CN114638845A - Quantum image segmentation method and device based on double thresholds and storage medium - Google Patents

Abstract

The invention discloses a quantum image segmentation method, device and storage medium based on double thresholds. The method includes: acquiring a grayscale digital image and preparing a corresponding NEQR quantum image; setting a high threshold and a low threshold, and constructing a high threshold quantum image Segmentation circuit, low-threshold quantum segmentation circuit, and quantum segmentation circuit between high and low thresholds; construct a comparator, and based on the comparator, divide each pixel of the NEQR quantum image into pixels whose gray value is greater than or equal to the high threshold, and whose gray value is less than the low threshold The pixels whose gray value is greater than or equal to the low threshold and less than the high threshold value; the high-threshold quantum segmentation circuit, the low-threshold quantum segmentation circuit and the quantum segmentation circuit between high and low thresholds respectively divide the pixels whose gray value is greater than the high threshold and the gray value Pixels smaller than the low threshold and pixels whose gray value is greater than or equal to the low threshold and less than or equal to the high threshold are segmented; the present invention is less complicated and can obtain an accurate and clear segmentation map at the same time.

Description

A kind of quantum image segmentation method, device and storage medium based on double threshold

technical field

The invention relates to a quantum image segmentation method, device and storage medium based on double thresholds, and belongs to the technical field of quantum image processing.

Background technique

Quantum image processing is an interdisciplinary subject of quantum computing and image processing, because it combines the parallelism of quantum computing and the high performance of entanglement, realizes quantum acceleration, and improves computing power. This makes it possible to solve some problems on quantum computers that cannot be solved by classical computers. Although the research on quantum image processing technology is gradually deepening, it is still in its infancy as a whole, and the development direction is uneven. And what can be done at present is to perform simple operations such as filtering, feature extraction and edge detection on the image, and deeper image processing algorithms still need further research. Image segmentation is the first step in image analysis, the foundation of computer vision, and an important part of image understanding. The most common image segmentation methods are: threshold-based segmentation, region-based segmentation, edge detection-based segmentation, and segmentation combined with specific tools. Due to the relatively few researches on quantum image segmentation and the immature technology, the current quantum image segmentation algorithms have less implementation of classical methods. In 2013, Li et al. proposed quantum image segmentation based on quantum search algorithm, in their algorithm, the Oracle operator for amplitude amplification is not provided, which makes the simulation very difficult. In 2014, Caraiman et al. proposed a histogram-based quantum image segmentation algorithm. They used the performance of quantum Fourier transform and quantum amplitude amplification, and achieved exponential speedup compared to the classical algorithm, but the GRover operator used quantum Oracle, there is no way to determine, and specific Oracle operators are required for circuit implementation in actual quantum algorithms. A year later, Caraiman et al. proposed a single-threshold-based quantum image segmentation method, they discussed the circuit implementation of the Oracle operator, and provided an example of segmenting synthetic images and real images, but the implementation of the algorithm requires 50 Qubits, which make it difficult to simulate on existing quantum computing platforms. None of these quantum image segmentation algorithms are implemented on a quantum simulator. In 2019, xia et al. proposed a new type of multi-bit quantum comparator and its application in image binarization. They chose a threshold for binary segmentation of quantum images, which required a relatively large number of qubits and complex algorithms. higher degree. None of the above algorithms have been simulated in a quantum simulator. In 2020, Yuan et al. proposed a double-threshold quantum image segmentation algorithm with fewer qubits and simulated it in a quantum simulator. However, the complexity of the algorithm increases with the increase of the gray level of the image, and the segmented image has many gray levels, and the segmentation effect is not obvious for some graphics that require detailed segmentation.

SUMMARY OF THE INVENTION

The purpose of the present invention is to overcome the deficiencies in the prior art, provide a quantum image segmentation method, device and storage medium based on double thresholds, solve the real-time problem of classical digital image processing and the high complexity of the existing quantum segmentation algorithm problem, and meet the purpose of accurate segmentation of quantum images.

To achieve the above object, the present invention adopts the following technical solutions to realize:

In a first aspect, the present invention provides a double-threshold-based quantum image segmentation method, including:

Acquire grayscale digital images and prepare corresponding NEQR quantum images;

Set high threshold and low threshold, and construct high threshold quantum segmentation circuit, low threshold quantum segmentation circuit and quantum segmentation circuit between high and low thresholds;

Build a comparator and divide each pixel of the NEQR quantum image into pixels with a gray value greater than or equal to the high threshold, pixels with gray values less than the low threshold, and pixels with gray values greater than or equal to the low threshold and less than the high threshold based on the comparator ;

Through the high-threshold quantum segmentation circuit, the low-threshold quantum segmentation circuit, and the quantum segmentation circuit between high and low thresholds, the pixels whose gray value is greater than or equal to the high threshold, the pixels whose gray value is less than the low threshold, and the pixels whose gray value is greater than or equal to the low threshold and less than the high threshold are respectively analyzed. Threshold the pixels for segmentation.

