27th IEEE International Conference on Consumer Electronics (ICCE 09), Las Vegas, USA, 10-14 January, 2009

Hiding Depth Map of an Object in its 2D Image: Reversible Watermarking for 3D Cameras Asifullah Khan, M. Tariq Mahmood, Asad Ali, Imran Usman, and Tae-Sun Choi*, Senior Member, IEEE

Abstract—3D cameras are capable of capturing image and depth map of an object simultaneously. We propose a method to hide depth map, as a watermark, in its corresponding 2D image. 3D cameras enabled with this functionality could serve two purposes; protection of the captured image and secure transmission of its depth map.

I. INTRODUCTION 3D cameras with depth sensing capabilities are becoming more and more popular and have wide range of applications in consumer electronics community. Web-conferencing, 3D gaming, objects tracking, face detection & tracking, automotive safety, mobile phones, robotics and medical devices are potential areas. These cameras compute depth using various techniques such as time of flight, stereo or triangulation, and monocular scanerless[1]. Embedding of depth map in its 2D image could be highly desirable in many scenarios. An example is the secure communication of classified 3D shape information related to injuries and skin conditions for the purpose of online negotiating interpretation and legal significance [2]. This type of secure transmission of depth information is priceless for forensic pathologists. Likewise, depth map information is very valuable for microsurgery and DNA studies [3]. As far as military applications are concerned, depth information corresponding to the 2D image could be highly confidential and would certainly require secure transmission. However, if it is intelligently embedded and secured through secret keys, no unauthorized person could extract it. After receiving the 2D image, depth map can be extracted and the cover image restored by an authorized person without compromising on its quality. In this paper, we introduce the concept of variable threshold based reversible watermarking for embedding depth map into its 2D image. Unlike conventional watermarking techniques, through reversible watermarking, we can recover original image after extracting watermark. II. REVIEW Depth sensing abilities distinguish 3D cameras from traditional image capturing devices. Broadly, there are two types of depth estimation methods, namely, passive and active. In active techniques, such as time of flight, stereo or This work was supported by the Higher Education Commission of Pakistan under the indigenous PhD scholarship program (17-5-1(Cu204)/HEC/Sch/2004) and Korea Science and Engineering Foundation (KOSEF) grant funded by the Korean government (MOST) (No. R01-2007000-20227-0).

triangulation, light, x-ray or laser are projected. While in passive methods, simply the reflection of light rays is captured. Currently, the active devices are widely used because they achieve high resolution and accuracy [1]. However, these devices are expensive and require high computational time as compared to passive devices [4]. In digital watermarking applications related to multimedia archives, military and medical image processing; only reversible degradation of the original data is favorable. The distortions introduced by conventional watermarking approaches in applications as listed above, can be eradicated by using a reversible or lossless watermarking scheme. Recently, the work by Xuan et al. [5] is based on reversible embedding of the watermark bits into the middle and high frequency integer wavelet coefficients. III. METHOD The proposed data hiding scheme utilizes integer wavelet transform, variable threshold for selective embedding, and histogram modification to avoid possible overflow. To increase bias between 0 and 1 and to avoid round-off error, we use the second generation wavelet transform, such as IDWT [6]. This wavelet transform maps integer to integer and has been adopted by JPEG2000 as well. Embedding is performed only in LH, HL, and HH, subbands. We perform pre-processing before embedding to avoid possible overflow. In order to further enhance imperceptibility of the marked image, we propose the use of variable threshold. We believe that the distribution of HH subband encompasses more high frequency content as compared to the LH and HL subbands. Even, for some images, there might be fair enough difference of frequency content between LH and HL subbands. Embedding is performed in a coefficient if its magnitude is less than the threshold value set for its respective subband. Else, embedding is not performed; however, we do need to push the non-selected coefficients away from the selected ones in terms of magnitude. Let X denotes the frequency domain coefficient in question, T denotes threshold, and b is the bit to be embedded. We can thus mathematically summarize the embedding strategy as:

