An anonymous method and system for jpeg images

Abstract

The present disclosure relates to the technical field of image information hiding, and proposes an anonymous method and system for a JPEG image. First noise residual is extracted from an obtained to-be-processed JPEG picture, and the first noise residual is subjected to discrete cosine transform and the alternating current part of the transformed coefficient is extracted. For the to-be-processed JPEG picture, the DCT coefficient after inverse quantization in the JPEG compression process is calculated. According to the attenuation requirement of the image noise error, the intensity parameter is adaptively selected, the difference between the DCT coefficient after inverse quantization and the alternating current part of the first noise residual transformed coefficient multiplied by the intensity parameter is calculated, the DCT coefficient is updated, and an anonymous image is obtained. The discrete cosine transform (DCT) coefficient and the JPEG compression process are combined, the noise residual information in the image is adaptively removed under the condition of ensuring the high quality of the image.

Description

Technical Field

[0001] This disclosure relates to the technical field of image information hiding technology, specifically to an anonymization method and system for JPEG images. Background Technology

[0002] The statements in this section are merely background information relating to this disclosure and do not necessarily constitute prior art.

[0003] Anonymization algorithms like PRNU are privacy-preserving techniques based on digital images, used to protect the identity of digital image owners. The PRNU algorithm uses the inherent noise patterns of the image sensor to generate a unique digital fingerprint called Photo Response Non-Uniformity (PRNU). This fingerprint can be used to identify images taken by a specific camera and is largely unalterable. Because the PRNU anonymization algorithm is based on the inherent noise patterns of the image itself, it is very difficult to remove or modify, which is one of the reasons for its widespread use. Furthermore, as a privacy-preserving technique, it is designed with strong security and confidentiality, further increasing its robustness. Although some researchers have attempted to remove PRNU fingerprints using image processing techniques, PRNU is very difficult to remove; typically only a small portion of the PRNU can be removed, and this often has a certain impact on image quality.

[0004] Achieving image anonymization requires not only considering decorrelation but also ensuring image quality as much as possible. Therefore, the whole process, though seemingly simple, is actually quite challenging. Thus, successfully achieving image anonymization is a significant challenge for researchers. The inventors found the following drawbacks in their research: (1) Previous methods for weakening PRNU fingerprints either only work under ideal conditions or produce low-quality images. Suppressing PRNU noise can easily affect image detail, especially high-frequency detail. (2) Existing techniques that interfere with image pixel matching may severely impact image quality. (3) Some algorithms require training data or use a depth-first image framework, resulting in high time complexity. Summary of the Invention

[0005] To address the aforementioned issues, this disclosure proposes an anonymization method and system for JPEG images. It combines Discrete Cosine Transform (DCT) coefficients with the JPEG compression process to adaptively remove noise residual information within the image while ensuring high image quality.

[0006] To achieve the above objectives, the present disclosure adopts the following technical solution:

[0007] One or more embodiments provide an anonymization method for JPEG images, comprising the following steps:

[0008] Extract the first noise residual from the acquired JPEG image to be processed, perform discrete cosine transform on the first noise residual, and extract the AC part of the coefficients after the transform.

[0009] For the JPEG image to be processed, calculate the DCT coefficients after inverse quantization during the JPEG compression process;

[0010] Based on the attenuation requirements of image noise error, an intensity parameter is adaptively selected. The difference between the dequantized DCT coefficients and the AC part of the coefficients after the first noise residual transformation multiplied by the intensity parameter is calculated to update the DCT coefficients and obtain the anonymized image.

[0011] One or more embodiments provide an anonymization system for JPEG images, including:

[0012] Noise Residual Processing Module: Configured to extract the first noise residual from the acquired JPEG image to be processed, perform discrete cosine transform on the first noise residual, and extract the AC part of the transformed coefficients;

[0013] Dequantization DCT coefficient calculation module: configured to calculate the DCT coefficients after dequantization of the JPEG compression process for the JPEG image to be processed;

[0014] Anonymous image output module: It is configured to adaptively select the intensity parameter according to the attenuation requirements of image noise error, subtract the AC part of the dequantized DCT coefficients from the first noise residual transformed coefficients multiplied by the intensity parameter, update the DCT coefficients, and obtain the anonymized image.

