PaperlayerView exact revision on arXiv

Source-linked AI summary

Very fast watermarking by reversible contrast mapping

Dinu Coltuc, Jean-Marc Chassery

arXiv:0707.0802v1cs.MMcs.CRcs.CVcs.IT

TL;DR

Reversible watermarking seeks high-capacity embedding without the added complexity of compression stages. The paper uses reversible contrast mapping on pixel pairs, exploiting transformed LSBs and adding cropping-robust and low-cost implementations. Its bit-rates are close to difference expansion, while complexity is considerably lower and larger groups can exceed 0.5 bpp in one iteration.

  • Problem

    Compression-based reversible watermarking increases mathematical complexity, whereas schemes without compression can provide low embedding capacity.

  • Method

    The scheme applies reversible contrast mapping to pixel pairs, uses transformed LSB space for hiding, and supports lookup-table implementation and cropping robustness.

  • Results

    The scheme provides bit-rates close to Tian’s difference expansion while having considerably lower mathematical complexity; extended RCM reaches 0.68 bpp for Lena in one iteration.

  • Takeaways & Limitations

    The proposed scheme is appropriate for real-time applications because lookup-table access and low-complexity bit manipulation reduce marking and decoding complexity.

Abstract

from arXiv · show

Reversible contrast mapping (RCM) is a simple integer transform that applies to pairs of pixels. For some pairs of pixels, RCM is invertible, even if the least significant bits (LSBs) of the transformed pixels are lost. The data space occupied by the LSBs is suitable for data hiding. The embedded information bit-rates of the proposed spatial domain reversible watermarking scheme are close to the highest bit-rates reported so far. The scheme does not need additional data compression, and, in terms of mathematical complexity, it appears to be the lowest complexity one proposed up to now. A very fast lookup table implementation is proposed. Robustness against cropping can be ensured as well.

I. INTRODUCTION

The paper introduces a spatial-domain reversible watermarking scheme based on reversible contrast mapping, targeting high embedding capacity without additional compression. It also proposes modifications for cropping robustness, distortion control, and low-complexity implementation.

  • Most reversible watermarking approaches use lossless compression, which increases mathematical complexity; schemes avoiding compression can have low embedding capacity.
  • RCM applies a simple integer transform to pixel pairs and leaves LSB space available for data hiding after transformed LSBs are lost.
  • The modified scheme addresses cropping robustness, distortion control, mathematical complexity, and implementation cost.
  • RCM provides almost similar embedding bit-rates to difference expansion while using considerably lower mathematical complexity.

II. REVERSIBLE CONTRAST MAPPING

RCM is a constrained integer transform on pixel pairs that increases contrast while preserving graylevel averages. For eligible pairs, inverse recovery remains exact even after transformed LSBs are lost.

  • The forward RCM maps pixel pairs within a restricted subdomain to prevent overflow and underflow.
  • The inverse transform uses a ceiling function and is designed to recover the original pair exactly after transformed LSBs are lost.
  • Except when both transformed LSBs are 1, the ceiling function recovers the correct results; the problematic cases correspond to odd pixel pairs.
  • After excluding ambiguous odd pairs, inverse RCM performs exactly even when the transformed pairs’ LSBs are lost.
  • RCM preserves graylevel averages, increases differences between transformed pixels, and consequently increases image contrast.

III. REVERSIBLE WATERMARKING

The watermarking procedure uses transformed-pair LSBs for embedding while preserving enough information to identify pairs and reverse the transform. Ambiguous odd pairs require special handling.

  • The LSB of the first pixel indicates whether a pair was transformed, using 1 for transformed pairs and 0 otherwise.
  • Odd pixel pairs can also carry data when the first-pixel LSB is set to 0 and both LSBs are tested during detection.
  • The inverse RCM fails to recover pairs subject to ambiguity, which are characterized by equations in odd numbers.
  • Only 170 ambiguous pairs are identified in the analyzed domain.

A. Marking

Marking partitions the image into pixel pairs, identifies transformable and nontransformable pairs, and overwrites selected LSBs with payload bits. A local marking design supports recovery after cropping except near borders.

  • A. Marking: The image is partitioned into pixel pairs along rows, columns, or a space-filling curve before marking.
  • A. Marking: Non-odd pairs are transformed, their first-pixel LSB marks them as transformed, and designated LSBs become available for embedding.
  • A. Marking: For odd pairs, the first-pixel LSB is set to 0 and the second LSB is considered available, while selected true values are saved when needed.
  • A. Marking: Marking overwrites identified LSBs with watermark bits, including payload and saved bits.
  • A. Marking: Except at borders where errors may appear, cropping allows exact recovery of the cropped image’s original pixels and embedded payload.

B. Detection and Original Recovery

Detection partitions the image into pixel pairs, extracts embedded LSBs, and restores original pairs using inverse RCM and saved true LSBs.