Optionally, the size of the grayscale digital image is ²ⁿ × ²ⁿ , and the grayscale range is [ ^0,2q -1]; the grayscale digital image needs 2n+q qubits to be stored, then the The expression of the NEQR quantum image is:

表示量子图像灰度值，k＝q-1,q-2,…,0；

|XY)＝|Y)|X>＝|Y_n-1，Y_n-2…Y_i…Y₀>|X_n-1，X_n-2…X_i…X₀>表示量子图像的位置，Y_i，X_i∈{0，1}。in,

Represents the quantum image gray value, k=q-1,q-2,...,0;

|XY)=|Y)|X>=|Y _n-1 , Y _n-2 ... Y _i ... Y ₀ >|X _n-1 , X _n-2 ... X _i ... X ₀ > represents the position of the quantum image , Y _i , Xi _∈ {0, 1}.

Optionally, the comparator is:

Among them, a and b are the comparator inputs, and y is the comparator output;

The comparator-based division of each pixel of the NEQR quantum image into pixels with a grayscale value greater than or equal to a high threshold, pixels with a grayscale value less than a low threshold, and pixels with a grayscale value greater than or equal to the low threshold and less than the high threshold include:

Obtain the gray value of each pixel of the NEQR quantum image, convert the gray value and threshold of each pixel from decimal to binary, and input the binary gray value and threshold into the comparator;

The comparator compares one by one from the low to high bits of the binary:

The first bit: input the first binary number a ₀ b ₀ into the comparator, and assign the output y ₀ to the auxiliary qubit h ₂ ;

The second bit: input the second binary number a ₁ b ₁ into the comparator, and assign the output y ₁ to the auxiliary qubit h ₁ ; analyze the comparison results of the first and second bits:

If the auxiliary qubit h ₁ is 1, the auxiliary qubit h ₁ is used as the output y ₁ ;

If the auxiliary qubit h ₁ is 0 and a ₁ b ₁ is not 10, the auxiliary qubit h ₁ is output through the combination of CNOT gate and Toffoli gate, specifically:

The auxiliary qubit h ₁ h ₀ is connected through the CNOT gate,

If the auxiliary qubit h ₁ is 0, the auxiliary qubit h ₀ is 1;

If the auxiliary qubit h ₁ is 1, the auxiliary qubit h ₀ is 0;

The auxiliary qubits h ₂ h ₀ are connected through Toffoli gates,

If the auxiliary qubit h ₂ h ₀ is 11, perform XOR processing on the auxiliary qubit h ₁ , and use the processing result as the output y ₁ ;

If the auxiliary qubit h ₁ is 0 and a ₁ b ₁ is 10, the auxiliary qubit h ₁ is output through the Toffoli gate, specifically:

XOR the auxiliary qubit h ₀ ;

The auxiliary qubits h ₂ h ₀ are connected through Toffoli gates,

If the auxiliary qubit h ₂ h ₀ is 11, perform XOR processing on the auxiliary qubit h ₁ , and use the processing result as the output y ₁ ; perform a reset operation on the auxiliary qubit h ₂ h ₀ ;

The remaining bits are executed sequentially according to the second bit method until all bits are compared.

Optionally, the high-threshold quantum segmentation circuit segmenting pixels whose grayscale values are greater than or equal to the high-threshold includes:

The qubits of the gray value of the pixel whose gray value is greater than or equal to the high threshold are all set to 1, and the specific process includes:

When the qubit of the gray value of the pixel whose gray value is greater than or equal to the high threshold is 0, use the CNOT gate to set the auxiliary qubit to 1;

When the two auxiliary qubits are both 1, use the Toffoli gate to perform XOR operation on the qubits of the gray value;

After the operation is completed, the auxiliary quantum position will be 0;

The above steps are repeated until all qubit operations whose gray value is greater than or equal to the gray value of the high threshold pixel are completed.

