, according to the shifting function of hardware configuration, with move to right 3 operation of each available point numerical value in the window, realize that 32 classes of available point are divided.

Step 106, two parts about window is divided into, add up respectively the number that belongs to each class in the M class about described window in the part:

The left-half statistical module with the rectangular window of buffer memory pixel according to first direction, second direction, third direction and four directions two parts about be divided into; For each direction, left-half has

Number, the number of adding up the number that belongs to each class of 32 classes the inside in the left-half; For left-half, the cumulative sum1～sum32 that obtains.

The right half part statistical module with the rectangular window of buffer memory pixel according to first direction, second direction, third direction and four directions two parts about be divided into; For each direction, right half part has

Number, the number of adding up the number that belongs to each class of 32 classes the inside in the right half part; For right half part, the cumulative sum1～sum32 that obtains.

Step 108 belongs to number and the χ of each class according to each available point of part about in the described window ²The Grad that histogram distribution is calculated current available point comprises:

Obtain the number that each available point in the predetermined size windows centered by current available point belongs to each class in accumulative total, can belong to according to each available point of part about in the described window number and the χ of each class ²Histogram distribution is calculated the Grad of current available point.Specifically calculate the Grad of current available point according to following formula:

${\mathrm{\χ}}^2=\frac{1}{2}\underset{i}{\mathrm{\Σ}}\frac{{(g_i-h_i)}^2}{g_i+h_i}$

Wherein, g _i, h _iPart belongs to the number of of a sort number about being respectively in the N*N size windows centered by current available point, and i is the class number of dividing, and the value of i is 32 here.

In sum, described method adopts χ ²Histogram distribution is come the compute gradient value, makes it possible to more rapidly the Grad that window that each available point to input calculates its representative has.And in the computation process, a plurality of computation processes can be distinguished concurrent operation, so that final eigenwert result of calculation is flow system output.Simultaneously can also the noise reduction impact and guarantee the degree of accuracy of gradient image.

The present invention provides a kind of image gradient calculation element simultaneously, please refer to Fig. 2, and it shows the block diagram of image gradient calculation element in an embodiment 200 among the present invention.Described image gradient calculation element 200 comprises view data cache module 202, sort module 204, left-half statistical module 206, right half part statistical module 208, image gradient computing module 210.

Described view data cache module 202, the concrete rectangular window that is used for employing N*N comes the view data of the capable N row of buffer memory N, adopt FIFO ((First Input First Output, First Input First Output) as the hardware configuration of cache lines data, its bit wide is 8, the degree of depth is X, and wherein bit wide is consistent with the required maximum bit wide of view data, and the degree of depth equals the number of data line; The matrix that the right of described FIFO is comprised of the register of N*N 8, view data enters uppermost FIFO and one group of register simultaneously by input end, wait for X all after date, the data that uppermost FIFO begins to read buffer memory are to second group of register, and second FIFO begins to write data; Wait for 2X all after date, second FIFO begins read data to the 3rd group of register, and the 3rd FIFO begins to write data simultaneously, and the rest may be inferred, waits until [X* (N-1)+N] individual all after dates, and the data buffer storage of the capable N row of image N is complete;

Wherein, X is the number of input picture data line, and N is the odd number more than or equal to 3.

Described sort module 204, concrete being used for carried out the dextroposition operation to each available point in the N*N window, and current available point is divided into the M class from small to large, the corresponding predetermined size of every class, described M is the integer greater than 0.

Described M is 32, and the default value of the pixel of image is the number between 0～255, and it is divided into 32 classes, namely remove 8 computings for pixel, according to the shifting function of hardware configuration, with move to right 3 operation of each available point numerical value in the window, realize that 32 classes of available point are divided.

Described left-half statistical module 206, concrete being used for the rectangular window of buffer memory pixel according to first direction, second direction, third direction and four directions two parts about be divided into; For each direction, left-half has Number, the number of adding up the number that belongs to each class of 32 classes the inside in the left-half; For left-half, the cumulative sum1～sum32 that obtains.

Described right half part statistical module 208, concrete being used for the rectangular window of buffer memory pixel according to first direction, second direction, third direction and four directions two parts about be divided into; For each direction, right half part has

Number, the number of adding up the number that belongs to each class of 32 classes the inside in the right half part; For right half part, the cumulative sum1～sum32 that obtains.