[0015] An electronic device includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, perform the steps described in the above method.

[0016] A computer-readable storage medium for storing computer instructions, which, when executed by a processor, perform the steps described in the above method.

[0017] Compared with the prior art, the beneficial effects of this disclosure are as follows:

[0018] In this disclosure, an adaptive PRNU anonymization method based on JPEG compression and discrete cosine transform is used to process the DCT coefficients after inverse quantization in the JPEG compression process. The method automatically searches for the optimal intensity coefficients of the noise residuals of the image to be processed in order to achieve anonymization and ensure the quality of the anonymized image. The method suppresses the correlation between the given image and its shooting device with a small algorithm time complexity, and the processed image is indistinguishable to the human eye.

[0019] This disclosure minimizes the impact on detail information while maintaining the best anonymity when processing high-frequency and low-frequency information in images.

[0020] The advantages of this disclosure, as well as its additional advantages, will be described in detail in the following specific embodiments. Attached Figure Description

[0021] The accompanying drawings, which form part of this disclosure, are used to provide a further understanding of this disclosure. The illustrative embodiments of this disclosure and their descriptions are used to explain this disclosure and do not constitute a limitation thereof.

[0022] Figure 1 This is a diagram of the zigzag scanning process of Embodiment 1 of this disclosure;

[0023] Figure 2 This is an anonymous before-and-after comparison of Embodiment 1 of this disclosure;

[0024] Figure 3 This is an anonymous method flowchart of Embodiment 1 of this disclosure. Detailed Implementation

[0025] The present disclosure will be further described below with reference to the accompanying drawings and embodiments.

[0026] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of this disclosure. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure pertains.

[0027] It should be noted that the terminology used herein is for descriptive purposes only and is not intended to limit the exemplary embodiments according to this disclosure. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof. It should be noted that, without conflict, the various embodiments and features within those embodiments can be combined with each other. The embodiments will now be described in detail with reference to the accompanying drawings.

[0028] Example 1

[0029] In one or more of the technical solutions disclosed in the embodiments, such as Figures 1 to 3 As shown, an anonymization method for JPEG images includes the following steps:

[0030] Step 1: Extract the first noise residual from the acquired JPEG image to be processed, perform discrete cosine transform on the first noise residual and extract the AC part of the transformed coefficients;

[0031] Step 2: For the JPEG image to be processed, calculate the DCT coefficients after inverse quantization during the JPEG compression process;

[0032] Step 3: Based on the image noise error attenuation requirements, adaptively select the intensity parameter α, subtract the AC part of the dequantized DCT coefficients from the first noise residual transformed coefficients multiplied by the intensity parameter α, update the DCT coefficients, and obtain the anonymized image.

[0033] Furthermore, in step 3, the method for adaptively selecting the intensity parameter α includes the following iterative process:

[0034] Step 31: Set the initial value of the strength parameter α; optionally, the initial strength parameter α can be set to 1;

[0035] Step 32: Update the DCT coefficients by subtracting the AC part of the coefficients after the dequantized DCT coefficients and the first noise residual transformed by multiplying by the intensity parameter α, and obtain the preliminary anonymized image; the AC part of the coefficients is the high-frequency part.

[0036] Step 33: Extract the second noise residual from the initial anonymized image and determine whether the second noise residual meets the requirements. If not, gradually increase the intensity parameter α and execute step 32; otherwise, output the anonymized image.

[0037] In this embodiment, the adaptive PRNU anonymization method based on JPEG compression and discrete cosine transform processes the DCT coefficients after inverse quantization during JPEG compression. It automatically searches for the optimal intensity coefficients in the noise residuals of the image to be processed to achieve anonymization and ensure the quality of the anonymized image. With a relatively small algorithm time complexity, it suppresses the correlation between the given image and its shooting device, and the processed image is indistinguishable to the human eye.

[0038] Optionally, in step 1, the noise residual is first extracted from the JPEG image to be processed using the maximum likelihood estimation method, which is the first noise residual.