Optionally, the low-threshold quantum segmentation circuit for segmenting pixels whose grayscale values are less than the low-threshold includes:

The qubits of the gray value of the pixel whose gray value is less than the low threshold are all set to 0, and the specific process includes:

When the qubit of the gray value of the pixel whose gray value is less than the low threshold is 1, use the CNOT gate to set the auxiliary qubit to 1;

When the two auxiliary qubits are both 1, use the Toffoli gate to perform XOR operation on the qubits of the gray value;

After the operation is completed, the auxiliary quantum position will be 0;

The above steps are repeated until all qubit operations of the gray value of the pixel whose gray value is less than the low threshold are completed.

Optionally, the quantum segmentation circuit between high and low thresholds divides pixels whose grayscale values are greater than or equal to the low threshold and less than the high threshold, including:

The first quantum position of the gray value of the pixel whose gray value is greater than or equal to the low threshold and less than the high threshold is set to 1, and the remaining quantum positions are 0; the specific process includes:

When the qubits other than the last qubit of the gray value of the pixel whose gray value is greater than or equal to the low threshold and less than the high threshold are 1, use the CNOT gate to set the auxiliary qubit to 1;

When the two auxiliary qubits are both 1, use the Toffoli gate to perform XOR operation on the qubits of the gray value;

After the operation is completed, the auxiliary quantum position will be 0;

Repeat the above steps until all qubits except the last qubit of the gray value of the pixel whose gray value is greater than or equal to the low threshold and less than the high threshold are completed;

When the last qubit of the gray value of the pixel whose gray value is greater than or equal to the low threshold and less than the high threshold is 0, use the CNOT gate to set the auxiliary qubit to 1;

When both auxiliary qubits are 1, the gray-valued qubits are XORed using a Toffoli gate.

In a second aspect, the present invention provides a double-threshold-based quantum image segmentation device, the device comprising:

Image preparation module for acquiring grayscale digital images and preparing corresponding NEQR quantum images;

The segmentation circuit module is used to set high threshold and low threshold, and construct high threshold quantum segmentation circuit, low threshold quantum segmentation circuit and quantum segmentation circuit between high and low thresholds;

The pixel segmentation module is used to construct a comparator, and based on the comparator, each pixel of the NEQR quantum image is divided into pixels whose gray value is greater than or equal to the high threshold, pixels whose gray value is less than the low threshold, and pixels whose gray value is greater than or equal to the low threshold and less than the high threshold pixels;

The image segmentation module is used to separate the pixels whose gray values are greater than or equal to the high threshold, the pixels whose gray values are less than the low threshold, and those whose gray values are greater than Pixels equal to the low threshold and less than the high threshold are segmented.

In a third aspect, the present invention provides a dual-threshold-based quantum image segmentation device, including a processor and a storage medium;

the storage medium is used for storing instructions;

The processor is adapted to operate in accordance with the instructions to perform steps in accordance with the above-described method.

In a fourth aspect, the present invention provides a computer-readable storage medium on which a computer program is stored, characterized in that, when the program is executed by a processor, the steps of the above method are implemented.

Compared with the prior art, the beneficial effects achieved by the present invention:

The invention provides a quantum image segmentation method, device and storage medium based on double thresholds. A NEQR quantum image is prepared by a grayscale digital image, and the pixels of the NEQR quantum image are segmented by setting a high threshold, a low threshold and a comparator. For each segmented pixel, different segmentation circuits are constructed for segmentation, which is less complex and can obtain an accurate and clear segmentation map at the same time.

Description of drawings

1 is a schematic flowchart of a method for dividing a quantum image based on double thresholds provided in Embodiment 1 of the present invention;

2 is a schematic diagram of a comparator provided in Embodiment 1 of the present invention;

3 is a schematic diagram of a high-threshold quantum segmentation circuit provided in Embodiment 1 of the present invention;

4 is a schematic diagram of a low-threshold quantum segmentation circuit provided in Embodiment 1 of the present invention;

5 is a schematic diagram of a quantum division circuit between high and low thresholds provided by Embodiment 1 of the present invention;

6 is a schematic diagram of a complete quantum image segmentation circuit provided by Embodiment 1 of the present invention;

7 is a schematic diagram of a grayscale digital image of an example provided by Embodiment 1 of the present invention;

8 is a schematic diagram of a quantum diagram for preparing an example grayscale digital image provided in Embodiment 1 of the present invention;

FIG. 9 is a comparative schematic diagram of an example provided by Embodiment 1 of the present invention;

10 is a schematic diagram of an example high-threshold quantum partitioning provided by Embodiment 1 of the present invention;

11 is a schematic diagram of an example low-threshold quantum segmentation provided by Embodiment 1 of the present invention;

12 is a schematic diagram of quantum division between high and low thresholds of an example provided by Embodiment 1 of the present invention;

FIG. 13 is a schematic diagram of an example segmentation result provided by Embodiment 1 of the present invention.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings. The following examples are only used to illustrate the technical solutions of the present invention more clearly, and cannot be used to limit the protection scope of the present invention.