⎧ 2 ⋅ X + b, if X < T ⎫ ⎪ q ⎪ ⎪ ⎪ X′ = ⎨ X +T , if X ≥ T q q ⎬ ⎪ ⎪ ⎪ X − (T − 1), if X ≤ −T ⎪ q q ⎭ ⎩

(1)

where X ′ represents the modified coefficient, and q=1,2,3 for LH, HL, and HH subbands respectively.The subband, where there is large high-frequency content, embedding of the bits is

encouraged. Therefore, we set high thresholds for subbands having large high-frequency content. This is the essence of our technique for improving the quality of the marked image. Similarly, the extraction stage could be mathematically described as such:

⎧ ′ ′ ⎪ ⎣⎢ X / 2 ⎦⎥ , if − 2Tq + 1 < X < 2Tq ⎪ X = ⎨ X ′−T , if X ′ ≥ 2T q q ⎪ ⎪ X ′ + (T − 1), if X ′ ≤ −2T + 1 q q ⎩

⎫ ⎪ ⎪ ⎬ ⎪ ⎪ ⎭

then easily extract and use the depth map, and recover the image. TABLE I.

PERFORMANCE COMPARISONS

Fixed Threshold PNSR BPP 39.37714 0.400356 37.22321 0.546167 36.04077 0.634967 35.37958 0.687978 34.97053 0.717611 34.84122 0.732722 34.67041 0.740378 34.56637 0.744344 34.55919 0.745944 34.38894 0.746622 34.31683 0.746656

(2)

where symbol ⎢⎣ p ⎦⎥ provides the largest integer value smaller than p. By applying formula (2), we can restore the frequency coefficients to their original values.

Variable Threshold PNSR BPP 42.871674 0.269867 39.238045 0.443700 37.24642 0.555900 36.051215 0.636100 35.374022 0.688133 35.033487 0.717622 34.841083 0.732722 34.670175 0.740378 34.55912 0.745944 34.389006 0.746622 34.316735 0.746656

IV. RESULTS For experimental purpose, we obtained a sequence of 60 images of TFT-LCD by varying distance of camera lens and its depth map is generated by applying Shape From Focus (SFF) method described in [7]. We applied reversible watermarking method described in section-III to secretly hide the depth map into its corresponding image. Fig. 1. shows depth map and the watermarked image. It can be observed that the distortion in watermarked image is hardly noticeable by a human eye. The total amount of watermark bits including the depth map and auxiliary information; such as histogram preprocessing related, is 41552. The size of the cover image is 300×300 in this case. Table I compares the performance of proposed technique with fixed threshold method [5]. It can be observed that the proposed method provides better imperceptibility for the same bit per pixel (bpp) compared to fixed threshold approach. The watermark (depth map) is extracted from the watermarked image. The depth map after extraction is exactly the same as was originally embedded. Figure 2(a) shows the restored image after watermark extraction has been performed. The restored image is the same as the original image. This fact is also indicated by the difference image (figure 2(b)), which is obtained by subtracting the original image from the restored image.

(a) (b) Fig. 2: (a) Restored TFT-LCD color filtor image (b) Difference image.

V. CONCLUSION In this paper, we have introduced the concept of embedding depth map of an object in its 2D image using reversible watermarking. The proposed method is fast, simple and compatible with JPEG 2000 and therefore, it could easily be employed in 3D cameras. REFERENCE [1]

[2]

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[5]

(a)

(b)

Fig. 1: (a) depth map of TFT-LCD color filter. (b) Watermarked TFT-LCD color filter image. Our watermark embedding and extraction methods are simple and computationally efficient. The embedding module can be employed in the form of a chip in a 3D camera. Similarly, a decoder module can be employed at the receiver side to extract the depth map after transmission [8]. The authorized person knowing the secret keys can

[6]

[7]

[8]

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