[0039] In this embodiment, the Discrete Cosine Transform (DCT) is used to transform the first noise residual. The DCT decomposes the signal, and the transformation formula is as follows:

[0040]

[0041]

[0042]

[0043] Where A represents the input image, B represents the output result, M and N represent the two dimensions of the image respectively, p and q represent the dimensions of the output result, and m and n represent the pixel indices.

[0044] The first term after transformation represents the DC component of the signal, and subsequent terms represent the AC components at different frequencies. Therefore, the first row of the stretched vector represents the DC component of each block. The DC component can be understood as the coefficients corresponding to the changing low-frequency parts in the image, and is usually used to represent the brightness and overall color distribution of the image. The calculation of the DC component involves a large number of matrix operations and data processing, and the changes in its coefficients have a significant impact on image quality. The AC component represents the high-frequency components in the signal, often containing features such as image texture and detail. By processing the AC component, noise reduction and compression operations can be performed on the signal. Therefore, this embodiment only processes the AC component.

[0045] Optionally, after performing a discrete cosine transform on the first noise residual, the AC component of the transformed coefficients is extracted using a zigzag sorting scan, and the AC component (or AC coefficient) in the transformed coefficients is retained.

[0046] Optionally, the alternating components of the transformed coefficients can be extracted using Zigzag sorting. Zigzag sorting is a special sorting algorithm where the order of elements changes back and forth during the sorting process, forming a zigzag pattern. Before sorting, the transformed coefficients are arranged into an array, with each coefficient representing a pixel position, and each pixel position represented by a square, which can form an array like this: Figure 1The grid diagram shown illustrates the Zigzag sorting process as follows: First, the first element of the array is taken as the starting element, considered as the sorted portion. Starting from the second element, each element in the array is traversed sequentially. If the current element is at an odd index and is less than its predecessor, the two elements are swapped to ensure the current element is greater than its predecessor. If the current element is at an even index and is greater than its predecessor, the two elements are swapped to ensure the current element is less than its predecessor. This process is repeated until the entire array has been traversed. After one complete traversal, the last element will be in the correct position, i.e., the end of the sorted portion. The process continues, starting from the third element and repeating the steps. This continues until all elements are in the correct positions, completing the sorting.

[0047] The image compression and quantization process can already remove some high-frequency information. This embodiment focuses on processing the AC coefficient range. The Discrete Cosine Transform (DCT) has an "energy concentration" characteristic; after the transform, the AC information is concentrated in the upper left corner. To better extract the transformed AC information, this scheme employs Zigzag scanning technology. The scanning process is as follows: Figure 1 It can effectively extract communication information, thus enabling better data reading. Stretching all elements in each 8×8 block into a 64×1 column vector yields a quantized coefficient matrix of size 64×n, where n = (h×w) / 64.

[0048] Step 2 involves calculating the DCT coefficients of the JPEG image after inverse quantization during compression. This may include the following steps:

[0049] Step 21: Based on the size of the image to be processed, obtain the JPEG compression coefficients of the image, including the quantized DCT coefficients and the quantization table.

[0050] Specifically, the DCT coefficients and quantization table of the luminance component (i.e., Y component) of the image are read.

[0051] Optionally, the libjpeg library, developed by the IJG (Independent JPEG Group) software organization, can be used to process the image data format. This library provides fast, efficient, and accurate processing capabilities for JPEG images. Its auxiliary functions can handle DCT transform and inverse transform, quantization, and inverse quantization. Assuming the original JPEG image is h×w in size, the libjpeg library can be used to extract the quantized DCT coefficients and the quantization table.

[0052] In this embodiment, the Y component of the image is manipulated. The Y component contains the most critical brightness information in the image, representing the grayscale information in the image. This meets the requirements of human eye image perception, can better preserve the biological characteristics of the image, improve the image quality after anonymization, and reduce the differences in the processed image that can be recognized by the human eye.

[0053] Step 21: Obtain the quantized coefficients after compression based on the determined compression coefficients, and calculate the dequantized coefficients according to the corresponding quantization table.

