2 This work considers digital images as covers and foundation is
3 spatial least significant-bit (LSB) replacement.
4 In this data hiding scheme a subset of all the LSB of the cover image is modified
5 with a secret bit stream depending on to a key, the cover, and the message to embed.
6 This well studied steganographic approach never decreases (resp. increases)
7 pixel with even value (resp. odd value) and may break structural symmetry.
8 These structural modification can be detected by statistical approaches
9 and thus by steganalysis methods~\cite{DBLP:journals/tsp/DumitrescuWW03,DBLP:conf/mmsec/FridrichGD01,Dumitrescu:2005:LSB:1073170.1073176}.
11 This drawback is avoided in LSB matching (LSBM) where
12 the $+1$ or $-1$ is randomly added to the cover pixel LSB value
13 only if this one does not match the secret bit.
14 Since probabilities of increasing or decreasing pixel value are the same, statistical approaches
15 cannot be applied there to discover stego-images in LSBM.
16 The most accurate detectors for this matching are universal steganalysers such as~\cite{LHS08,DBLP:conf/ih/2005,FK12}
17 which classify images thanks to extracted features from neighboring elements of noise residual.
20 LSB matching revisited (LSBMR)~\cite{Mielikainen06} have been recently introduced.
21 For a given pair of pixels, in which the LSB
22 of the first pixel carries one bit of secret message, and the relationship
23 (odd–even combination) of the two pixel values carries
24 another bit of secret message.
28 In such a way, the modification
29 rate of pixels can decrease from 0.5 to 0.375 bits/pixel
30 (bpp) in the case of a maximum embedding rate, meaning fewer
31 changes to the cover image at the same payload compared to
32 LSB replacement and LSBM. It is also shown that such a new
33 scheme can avoid the LSB replacement style asymmetry, and
34 thus it should make the detection slightly more difficult than the
35 LSBM approach. % based on our experiments
41 Instead of (efficiently) modifying LSBs, there is also a need to select pixels whose value
42 modification minimizes a distortion function.
43 This distortion may be computed thanks to feature vectors that are embedded for instance in steganalysers
45 Highly Undetectable steGO (HUGO) method~\cite{DBLP:conf/ih/PevnyFB10} is one of the most efficient instance of such a scheme.
46 It takes into account SPAM features (whose size is larger than $10^7$) to avoid overfitting a particular
47 steganalyser. Thus a distortion measure for each pixel is individually determined as the sum of differences between
48 features of SPAM computed from the cover and from the stego images.
49 Thanks to this feature set, HUGO allows to embed $7\times$ longer messages with the same level of
50 indetectability than LSB matching.
51 However, this improvement is time consuming, mainly due to the distortion function
54 There remains a large place between random selection of LSB and feature based modification of pixel values.
55 We argue that modifying edge pixels is an acceptable compromise.
56 Edges form the outline of an object: they are the boundary between overlapping objects or between an object
57 and the background. A small modification of pixel value in the stego image should not be harmful to the image quality:
58 in cover image, edge pixels already break its continuity and thus already contains large variation with neighbouring
59 pixels. In other words, minor changes in regular area are more dramatic than larger modifications in edge ones.
60 Our proposal is thus to embed message bits into edge shapes while preserving other smooth regions.
62 Edge based steganographic schemes have bee already studied~\cite{Luo:2010:EAI:1824719.1824720,DBLP:journals/eswa/ChenCL10}.
63 In the former, the authors show how to select sharper edge regions with respect
64 to embedding rate: the larger the number of bits to be embedded, the coarse the edge regions are.
65 Then the data hiding algorithm is achieved by applying LSBMR on pixels of this region.
66 The authors show that this method is more efficient than all the LSB, LSBM, LSBMR approaches
67 thanks to extensive experiments.
68 However, it has been shown that the distinguish error with LSB embedding is fewer than the one with some binary embedding~\cite{DBLP:journals/tifs/FillerJF11}.
69 We thus propose to take benefit of these optimized embedding, provided it is not too time consuming.
70 Experiments have confirmed such a fact\JFC{Raphael....}.
73 \JFC{Christophe : énoncer la problématique du besoin de crypto et de ``cryptographiquement sûr'', les algo déjà cassés....
74 l'efficacité d'un encodage/décodage ...}
75 To deal with security issues, message is encrypted
77 In this paper, we thus propose to combine tried and tested techniques of signal theory (the adaptive edge detection), coding (the binary embedding), and cryptography
78 (the encrypt the message) to compute an efficient steganography scheme that is amenable to be executed on small devices.
80 The rest of the paper is organised as follows.
81 Section~\ref{sec:ourapproach} presents the details of our steganographic scheme.
82 Section~\ref{sec:experiments} shows experiments on image quality, steganalytic evaluation, complexity of our approach
83 and compare them to state of the art steganographic schemes.
84 Finally, concluding notes and future works are given in section~\ref{sec:concl}
