Abstract
JPEG2000 is known as an efficient standard to encode images. However, at very low bit-rates, artifacts or distortions can be observed in decoded images. In order to improve the visual quality of decoded images and make them perceptually acceptable, we propose in this work a new preprocessing scheme. This scheme consists in preprocessing the image to be encoded using a nonlinear filtering, considered as a prior phase to JPEG 2000 compression. More specifically, the input image is decomposed into low- and high-frequency sub-images using morphological filtering. Afterward, each sub-image is compressed using JPEG2000, by assigning different bit-rates to each sub-image. To evaluate the quality of the reconstructed image, two different metrics have been used, namely (a) peak signal to noise ratio, to evaluate the visual quality of the low-frequency sub-image, and (b) structural similarity index measure, to evaluate the visual quality of the high-frequency sub-image. Based on the reconstructed images, experimental results show that, at low bit-rates, the proposed scheme provides better visual quality compared to a direct use of JPEG2000 (excluding any preprocessing).
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Abbreviations
- JPEG2000:
-
Joint Photographic Experts Group committee in 2000
- DWT:
-
Discrete wavelet transform
- DCT:
-
Discrete cosine transform
- IDWT:
-
Inverse discrete wavelet transform
- \(I(x,y)\) :
-
Image with spatial coordinate \(x\) and \(y\)
- \(S\) :
-
Structuring element
- \(I\oplus S\) :
-
Dilation of \(I\) by \(S\)
- \(I\ominus S\) :
-
Erosion of \(I\) by \(S\)
- \(I\circ S\) :
-
Morphological opening of \(I\) by \(S\)
- \(I{\bullet } S\) :
-
Morphological closing of \(I\) by \(S\)
- \(g, f\) :
-
\(g\) is the mask and \(f\) is the marker
- \(R_{g}(f)\) :
-
Reconstruction of g from \(f\)
- \(\gamma ^{(\mathrm{rec})}(f, g)\) :
-
Opening by reconstruction of \(g\) from \(f\)
- \(I_{\mathrm{Low}}\) :
-
Decomposed image \(I\) at low frequency
- \(I_{\mathrm{High}}\) :
-
Decomposed image \(I\) at high frequency
- Rate:
-
Compression ratio
- \(\alpha \) :
-
Compression ratio of the low-frequency sub-image (bit per pixel)
- \(\beta \) :
-
Compression ratio of the high-frequency sub-image (bit per pixel)
- \(\varPsi (I_{\mathrm{Low}},\alpha )\) :
-
Compression operator of \(I_{\mathrm{Low}}\) by \(\alpha \)
- \(\varPsi (I_\mathrm{High},\beta )\) :
-
Compression operator of \(I_\mathrm{High}\) by \(\beta \)
- \(\hbox {Comp}_{\mathrm{Low}}\) :
-
Compressed low-frequency sub-image
- \(\hbox {Comp}_{\mathrm{High}}\) :
-
Compressed high-frequency sub-image
- \(\varPsi ^{-1}(I_{\mathrm{Low}},\alpha )\) :
-
The inverse compression operator of \(I_{\mathrm{Low}}\) by \(\alpha \)
- \(\varPsi ^{-1}(I_{\mathrm{High}},\beta )\) :
-
The inverse compression operator of \(I_{\mathrm{High}}\) by \(\beta \)
- bpp:
-
Bit per pixel
- MSE:
-
Mean square error
- PSNR:
-
Peak signal to noise ratio
- SSIM:
-
Structural SIMilarity
- \(l()\) :
-
Luminance comparison function
- \(c()\) :
-
Contrast comparison function
- \(s()\) :
-
Structure comparison function
- \(\mu _{f}\) :
-
The average of \(f\)
- \(\sigma _{f}^2\) :
-
The variance of \(f\)
- \(\sigma _{fg} \) :
-
The covariance between \(f\) and \(g\)
-
: -
The dynamic range of the pixel values
- \(B\) :
-
The bit depth used for noncompressed image coding
- \(C_{1},C_{2}\) :
-
Two variables to stabilize the division with weak denominator
- \(\hbox {PSNR}_{\mathrm{New}}\) :
-
Proposed image quality metrics
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Bennacer, L., Bouledjfane, B. & Nait-Ali, A. Artifact reduction in JPEG2000 compressed images at low bit-rate using mathematical morphology filtering. SIViP 8, 677–686 (2014). https://doi.org/10.1007/s11760-013-0583-6
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DOI: https://doi.org/10.1007/s11760-013-0583-6