Described image gradient computing module 210, the concrete Grad that is used for calculating according to following formula current available point:

${\mathrm{\χ}}^2=\frac{1}{2}\underset{i}{\mathrm{\Σ}}\frac{{(g_i-h_i)}^2}{g_i+h_i}$

Wherein, g _i, h _iPart belongs to the number of of a sort number about being respectively in the N*N size windows centered by current available point, and i is the class number of dividing, and the value of i is 32 here.

According to χ ²Computing formula is carried out additive operation, subtraction, multiplying and division arithmetic one time for each class in the 1-32 classification, and is again that the result is cumulative, just obtains final Grad divided by 2.Among the present invention, subtraction is finished prior to the multiplying one-period, and the result that subtraction is obtained gives multiplying.The clock of additive operation and multiplying must be synchronously, because the result that the result that multiplication obtains and addition obtain will do division arithmetic, if the nonsynchronous words of clock, mistake will appear in the result.Division arithmetic utilizes IP kernel to realize, through 27 correct results of cycles output, except 2 computings realize by one the operation of moving to right.

In sum, described device adopts χ ²Histogram distribution is come the compute gradient value, makes it possible to more rapidly the Grad that window that each available point to input calculates its representative has.And in the computation process, a plurality of computation processes can be distinguished concurrent operation, so that final Grad result of calculation is flow system output.Simultaneously can also the noise reduction impact and guarantee the degree of accuracy of gradient image.

Need to prove: the image gradient calculation element that above-described embodiment provides is when this paper describes, only the division with above-mentioned each functional module is illustrated, in the practical application, can as required the above-mentioned functions distribution be finished by different functional modules, the inner structure that is about to device is divided into different functional modules, to finish all or part of function described above.In addition, the Grad calculation element that above-described embodiment provides and Grad computing method embodiment belong to same design, and its specific implementation process sees embodiment of the method for details, repeats no more here.

The all or part of step that one of ordinary skill in the art will appreciate that realization above-described embodiment can be finished by hardware, also can come the relevant hardware of instruction finish by program, and described program can be stored in ROM (read-only memory), disk or CD etc.

Above-mentioned explanation has fully disclosed the specific embodiment of the present invention.It is pointed out that and be familiar with the scope that any change that the person skilled in art does the specific embodiment of the present invention does not all break away from claims of the present invention.Correspondingly, the scope of claim of the present invention also is not limited only to described embodiment.

Claims (11)

1. image gradient computing method and device is characterized in that, described method comprises:

Input image data is carried out the buffer memory of N*N window size;

Respectively each available point in the N*N window is carried out the right shift operation, available point is divided into the M class;

Two parts about window is divided into are added up respectively the number that belongs to each class in the M class about described window in the part;

The number and the χ that belong to each class according to each available point of part about in the described window ²Histogram distribution is calculated the Grad of current available point.

2. image gradient computing method according to claim 1 is characterized in that, the described buffer memory that input image data is carried out the N*N window size comprises:

Needs according to image buffer storage, the image buffer storage district adopts the rectangular window of N*N to come the view data of the capable N row of buffer memory N, described image buffer adopts FIFO as the hardware configuration of cache lines data, its bit wide is 8, the degree of depth is X, wherein bit wide is consistent with the required maximum bit wide of view data, and the degree of depth equals the number of data line; The matrix that the right of described FIFO is comprised of the register of N*N 8, view data enters uppermost FIFO and one group of register simultaneously by input end, wait for X all after date, the data that uppermost FIFO begins to read buffer memory are to second group of register, and second FIFO begins to write data; Wait for 2X all after date, second FIFO begins read data to the 3rd group of register, and the 3rd FIFO begins to write data simultaneously, and the rest may be inferred, waits until [X* (N-1)+N] individual all after dates, and the data buffer storage of the capable N row of image N is complete;

Wherein, X is the number of input picture data line, and N is the odd number more than or equal to 3.

3. image gradient computing method according to claim 1 is characterized in that, describedly respectively each available point in the N*N window are carried out right shift operation, available point is divided into the M class comprises:

Each available point in the N*N window is carried out the dextroposition operation, current available point is divided into the M class from small to large, the corresponding predetermined size of every class, described M is the integer greater than 0.

4. image gradient computing method according to claim 3 is characterized in that,

Described M is 32, and the default value of the pixel of image is the number between 0～255, and it is divided into 32 classes, namely remove 8 computings for pixel, according to the shifting function of hardware configuration, with move to right 3 operation of each available point numerical value in the window, realize that 32 classes of available point are divided.