Example 1:

As shown in FIG. 1 , an embodiment of the present invention provides a quantum image segmentation method based on double thresholds, including:

1. Acquire a grayscale digital image and prepare the corresponding NEQR quantum image.

The size of the grayscale digital image is ²ⁿ × ²ⁿ , and the grayscale range is [0, 2q-1]; the grayscale digital image needs 2n+ ^q qubits for storage, then the expression of the NEQR quantum image is:

表示量子图像灰度值，k＝q-1，q-2，…，0，

|XY>＝|Y>|X>＝|Y_n-1，Y_n-2…Y_i…Y₀>|X_n-1，X_n-2…X_i…X₀>表示量子图像的位置，Y_i，X_i∈{0，1}。in,

Represents the gray value of the quantum image, k=q-1, q-2, ..., 0,

|XY>=|Y>|X>=|Y _n-1 , Y _n-2 …Y _i …Y ₀ >|X _n-1 , X _n-2 …X _i … X ₀ >represents the position of the quantum image , Y _i , Xi _∈ {0, 1}.

2. Set high threshold and low threshold, and construct high-threshold quantum division circuit, low-threshold quantum division circuit, and quantum division circuit between high and low thresholds.

3. Build a comparator, and based on the comparator, divide each pixel of the NEQR quantum image into pixels whose gray value is greater than or equal to the high threshold, pixels whose gray value is less than the low threshold, and pixels whose gray value is greater than or equal to the low threshold and less than the high threshold of pixels.

As shown in Figure 2, the comparator is:

Among them, a and b are the comparator inputs, and y is the comparator output;

Based on the comparator, each pixel of the NEQR quantum image is divided into pixels whose gray value is greater than or equal to the high threshold, pixels whose gray value is less than the low threshold, and pixels whose gray value is greater than or equal to the low threshold and less than the high threshold, including:

Obtain the gray value of each pixel of the NEQR quantum image, convert the gray value and threshold of each pixel from decimal to binary, and input the binary gray value and threshold into the comparator;

The comparator compares one by one from the low-order to high-order bits of the binary:

The first bit: input the first binary number a ₀ b ₀ into the comparator, and assign the output y ₀ to the auxiliary qubit h ₂ ;

The second bit: input the second binary number a ₁ b ₁ into the comparator, and assign the output y ₁ to the auxiliary qubit h ₁ ; analyze the comparison results of the first and second bits:

If the auxiliary qubit h ₁ is 1, the auxiliary qubit h ₁ is used as the output y ₁ ;

If the auxiliary qubit h ₁ is 0 and a ₁ b ₁ is not 10, the auxiliary qubit h ₁ is output through the combination of CNOT gate and Toffoli gate, specifically:

The auxiliary qubit h ₁ h ₀ is connected through the CNOT gate,

If the auxiliary qubit h ₁ is 0, the auxiliary qubit h ₀ is 1;

If the auxiliary qubit h ₁ is 1, the auxiliary qubit h ₀ is 0;

The auxiliary qubits h ₂ h ₀ are connected through Toffoli gates,

If the auxiliary qubit h ₂ h ₀ is 11, perform XOR processing on the auxiliary qubit h ₁ , and use the processing result as the output y ₁ ;

If the auxiliary qubit h ₁ is 0 and a ₁ b ₁ is 10, the auxiliary qubit h ₁ is output through the Toffoli gate, specifically:

XOR the auxiliary qubit h ₀ ;

The auxiliary qubits h ₂ h ₀ are connected through Toffoli gates,

If the auxiliary qubit h ₂ h ₀ is 11, perform XOR processing on the auxiliary qubit h ₁ , and use the processing result as the output y ₁ ; perform a reset operation on the auxiliary qubit h ₂ h ₀ ;

The remaining bits are executed sequentially according to the second bit method until all bits are compared.

4. Through the high-threshold quantum segmentation circuit, the low-threshold quantum segmentation circuit, and the quantum segmentation circuit between high and low thresholds, the pixels whose gray value is greater than or equal to the high threshold, the pixels whose gray value is less than the low threshold, and the pixels whose gray value is greater than or equal to the low threshold and Pixels smaller than a high threshold are segmented.