[0054] Specifically, the quantization step in the JPEG compression process has already processed some high-frequency data to 0, meaning that some high-frequency information is discarded after quantization. However, noise residual information still exists extensively in the image. Therefore, in order to weaken the image's source tracing ability, this embodiment starts with the quantized DCT coefficients to further attenuate the noise residual information. The formula for calculating the dequantized DCT coefficients is as follows:

[0055] ψ(i,j)=γ(i,j).e(i,j) (2)

[0056] Where γ(i,j) are the quantized coefficients in JPEG compression, θ(i,j) is the quantization table extracted from the libjpeg library, and ψ(i,j) represents the dequantized DCT coefficients.

[0057] Since the traceability of an image depends entirely on the correlation between the noise residual and the PRNU of the capturing device, this embodiment extracts the noise residual from the image under test in step 1 to better remove the traceability information of the image itself. To ensure consistency with JPEG image processing, the noise residual is subjected to discrete cosine transform.

[0058] To continuously weaken the image's source tracing capability, the difference between the DCT coefficients ψ(i,j) after the JPEG image is dequantized and the AC component σ(i,j) of the transformed coefficients of the first noise residual is calculated:

[0059] ψ′(i,j)=ψ(i,j)-σ(i,j) (3)

[0060] In step 3, the DCT coefficients are updated by subtracting the AC part of the dequantized DCT coefficients and the coefficients after the first noise residual transformation to obtain a preliminary anonymized image. Specifically, the difference result, i.e. the updated DCT coefficients, is quantized according to the quantization table, and JPEG compression is performed. After saving, the preliminary anonymized image is obtained.

[0061] The quantification formula is:

[0062]

[0063] Where Q(i,j) represents the coefficients after DCT transformation, ψ′(,j) are the updated DCT coefficients after subtraction, and θ(i,j) represents the quantization table.

[0064] In step 33, the second noise residual extracted from the preliminary anonymized image must meet the following requirements: for the shooting device of the JPEG image to be processed, calculate the average noise residual of the shooting device as a reference PRNU value, calculate the peak correlation energy (PCE) estimated by the second noise residual of the preliminary anonymized image and the reference PRNU, and determine that the second noise residual meets the requirements when the PCE is less than the set threshold.

[0065] Specifically, the method for determining the second noise residual requirement includes the following steps:

[0066] Step 41: Select multiple reference images from the shooting device (such as a camera), if possible, select no fewer than 50 images;

[0067] Step 42: Use PRNU estimation based on MLE to obtain the noise residual of the acquired reference image;

[0068] Step 43: Perform a weighted average of the noise residuals extracted from the reference image, which can be denoted as ref; this is used to control the end time of the anonymization process.

[0069] Step 44: Calculate the peak-to-correlation energy (PCE) between the second noise residual of the initial anonymized image and the reference PRNU (ref) to determine whether the image belongs to this camera.

[0070] The formula for peak correlation energy (PCE) is as follows:

[0071]

[0072] Where L is the total number of pixels in the image output, ρ[l] represents the cyclic cross-correlation coefficient at position l in the image, and ε represents the neighborhood of the normalized cross-correlation maximum value max(ρ[l]). ρ is calculated as follows:

[0073]

[0074] Where L is the total number of pixels in the image output, s represents the number of cyclic shifts, and ||·|| is the L2 norm. K represents the reference PRNU of the known imaging device. This indicates that the mean of PRNU is being referenced. This represents the second noise residual extracted from the initially anonymized image. This represents the mean of the second noise residual.

[0075] A single residual has weakened the image's ability to trace its source, but not thoroughly enough, indicating a strong correlation between the two. Therefore, this scheme considers introducing a double intensity. The results show that while the PCE value decreases, the magnitude is small. Introducing a tenfold intensity significantly reduces image quality. To address this issue, a suitable intensity value can be found to achieve the expected experimental results. The experiment terminates and saves the result image when the correlation between the image and the source device reaches a set threshold. In this scheme, an intensity coefficient α is introduced, and the source device reference PRNU is used to control the progress. The optimal α intensity coefficient is automatically searched in a loop to achieve the desired result. At this point, subtracting the two parts of Equation 3 transforms it into:

[0076] ψ′(i,j)=ψ(i,j)-ασ(i,j) (7)

[0077] This process improves the efficiency and accuracy of the experiment, achieving the goal of protecting the privacy of the image photographer. In this embodiment, the PCE can optionally be set to not exceed a PCE threshold; that is, when the PCE is less than the PCE threshold, anonymization is successful, i.e., argminPCE(W,P) < PCE threshold. When the PCE value meets this range, the loop exits, and the final anonymized image is saved.

