Method for detecting and localizing a falsified area in JPEG images

1 . A method comprising

capturing Joint Photographic Experts Group (JPEG) image;

using at least one hardware processor to:

receive the captured Joint Photographic Experts Group (JPEG) image;

compute discrete cosine transform (DCT) coefficients of the JPEG image;

save information about the position of the 8×8 pixel blocks corresponding to the coefficients;

wherein computing DCT coefficients of the JPEG image comprises:

complementing sides of the JPEG image up to a multiplicity with eight black pixels;

transforming the JPEG image from a red-green-blue (RGB) color space to a luma-blue-difference-chroma-red-difference-chroma (YCbCr) color space;

splitting a brightness channel in the YCbCr color space into a plurality of blocks of 8×8 pixels;

applying a discrete cosine transform to each of the plurality of blocks; and

discarding any of the plurality of blocks that contains pixels with saturated values;

estimate a quantization matrix of the JPEG image based on the computed DCT coefficients;

wherein estimating the quantization matrix of the JPEG image based on the computed DCT coefficients comprises, for each of 64 frequencies in each of the plurality of blocks:

calculating a factorial histogram h, wherein h(x) is a number of DCT coefficients that do not have a remainder when divided by x, for each integer x in range from 1 to 1000;

normalizing the factorial histogram h by a total number of DCT coefficients; and

estimating a quantization step of the quantization matrix for the frequency using the normalized factorial histogram h;

wherein estimating the quantization step of the quantization matrix using the normalized factorial histogram h comprises:

calculating =max{x|h(x)≥T 1 }, wherein T 1 is a predefined threshold;

when >2, estimating the quantization step for the frequency as ; and

when ≤2,

calculating y=max{x|h(x)≥T 2 }, wherein T 2 is a predefined threshold,

when y<4, estimating the quantization step for the frequency as , and

when y≥4,

constructing a modified factorial histogram h , wherein h (x) is the number of DCT coefficients that do not have a remainder when divided by x and do not belong to a set M={ky±1, k∈2}, wherein k is an integer value within a range Z,

normalizing the modified factorial histogram h by the total number of DCT coefficients that do not belong to the set M,

calculating =max{x|h(x)≥T 3 }, wherein T 3 is a predefined threshold,

when >3, estimating the quantization step for the frequency as , and

when ≤3, estimating the quantization step for the frequency as ,

search for discrepancies between the computed DCT coefficients and the estimated quantization matrix; and

determine whether the JPEG image contains any falsified areas based on a result of the search;

localizing the falsified areas;

outputting the result of localizing the falsified areas.

2 . The method of claim 1 , further comprising using the at least one hardware processor to, when determining that the JPEG image contains one or more falsified areas, identify a location of each of the one or more falsified areas.

3 . The method of claim 1 , wherein estimating the quantization step of the quantization matrix further comprises estimating a quantization step over an entirety of the JPEG image based on the quantization step estimated for each of the 64 frequencies of each of the plurality of blocks.

4 . The method of claim 1 , wherein searching for discrepancies between the computed DCT coefficients and the estimated quantization matrix comprises:

generating a first image I 1 in which each of the plurality of blocks is assigned a pixel, wherein each pixel for each of the plurality of blocks has a value representing a number of frequencies at which a DCT coefficient corresponding to the block does belong to a range {[k{circumflex over (q)}−1, k{circumflex over (q)}+1], k∈Z}, wherein k is an integer value within a range Z, and {circumflex over (q)} is the estimated quantization step for a respective frequency;

determining a set M 2 of frequencies, for which at least one of the plurality of blocks at one of the frequencies in set M 2 has a computed DCT coefficient not belonging to the range {[k{circumflex over (q)}−1, k{circumflex over (q)}+1], k∈Z};

generating a second image I 2 in which each of the plurality of blocks is assigned a pixel, wherein a size of the second image I 2 is a same size as the first image I 1 , and wherein each pixel for each of the plurality of blocks in the second image I 2 has a value representing a number of frequencies at which the DCT coefficient corresponding to the block has an absolute value greater than one; and

generating a third image I 3 , with a same size as the first image I 1 and the second image I 2 , according to:

I

3

(

u

)

=

max

⁢

{

I

1

(

u

)

-

t

I

2

(

u

)

+

1

,

0

}

wherein u is a pixel position, and t is a predefined value.

5 . The method of claim 4 , further comprising using the at least one hardware processor to, when determining that the JPEG image contains one or more falsified areas, identify a location of each of the one or more falsified areas by:

generating a fourth image I 4 by applying a morphological operation to the third image I 3 ; and

generating a fifth image I s with a same size as the JPEG image, wherein each pixel within each of the plurality of blocks in the fifth image I s has a value equal to a value of a pixel in the fourth image I 4 that corresponds to that block.

6 . The method of claim 5 , further comprising using the at least one hardware processor to calculate a probability of manipulation based on the fourth image 14 .

7 . The method of claim 1 , further comprising using the at least one hardware processor to search for a position of a JPEG compression grid for the JPEG image.