4.1. As shown in Figure 3, the high-threshold quantum segmentation circuit divides the pixels whose gray value is greater than or equal to the high threshold (y _H = 0), including:

The qubits of the gray value of the pixel whose gray value is greater than or equal to the high threshold are all set to 1, and the specific process includes:

When the qubit (C ₀ C ₁ . . . C _q-1 ) of the gray value of the pixel whose gray value is greater than or equal to the high threshold is 0, use the CNOT gate to set the auxiliary qubit to 1;

When the two auxiliary qubits are both 1, use the Toffoli gate to perform XOR operation on the qubits of the gray value;

After the operation is completed, the auxiliary quantum position will be 0;

The above steps are repeated until all qubit operations whose gray value is greater than or equal to the gray value of the high threshold pixel are completed.

4.2. As shown in Figure 4, the low-threshold quantum segmentation circuit divides the pixels whose gray value is less than the low threshold (yL=1), including:

The qubits (C ₀ C ₁ . . . C _q-1 ) of the gray value of the pixel whose gray value is less than the low threshold are all set to 0, and the specific process includes:

When the qubit of the gray value of the pixel whose gray value is less than the low threshold is 1, use the CNOT gate to set the auxiliary qubit to 1;

When the two auxiliary qubits are both 1, use the Toffoli gate to perform XOR operation on the qubits of the gray value;

After the operation is completed, the auxiliary quantum position will be 0;

The above steps are repeated until all qubits (C ₀ C ₁ . . . C _q-1 ) of the gray value of the pixel whose gray value is less than the low threshold are completed.

4.3. As shown in Figure 5, the quantum segmentation circuit between high and low thresholds divides the pixels (y _H =1 and y _L =0) whose gray value is greater than or equal to the low threshold and less than the high threshold (y H =1 and y L =0) including:

The first qubit C ₀ of the gray value of the pixel whose gray value is greater than or equal to the low threshold and less than the high threshold is set to 1, and the remaining qubits C ₁ . . . C _q-1 are set to 0; the specific process includes:

When the _qubits C ₀ C ₁ . ;

When the two auxiliary qubits are both 1, use the Toffoli gate to perform XOR operation on the qubits of the gray value;

After the operation is completed, the auxiliary quantum position will be 0;

Repeat the above steps until all the qubits C ₀ C ₁ . . . C _q-2 except the last qubit of the gray value of the pixel whose gray value is greater than or equal to the low threshold and less than the high threshold are completed;

When the last qubit C _q-1 of the gray value of the pixel whose gray value is greater than or equal to the low threshold and less than the high threshold is 0, use the CNOT gate to set the auxiliary qubit to 1;

When both auxiliary qubits are 1, the gray-valued qubits are XORed using a Toffoli gate.

5. As shown in FIG. 6 , the comparator U _C , the high-threshold quantum dividing circuit S ₁ , the low-threshold quantum dividing circuit S ₂ , and the quantum dividing circuit S ₃ between high and low thresholds are integrated into a complete quantum image dividing circuit, _TH and _TL are the high and low thresholds, respectively.

6. Complexity analysis of the complete quantum image segmentation circuit:

Single-qubit gates and two-qubit gates are fundamental quantum logic gates that can operate on arbitrary qubits. We evaluate algorithm complexity using the number of underlying logic gates. Circuit quantum cost analysis of a quantum image segmentation algorithm based on circuits in graphs. It is assumed that the size of the quantum image is 2 ⁿ × 2 ⁿ , and the grayscale range is 0 to 2 ^q -1. The required basic quantum gates are calculated as follows. A quantum comparator needs 3q-2 Toffoli gates, q-1 CNOT gates and 2q-2 reset gates, which contains 18q-13 basic quantum logic gates in total, and we need two quantum comparators. Furthermore, the split operation requires 3q+1 Toffoli gates, 3q+2 CNOT gates and 3q+3 reset gates. In addition, 2q NOT gates and q reset gates are required to set the threshold. In general, the preparation and measurement process of NEQR quantum images is not considered part of quantum image processing. Therefore, the double-threshold quantum image segmentation algorithm requires a total of 60q-6 basic quantum logic gates. Therefore, the quantum cost of the circuit is 60q-6, and the complexity of the circuit is O(q), which means that the complexity is only related to the gray value q, and the complexity of the circuit does not increase with the increase of the quantum image size.

As shown in Figure 7, taking a grayscale digital image randomly selected as an example, the size of the image is 2 ² × 2 ² , the grayscale range is [0, 7], and 4+3 qubits are used to store it, we get Quantum image |I _YX >, as shown in Figure 8.

Set the high threshold to 100.