5. image gradient computing method according to claim 1 is characterized in that, described window is divided into about two parts, add up respectively about described window the number that belongs to each class in the M class in the part and comprise:

With the rectangular window of buffer memory pixel according to first direction, second direction, third direction and four directions two parts about be divided into; For each direction, about the part respectively have

Number belongs to respectively the number of the number of each class of 32 classes the inside in two parts about the statistics; For about part, the respectively cumulative sum1～sum32 that obtains.

6. image gradient computing method according to claim 1 is characterized in that, described number and the χ that belongs to each class according to each available point of part about in the described window ²The Grad that histogram distribution is calculated current available point comprises:

Calculate the Grad of current available point according to following formula:

${\mathrm{\χ}}^2=\frac{1}{2}\underset{i}{\mathrm{\Σ}}\frac{{(g_i-h_i)}^2}{g_i+h_i}$

Wherein, g _i, h _iPart belongs to the number of of a sort number about being respectively in the N*N size windows centered by current available point, and i is the class number of dividing, and the value of i is 32 here.

7. an image gradient calculation element is characterized in that, it comprises:

The view data cache module is for the buffer memory that input image data is carried out the N*N window size;

Sort module is used for each available point in the N*N window is carried out the right shift operation, and available point is divided into the M class;

The left-half statistical module is used for adding up the number that belongs to each class of M class in the described window left-half;

The right half part statistical module is used for adding up the number that belongs to each class of M class in the described window right half part;

The image gradient computing module is used for belonging to according to each available point of part about in the described window number and the χ of each class ²Histogram distribution is calculated the Grad of current available point.

8. image gradient calculation element according to claim 7, it is characterized in that, described view data cache module, the concrete rectangular window that is used for employing N*N comes the view data of the capable N row of buffer memory N, described image buffer adopts FIFO as the hardware configuration of cache lines data, and its bit wide is 8, and the degree of depth is X, wherein bit wide is consistent with the required maximum bit wide of view data, and the degree of depth equals the number of data line; The matrix that the right of described FIFO is comprised of the register of N*N 8, view data enters uppermost FIFO and one group of register simultaneously by input end, wait for X all after date, the data that uppermost FIFO begins to read buffer memory are to second group of register, and second FIFO begins to write data; Wait for 2X all after date, second FIFO begins read data to the 3rd group of register, and the 3rd FIFO begins to write data simultaneously, and the rest may be inferred, waits until [X* (N-1)+N] individual all after dates, and the data buffer storage of the capable N row of image N is complete;

Wherein, X is the number of input picture data line, and N is the odd number more than or equal to 3.

9. image gradient calculation element according to claim 7 is characterized in that,

Described sort module, concrete being used for carried out the dextroposition operation to each available point in the N*N window, and current available point is divided into the M class from small to large, the corresponding predetermined size of every class, described M is the integer greater than 0;

Described M is 32, and the default value of the pixel of image is the number between 0～255, and it is divided into 32 classes, namely remove 8 computings for pixel, according to the shifting function of hardware configuration, with move to right 3 operation of each available point numerical value in the window, realize that 32 classes of available point are divided.

10. image gradient calculation element according to claim 7 is characterized in that,

Described left-half statistical module, concrete being used for the rectangular window of buffer memory pixel according to first direction, second direction, third direction and four directions two parts about be divided into; For each direction, left-half has Number, the number of adding up the number that belongs to each class of 32 classes the inside in the left-half; For left-half, the cumulative sum1～sum32 that obtains;

Described right half part statistical module, concrete being used for the rectangular window of buffer memory pixel according to first direction, second direction, third direction and four directions two parts about be divided into; For each direction, right half part has Number, the number of adding up the number that belongs to each class of 32 classes the inside in the right half part; For right half part, the cumulative sum1～sum32 that obtains.

11. image gradient calculation element according to claim 7 is characterized in that, described image gradient computing module, and the concrete Grad that is used for calculating according to following formula current available point:

${\mathrm{\χ}}^2=\frac{1}{2}\underset{i}{\mathrm{\Σ}}\frac{{(g_i-h_i)}^2}{g_i+h_i}$

Wherein, g _i, h _iPart belongs to the number of of a sort number about being respectively in the N*N size windows centered by current available point, and i is the class number of dividing, and the value of i is 32 here.

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