8 . A system comprising:

means for capturing Joint Photographic Experts Group (JPEG) image;

using at least one hardware processor; and

software configured to, when executed by the at least one hardware processor,

receive the captured Joint Photographic Experts Group (JPEG) image;

compute discrete cosine transform (DCT) coefficients of the JPEG image;

save information about the position of the 8×8 pixel blocks corresponding to the coefficients;

wherein computing DCT coefficients of the JPEG image comprises:

complementing sides of the JPEG image up to a multiplicity with eight black pixels;

transforming the JPEG image from a red-green-blue (RGB) color space to a luma-blue-difference-chroma-red-difference-chroma (YCbCr) color space;

splitting a brightness channel in the YCbCr color space into a plurality of blocks of 8×8 pixels;

applying a discrete cosine transform to each of the plurality of blocks; and

discarding any of the plurality of blocks that contains pixels with saturated values;

estimate a quantization matrix of the JPEG image based on the computed DCT coefficients;

wherein estimating the quantization matrix of the JPEG image based on the computed DCT coefficients comprises, for each of 64 frequencies in each of the plurality of blocks:

calculating a factorial histogram h, wherein h(x) is a number of DCT coefficients that do not have a remainder when divided by x, for each integer x in range from 1 to 1000;

normalizing the factorial histogram h by a total number of DCT coefficients; and

estimating a quantization step of the quantization matrix for the frequency using the normalized factorial histogram h;

wherein estimating the quantization step of the quantization matrix using the normalized factorial histogram h comprises:

calculating =max{x|h(x)≥T 1 }, wherein T 1 is a predefined threshold;

when >2, estimating the quantization step for the frequency as ; and

when ≤2,

calculating y=max{x|h(x)≥T 2 }, wherein T 2 is a predefined threshold,

when y<4, estimating the quantization step for the frequency as , and

when y≥4,

constructing a modified factorial histogram h , wherein h (x) is the number of DCT coefficients that do not have a remainder when divided by x and do not belong to a set M={ky±1, k∈Z}, wherein k is an integer value within a range Z,

normalizing the modified factorial histogram h by the total number of DCT coefficients that do not belong to the set M,

calculating =max{x| h (x)≥T 3 }, wherein T 3 is a predefined threshold,

when >3, estimating the quantization step for the frequency as , and

when ≤3, estimating the quantization step for the frequency as ,

search for discrepancies between the computed DCT coefficients and the estimated quantization matrix; and

determine whether the JPEG image contains any falsified areas based on a result of the search;

localizing the falsified areas;

outputting the result of localizing the falsified areas.

9 . A non-transitory computer-readable medium having instructions stores thereon, wherein the instructions, when executed by a processor, cause the processor to:

receive a captured Joint Photographic Experts Group (JPEG) image;

compute discrete cosine transform (DCT) coefficients of the JPEG image;

save information about the position of the 8×8 pixel blocks corresponding to the coefficients;

wherein computing DCT coefficients of the JPEG image comprises:

complementing sides of the JPEG image up to a multiplicity with eight black pixels;

transforming the JPEG image from a red-green-blue (RGB) color space to a luma-blue-difference-chroma-red-difference-chroma (YCbCr) color space;

splitting a brightness channel in the YCbCr color space into a plurality of blocks of 8×8 pixels;

applying a discrete cosine transform to each of the plurality of blocks; and

discarding any of the plurality of blocks that contains pixels with saturated values;

estimate a quantization matrix of the JPEG image based on the computed DCT coefficients;

wherein estimating the quantization matrix of the JPEG image based on the computed DCT coefficients comprises, for each of 64 frequencies in each of the plurality of blocks:

calculating a factorial histogram h, wherein h (x) is a number of DCT coefficients that do not have a remainder when divided by x, for each integer x in range from 1 to 1000;

normalizing the factorial histogram h by a total number of DCT coefficients; and

estimating a quantization step of the quantization matrix for the frequency using the normalized factorial histogram h;

wherein estimating the quantization step of the quantization matrix using the normalized factorial histogram h comprises:

calculating =max{x|h(x)≥T 1 }, wherein T 1 is a predefined threshold;

when >2, estimating the quantization step for the frequency as ; and

when ≤2,

calculating y=max{x|h(x)≥T 2 }, wherein T 2 is a predefined threshold,

when y<4, estimating the quantization step for the frequency as , and

when y≥4,

constructing a modified factorial histogram h , wherein h (x) is the number of DCT coefficients that do not have a remainder when divided by x and do not belong to a set M={ky±1, k∈Z}, wherein k is an integer value within a range Z,

normalizing the modified factorial histogram h by the total number of DCT coefficients that do not belong to the set M,

calculating =max{x|h(x)≥T 3 }, wherein T 3 is a predefined threshold,

when >3, estimating the quantization step for the frequency as , and

when ≤3, estimating the quantization step for the frequency as ,

search for discrepancies between the computed DCT coefficients and the estimated quantization matrix; and

determine whether the JPEG image contains any falsified areas based on a result of the search;

localizing the falsified areas;

outputting the result of localizing the falsified areas.