As shown in Figure 9, according to the selected image, we use a 3-qubit quantum comparator to compare the grayscale value and threshold of the image, and we only need to know the two relations a≥b and a<b. As shown in Figure 9 below, in the figure a and b are used as inputs, indicating the two numbers to be compared, and y is the output of the comparison result. If a≥b, then y=0; if a<b, then y=1. h represents auxiliary qubits, and we compare them one by one from low to high. When a ₀ =0, b ₀ =1, that is, when a ₀ <b ₀ , h ₂ =1, otherwise h ₂ =0. At this time, the first comparison is over, and the second is compared according to the same comparison method. After the comparison, we need to analyze the comparison results of the two. When the second comparison result is 1, the result is output directly; when the second comparison result is 0 and a ₁ b ₁ is not 10, we use the CNOT gate and Toffoli gate to combine the output comparison result; when the second comparison result is 0 and a 1 b 1 is not 10 When a 1 b 1 is 0 and a ₁ b ₁ is 10, it means a<b, and the Toffoli gate needs to be used to deal with this situation separately before outputting. Following this comparison method, we compare sequences of 3 qubits.

As shown in FIG. 10 , after the threshold comparison, according to the comparison result y _H =0, those pixels that are greater than or equal to the high threshold are divided, and their grayscale values are set to 111. When y _H =0, the auxiliary qubit is set to 1 using the CNOT gate. The gray value information qubits are transformed one by one. The specific operation is shown in Figure 10 below. When C=0, use the CNOT gate to set the auxiliary qubit to 1, and when both auxiliary qubits are 1, use the Toffoli gate to perform the XOR operation on C. When the operation of one gray value qubit is completed, it is only necessary to set the auxiliary qubit to 0, and then the transformation operation of the next gray value qubit can be continued.

Set the low threshold to 010.

As shown in FIG. 11 , after the threshold comparison, according to the comparison result y _L =1, those pixels smaller than the low threshold are divided, and their grayscale values are set to 000. When y _L =1, the auxiliary qubit is set to 1 using the CNOT gate. The gray value information qubits are transformed one by one. The specific operation is shown in Figure 11 below. When C=1, use the CNOT gate to set the auxiliary qubit to 1, and when both auxiliary qubits are 1, use the Toffoli gate to perform the XOR operation on C. When the operation of one gray value qubit is completed, it is only necessary to set the auxiliary qubit to 0, and then the transformation operation of the next gray value qubit can be continued.

As shown in Figure 12, after the threshold comparison, according to the comparison result, the pixels between the high and low thresholds are divided, and their gray value is set to 100. When y _L =0 and y _H =1, the auxiliary qubit is set to 1 using a Toffoli gate. The gray value information qubits are transformed one by one. The specific operation is shown in Figure 12 below. When C ₂ =0, use the CNOT gate to set the auxiliary qubit to 1, and when both auxiliary qubits are 1, use the Toffoli gate to perform the XOR operation on C. When C ₀ C ₁ =11, the CNOT gate is used to set the auxiliary qubit to 1, and when both auxiliary qubits are 1, the Toffoli gate is used to perform the XOR operation on C. When the operation of one gray value qubit is completed, it is only necessary to set the auxiliary qubit to 0, and then the transformation operation of the next gray value qubit can be continued.

As shown in Figure 13, it is the image after segmentation.

Embodiment 2:

An embodiment of the present invention provides a double-threshold-based quantum image segmentation device, the device comprising:

Image preparation module for acquiring grayscale digital images and preparing corresponding NEQR quantum images;

The segmentation circuit module is used to set high threshold and low threshold, and construct high threshold quantum segmentation circuit, low threshold quantum segmentation circuit and quantum segmentation circuit between high and low thresholds;

The pixel segmentation module is used to construct a comparator, and based on the comparator, each pixel of the NEQR quantum image is divided into pixels whose gray value is greater than or equal to the high threshold, pixels whose gray value is less than the low threshold, and pixels whose gray value is greater than or equal to the low threshold and less than the high threshold pixels;

The image segmentation module is used to separate the pixels whose gray values are greater than or equal to the high threshold, the pixels whose gray values are less than the low threshold, and those whose gray values are greater than Pixels equal to the low threshold and less than the high threshold are segmented.

Embodiment three:

Based on the first embodiment, an embodiment of the present invention provides a dual-threshold-based quantum image segmentation device, including a processor and a storage medium;

storage medium for storing instructions;

A processor is operable in accordance with the instructions to perform steps in accordance with the above-described method.

Embodiment 4:

Based on the first embodiment, the present invention provides a computer-readable storage medium on which a computer program is stored, characterized in that, when the program is executed by a processor, the steps of the above method are implemented.