[0078] The image anonymization method in this embodiment first extracts the noise residual from the JPEG image to be processed using maximum likelihood estimation, and then performs a discrete cosine transform on it. Zigzag sorting is used to extract the AC component of the transformed coefficients. The libjpeg library is used to extract the quantization table and quantized DCT coefficients of the image, and the dequantized DCT coefficients are calculated (only the AC coefficients are processed). The difference between the dequantized DCT coefficients and the AC component of the transformed noise residual coefficients is calculated. The quantized DCT coefficients are then calculated based on the quantization table, and a series of post-processing operations are performed to obtain the preliminary anonymized image. Next, the noise residual of the preliminary anonymized image is extracted, and the PRNU of the capturing device is calculated from the reference image. The PCE values ​​of both are calculated. If the PCE value meets a set threshold, the experiment ends and the results are saved; otherwise, an intensity parameter is introduced to control the intensity of the subtracted noise residual until the PCE threshold is reached. Optionally, the PCE threshold is no greater than 30.

[0079] The anonymization method in this embodiment has low algorithm complexity, can formulate a scheme to associate a given image with its shooting device, and the processed image is indistinguishable to the human eye.

[0080] To illustrate the effectiveness of this embodiment, it was verified to perform well on the Dresden dataset, indicating that the algorithm successfully anonymizes natural images.

[0081] This embodiment can preserve the biometric features of an image while anonymizing it, and it has been verified on the MICHE-I dataset, showing that the algorithm successfully anonymizes biometric images.

[0082] Using the anonymization method of this embodiment, a comparison of the results before and after image anonymization is shown in the image below. Figure 2 ,from Figure 2 It can be seen that there is no obvious difference between the images before and after anonymization by visual inspection, which shows that image quality can be maintained while anonymizing the images.

[0083] Example 2

[0084] Based on Embodiment 1, this embodiment provides an anonymization system for JPEG images, including:

[0085] Noise Residual Processing Module: Configured to extract the first noise residual from the acquired JPEG image to be processed, perform discrete cosine transform on the first noise residual, and extract the AC part of the transformed coefficients;

[0086] Dequantization DCT coefficient calculation module: configured to calculate the DCT coefficients after dequantization of the JPEG compression process for the JPEG image to be processed;

[0087] Anonymous image output module: It is configured to adaptively select the intensity parameter according to the attenuation requirements of image noise error, subtract the AC part of the dequantized DCT coefficients from the first noise residual transformed coefficients multiplied by the intensity parameter, update the DCT coefficients, and obtain the anonymized image.

[0088] It should be noted that each module in this embodiment corresponds one-to-one with each step in embodiment 1, and their specific implementation process is the same, so it will not be repeated here.

[0089] Example 3

[0090] This embodiment provides an electronic device, including a memory and a processor, as well as computer instructions stored in the memory and running on the processor. When the processor executes the computer instructions, it performs the steps described in the method of Embodiment 1.

[0091] Example 4

[0092] This embodiment provides a computer-readable storage medium for storing computer instructions, which, when executed by a processor, complete the steps described in the method of Embodiment 1.

[0093] The above description is merely a preferred embodiment of this disclosure and is not intended to limit this disclosure. Various modifications and variations can be made to this disclosure by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this disclosure should be included within the scope of protection of this disclosure.

[0094] While the specific embodiments of this disclosure have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of this disclosure. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of this disclosure are still within the scope of protection of this disclosure.