  • The recovery procedure partitions the entire image into pairs of pixels before examining each pair.
  • Pairs requiring saved LSBs are recovered by replacing the marked LSB with its corresponding true value from the watermark sequence.
  • Pairs with embedded information yield watermark bits from designated LSBs and are restored by inverse transform.
  • The procedure stores extracted LSBs into the detected watermark sequence while setting selected transformed-pair LSBs to one during recovery.

C. Data Hiding Capacity

The scheme provides embedding space when enough pixel pairs are transformed, and chained iterations increase hiding capacity while increasing distortion.

  • Only the available LSB space remains usable after storing the payload and the LSBs needed for recovery.
  • The scheme’s bit-rate is determined from the number of pairs carrying embedded information relative to the total number of pairs.
  • Embedding space is provided when at least half of the total pixel pairs are transformed.
  • Multiple chained iterations increase hiding bit-rate, but each new iteration also increases image distortion.

D. Distortion Control

Distortion control limits transformation to pixel pairs whose introduced error stays below a predefined threshold, adding a constraint to the transform domain.

  • A predefined error threshold can restrict transformations when low hiding bit-rates are required.
  • The threshold-based rule introduces a supplementary constraint on eligible pixel pairs.
  • Equation (5) defines a strip-shaped domain for the error-controlled transform.
  • With error control, the RCM domain becomes an intersection, and each candidate pair is checked against the threshold.This verification causes a slight increase in mathematical complexity.

IV. VERY LOW COMPLEXITY IMPLEMENTATION

The implementation replaces repeated arithmetic on pixel pairs with lookup-table addressing and bit manipulation, substantially reducing the operational cost of marking and detection.

  • IV. VERY LOW COMPLEXITY IMPLEMENTATION: The forward RCM marking stage uses shifts, subtractions, comparisons, and low-cost logical and bit-manipulation operations.
  • IV. VERY LOW COMPLEXITY IMPLEMENTATION: Lookup tables precompute results for all possible pixel pairs and supply answers through memory lookup instead of repeated calculation.
  • IV. VERY LOW COMPLEXITY IMPLEMENTATION: For eight-bit pixels, the marking LUT contains 256 × 256 entries with transformed pixels and flags for embedding or LSB preservation.
  • IV. VERY LOW COMPLEXITY IMPLEMENTATION: Detection LUT entries encode recovered values, embedded-data locations, and restoration of saved true LSBs.
  • IV. VERY LOW COMPLEXITY IMPLEMENTATION: The LUT implementation performs marking, detection, and recovery through memory addressing and bit manipulation.

V. EXPERIMENTAL RESULTS

Experiments show that embedding capacity varies with image content and increases across iterations, while higher capacity brings greater distortion. The scheme approaches competing capacity levels, exceeds compression-based methods, and retains low-complexity advantages.

  • 0.499 bpp is obtained for Lena without distortion control, close to the 0.5 bpp theoretical upper bound.Further iterations increase the rate to 0.98, 1.40, 1.73, and 1.86 bpp.
  • Higher hiding capacity increases noise, and the marked copies range from 0.40 bpp at 37.17 dB to 1.80 bpp at 16.23 dB.
  • 1.53 bpp is the maximum hiding capacity for Boat, while highly textured Mandrill provides 0.84 bpp.The lower capacities are attributed to Boat’s greater detail and Mandrill’s high texture.
  • The proposed method largely outperforms compression-based schemes, whose Celik baseline reaches 0.17 bpp for Mandrill and 0.68 bpp for Lena and Boat.
  • Tian’s difference expansion scheme performs slightly better on Lena, reaching 1.97 bpp, or 5% higher than the proposed scheme.
  • Tian’s scheme has lower marking distortions at 0.24, 0.46, and 1.44 bpp, outperforming the proposed scheme by 1.42, 2.87, and 3.42 dB, respectively.Its complexity is considerably higher than that of RCM.
  • The extended RCM scheme provides more than 0.5 bpp in one iteration, including 0.68 bpp for Lena, while retaining very low mathematical complexity.Its LUT implementation becomes costly as the transformed groups grow larger.

VI. CONCLUSIONS

The proposed spatial-domain reversible watermarking scheme combines high embedding rates with very low mathematical complexity and does not require additional compression. LUT-based processing supports real-time use, while data distribution and saved values provide cropping robustness.

  • The scheme offers high embedding bit-rates at very low mathematical complexity without additional data compression.
  • Its bit-rates largely outperform most reported reversible watermarking schemes and nearly match difference expansion methods.
  • The scheme appears to have the lowest mathematical complexity among proposed reversible watermarking methods.
  • LUT access for each pixel pair and low-complexity bit manipulation reduce marking and decoding computation for real-time applications.
  • Distributing the location map and storing saved true values near corresponding pixel pairs provides robustness against cropping.
Loading 0707.0802v1…