As will be appreciated by those skilled in the art, the embodiments of the present application may be provided as a method, a system, or a computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) having computer-usable program code embodied therein.

The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the present application. It will be understood that each flow and/or block in the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to the processor of a general purpose computer, special purpose computer, embedded processor or other programmable data processing device to produce a machine such that the instructions executed by the processor of the computer or other programmable data processing device produce Means for implementing the functions specified in a flow or flow of a flowchart and/or a block or blocks of a block diagram.

These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory result in an article of manufacture comprising instruction means, the instructions The apparatus implements the functions specified in the flow or flow of the flowcharts and/or the block or blocks of the block diagrams.

These computer program instructions can also be loaded on a computer or other programmable data processing device to cause a series of operational steps to be performed on the computer or other programmable device to produce a computer-implemented process such that The instructions provide steps for implementing the functions specified in the flow or blocks of the flowcharts and/or the block or blocks of the block diagrams.

The above are only the preferred embodiments of the present invention. It should be pointed out that for those skilled in the art, without departing from the technical principles of the present invention, several improvements and modifications can be made. These improvements and modifications It should also be regarded as the protection scope of the present invention.

Claims (9)

1. A quantum image segmentation method based on double thresholds is characterized by comprising the following steps:

acquiring a gray digital image and preparing a corresponding NEQR quantum image;

setting a high threshold value and a low threshold value, and constructing a high threshold value quantum partitioning circuit, a low threshold value quantum partitioning circuit and an inter-high-low-threshold value quantum partitioning circuit;

constructing a comparator, and dividing each pixel of the NEQR quantum image into a pixel with a gray value larger than or equal to a high threshold value, a pixel with a gray value smaller than a low threshold value and a pixel with a gray value larger than or equal to the low threshold value and smaller than the high threshold value on the basis of the comparator;

the pixels with the gray values larger than or equal to the high threshold value, the pixels with the gray values smaller than the low threshold value and the pixels with the gray values larger than or equal to the low threshold value and smaller than the high threshold value are respectively divided by the high-threshold-value quantum dividing circuit, the low-threshold-value quantum dividing circuit and the high-low-threshold-value quantum dividing circuit.

2. The dual-threshold-based quantum image segmentation method as claimed in claim 1, wherein the size of the grayscale digital image is 2ⁿ×2ⁿThe gray scale range is [0,2 ]^q-1](ii) a The gray-scale digital image requires 2n + q qubits for storage, and the expression of the NEQR quantum image is:

wherein,

represents the quantum image gray scale value, k-q-1, q-2, …, 0;

|XY>＝|Y>|X>＝|Y_n-1,Y_n-2…Y_i…Y₀>|X_n-1,X_n-2…X_i…X₀>indicating the position of the quantum image, Y_i,X_i∈{0,1}。

3. The quantum image segmentation method based on the background subtraction method as claimed in claim 1, wherein the comparator is:

where a and b are comparator inputs and y is the comparator output;

the dividing of each pixel of the NEQR quantum image into a pixel with a gray value greater than or equal to a high threshold, a pixel with a gray value less than a low threshold, and a pixel with a gray value greater than or equal to the low threshold and less than the high threshold based on the comparator comprises:

acquiring the gray value of each pixel of the NEQR quantum image, converting the gray value and the threshold value of each pixel into binary system from decimal system, and inputting the binary gray value and the threshold value into a comparator;

the comparators compare one by one from the low bit to the high bit of the binary system:

the first bit: the first binary digit a₀b₀Input to a comparator and output y₀Assign to the auxiliary qubit h₂；

Second position: a second binary digit a₁b₁Input to a comparator and output y₁Assign to the auxiliary qubit h₁(ii) a Analyzing the comparison result of the first bit and the second bit:

if the auxiliary qubit h₁When 1, the auxiliary qubit h will be₁As an output y₁；

If the auxiliary qubit h₁Is 0 and a₁b₁When the frequency is not 10, auxiliary quantum bit h is output through the combination of CNOT gate and Toffoli gate₁The method specifically comprises the following steps:

connecting auxiliary qubits h through CNOT gates₁h₀，

If the auxiliary qubit h₁When 0, the auxiliary qubit h₀Is 1;

if the auxiliary qubit h₁When 1, the auxiliary qubit h₀Is 0;

connecting auxiliary qubits h by Toffoli gate₂h₀，

If auxiliary qubit h₂h₀To 11, for the auxiliary qubit h₁Exclusive OR processing is carried out, and the processing result is taken as output y₁；

If the auxiliary qubit h₁Is 0 and a₁b₁At 10, the auxiliary qubit h is output via the Toffoli gate₁The method specifically comprises the following steps:

for auxiliary qubit h₀Carrying out XOR processing;

connecting auxiliary qubits h by Toffoli gate₂h₀，

If auxiliary qubit h₂h₀To 11, for the auxiliary qubit h₁Exclusive OR processing is carried out, and the processing result is taken as output y₁(ii) a And for the auxiliary qubit h₂h₀Carrying out reset operation;

the remaining bits are sequentially executed according to the second bit method until all bit comparisons are completed.