Claims

1. A method for anonymizing JPEG images, characterized in that, Includes the following steps: Extract the first noise residual from the acquired JPEG image to be processed, perform discrete cosine transform on the first noise residual, and extract the AC part of the coefficients after the transform. For the JPEG image to be processed, calculate the DCT coefficients after inverse quantization during the JPEG compression process; The formula for calculating the dequantized DCT coefficients is: ； in, These are the quantized coefficients in JPEG compression. It is a quantization table extracted from the libjpeg library. Represents the dequantized DCT coefficients; Based on the attenuation requirements of image noise error, the intensity parameter is adaptively selected. The difference between the dequantized DCT coefficients and the AC part of the coefficients after the first noise residual transformation multiplied by the intensity parameter is calculated to update the DCT coefficients and obtain the anonymized image. The method for adaptively selecting intensity parameters includes the following iterative process: Step 31: Set initial values ​​for strength parameters; Step 32: Update the DCT coefficients by subtracting the AC part of the transformed coefficients of the first noise residual multiplied by the intensity parameter after dequantization of the DCT coefficients, and obtain the preliminary anonymized image; Step 33: Extract the second noise residual from the initial anonymized image and determine whether the second noise residual meets the requirements. If not, gradually increase the intensity parameter and execute step 32; otherwise, output the anonymized image. The second noise residual extracted from the initial anonymized image must meet the following requirements: For the shooting device of the JPEG image to be processed, calculate the average noise residual of the shooting device as a reference PRNU value, calculate the peak correlation energy between the second noise residual of the initial anonymized image and the reference PRNU, and determine that the second noise residual meets the requirements when the peak correlation energy is less than the set PCE threshold.

2. The anonymization method for JPEG images as described in claim 1, characterized in that: Set the PCE threshold to no more than 30.

3. The anonymization method for JPEG images as described in claim 1, characterized in that: The maximum likelihood estimation method is used to extract the first noise residual from the acquired JPEG image to be processed.

4. The anonymization method for JPEG images as described in claim 1, characterized in that: After performing a discrete cosine transform on the first noise residual, a zigzag sorting scan is used to extract the AC component of the transformed coefficients.

5. The anonymization method for JPEG images as described in claim 1, characterized in that, For the JPEG image to be processed, the DCT coefficients after inverse quantization during JPEG compression are calculated, including the following steps: Based on the size of the image to be processed, obtain the JPEG compression coefficients of the image, determine the DCT coefficients for quantization, and the quantization table; Based on the obtained compression coefficients, the quantized coefficients in JPEG compression are obtained, and the inverse quantized coefficients are calculated according to the corresponding quantization table.

6. An anonymization system for JPEG images, characterized in that, include: Noise Residual Processing Module: Configured to extract the first noise residual from the acquired JPEG image to be processed, perform discrete cosine transform on the first noise residual, and extract the AC part of the transformed coefficients; Dequantization DCT coefficient calculation module: configured to calculate the DCT coefficients after dequantization of the JPEG compression process for the JPEG image to be processed; The formula for calculating the dequantized DCT coefficients is: ； in, These are the quantized coefficients in JPEG compression. It is a quantization table extracted from the libjpeg library. Represents the dequantized DCT coefficients; Anonymous image output module: It is configured to adaptively select the intensity parameter according to the attenuation requirements of image noise error, subtract the AC part of the dequantized DCT coefficients and the first noise residual transformed coefficients multiplied by the intensity parameter, update the DCT coefficients, and obtain the anonymized image; The method for adaptively selecting intensity parameters includes the following iterative process: Step 31: Set initial values ​​for strength parameters; Step 32: Update the DCT coefficients by subtracting the AC part of the transformed coefficients of the first noise residual multiplied by the intensity parameter after dequantization of the DCT coefficients, and obtain the preliminary anonymized image; Step 33: Extract the second noise residual from the initial anonymized image and determine whether the second noise residual meets the requirements. If not, gradually increase the intensity parameter and execute step 32; otherwise, output the anonymized image. The second noise residual extracted from the initial anonymized image must meet the following requirements: For the shooting device of the JPEG image to be processed, calculate the average noise residual of the shooting device as a reference PRNU value, calculate the peak correlation energy between the second noise residual of the initial anonymized image and the reference PRNU, and determine that the second noise residual meets the requirements when the peak correlation energy is less than the set PCE threshold.

7. An electronic device, characterized in that, It includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, which, when executed by the processor, perform the steps of any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, Used to store computer instructions, which, when executed by a processor, perform the steps of any one of claims 1-5.

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