4. The method of claim 1, wherein the high-threshold quantum segmentation circuit segments the pixels with gray values equal to or greater than the high threshold value by:

setting the quantum bits with the gray value greater than or equal to the gray value of the pixel with the high threshold value to be 1, and the specific process comprises the following steps:

when the quantum bit with the gray value larger than or equal to the gray value of the pixel with the high threshold is 0, the CNOT gate is used for setting the auxiliary quantum bit to be 1;

when the two auxiliary qubits are both 1, performing exclusive-or operation on the qubits of the gray value by using a Toffoli gate;

after the operation is finished, the auxiliary quantum position is 0;

and repeating the steps until all the qubit operations of which the gray value is greater than or equal to the gray value of the pixel with the high threshold are completed.

5. The method of claim 1, wherein the low-threshold quantum segmentation circuit segments the pixels with gray values smaller than the low threshold value by:

setting the quantum bits of the gray values of the pixels with the gray values smaller than the low threshold value to be 0, and the specific process comprises the following steps:

when the qubit of the gray value of the pixel with the gray value smaller than the low threshold value is 1, using the CNOT gate to set the auxiliary qubit to 1;

when the two auxiliary qubits are both 1, performing exclusive-or operation on the qubits of the gray value by using a Toffoli gate;

after the operation is finished, the auxiliary quantum position is 0;

and repeating the steps until all the qubit operations of the gray value of the pixel with the gray value smaller than the low threshold value are completed.

6. The method of claim 1, wherein the inter-high-and-low-threshold quantum partitioning circuit partitions the pixels having gray values equal to or greater than the low threshold and less than the high threshold, and comprises:

enabling the gray value to be greater than or equal to the first quantum position 1 and the remaining quantum position 0 of the gray value of the pixel with the low threshold and smaller than the high threshold; the specific process comprises the following steps:

when the quantum bits except the last quantum bit of the gray value of the pixel with the gray value being more than or equal to the low threshold and less than the high threshold are 1, using the CNOT gate to set the auxiliary quantum bit to be 1;

when the two auxiliary qubits are both 1, performing exclusive-or operation on the qubits of the gray value by using a Toffoli gate;

after the operation is finished, the auxiliary quantum position is 0;

repeating the steps until all the qubits except the last qubit of the gray value of the pixel with the gray value being more than or equal to the low threshold and less than the high threshold are operated;

when the last qubit of the gray value of the pixel with the gray value being more than or equal to the low threshold and less than the high threshold is 0, using the CNOT gate to set the auxiliary qubit to 1;

when both the two auxiliary qubits are 1, the qubits of the grey value are xor-ed using a Toffoli gate.

7. A dual-threshold based quantum image segmentation apparatus, the apparatus comprising:

the image preparation module is used for acquiring the gray digital image and preparing a corresponding NEQR quantum image;

the dividing circuit module is used for setting a high threshold value and a low threshold value and constructing a high threshold value quantum dividing circuit, a low threshold value quantum dividing circuit and an inter-high-low-threshold value quantum dividing circuit;

the pixel segmentation module is used for constructing a comparator and dividing each pixel of the NEQR quantum image into a pixel with a gray value larger than or equal to a high threshold value, a pixel with a gray value smaller than a low threshold value and a pixel with a gray value larger than or equal to the low threshold value and smaller than the high threshold value on the basis of the comparator;

and the image segmentation module is used for respectively segmenting the pixels with the gray values larger than or equal to the high threshold, the pixels with the gray values smaller than the low threshold and the pixels with the gray values larger than or equal to the low threshold and smaller than the high threshold through the high-threshold quantum segmentation circuit, the low-threshold quantum segmentation circuit and the high-low inter-threshold quantum segmentation circuit.

8. A quantum image segmentation device based on double thresholds is characterized by comprising a processor and a storage medium;

the storage medium is used for storing instructions;

the processor is configured to operate in accordance with the instructions to perform the steps of the method according to any one of claims 1 to 6.

9. Computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the method according to any one of claims 1 to 6.

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