iccv iccv2013 iccv2013-413 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Pei-Hen Tsai, Yung-Yu Chuang
Abstract: This paper investigates an approach for generating two grating images so that the moir e´ pattern of their superposition resembles the target image. Our method is grounded on the fundamental moir e´ theorem. By focusing on the visually most dominant (1, −1)-moir e´ component, we obtain the phase smto ddoumlaintiaonnt c (o1n,s−tr1a)in-mt on the phase shifts bee otwbteaeinn the two grating images. For improving visual appearance of the grating images and hiding capability the embedded image, a smoothness term is added to spread information between the two grating images and an appearance phase function is used to add irregular structures into grating images. The grating images can be printed on transparencies and the hidden image decoding can be performed optically by overlaying them together. The proposed method enables the creation of moir e´ art and allows visual decoding without computers.
Reference: text
sentIndex sentText sentNum sentScore
1 Target-Driven Moir e´ Pattern Synthesis by Phase Modulation Pei-Hen Tsai Yung-Yu Chuang∗ National Taiwan University Abstract This paper investigates an approach for generating two grating images so that the moir e´ pattern of their superposition resembles the target image. [sent-1, score-1.53]
2 Our method is grounded on the fundamental moir e´ theorem. [sent-2, score-0.815]
3 By focusing on the visually most dominant (1, −1)-moir e´ component, we obtain the phase smto ddoumlaintiaonnt c (o1n,s−tr1a)in-mt on the phase shifts bee otwbteaeinn the two grating images. [sent-3, score-0.765]
4 For improving visual appearance of the grating images and hiding capability the embedded image, a smoothness term is added to spread information between the two grating images and an appearance phase function is used to add irregular structures into grating images. [sent-4, score-1.745]
5 The grating images can be printed on transparencies and the hidden image decoding can be performed optically by overlaying them together. [sent-5, score-0.651]
6 The proposed method enables the creation of moir e´ art and allows visual decoding without computers. [sent-6, score-0.83]
7 One property that makes moir e´ patterns mysterious and interesting is that they consist of new patterns which are clearly visible in the superposition but never appear in any of the original structures [1]. [sent-9, score-1.03]
8 For computer graphics and computer vision, moir e´ patterns are often unwanted artifacts produced by rendering programs or digital cameras, due to undersampling or unexpected interaction between overlaid structures. [sent-10, score-0.842]
9 In this paper, we study an opposite problem where moir e´ phenomenon is not abandoned but utilized for synthesizing the desired patterns. [sent-12, score-0.867]
10 More formally, given a target image, we want to find two grating images so that their superposition resembles the target image through moir e´ effects but none of each reveals the target image individually. [sent-13, score-1.624]
11 The moir e´ phenomenon is intriguing because it is mysterious and unexpected. [sent-14, score-0.845]
12 Fortunately, for years, scientists have developed techniques for analyzing moir e´ patterns with the given structures, such as frequency-domain analysis, geometrical approaches and interferometric methods. [sent-17, score-0.817]
13 Our method is grounded on the fundamental moir e´ theorem which, through frequency-domain analysis, provides a mathematical formulation of the moir e´ components between curvilinear grating images, one kind of repetitive non-periodic grating images (such as L1 and L2 in Figure 1). [sent-18, score-2.611]
14 By focusing on the visually most dominating (1, −1)-moir e´ component, we obtain the phase modulation c(1o,n−str1a)-inmt owirh ´eic cho gives ethnte, c woend oibttioanin o thf eth peh phase oshduifltas iboentween the two grating images for synthesizing the required target image. [sent-19, score-0.921]
15 Direct application of the phase modulation constraint generates two grating images whose superposition resembles the desired target image. [sent-20, score-0.924]
16 Unfortunately, the grating image alone could also reveal the target image although only obscurely. [sent-21, score-0.521]
17 To make the grating images more uncorrelated to the target image, a smoothness term is used to enforce information spread between the two grating images. [sent-22, score-1.03]
18 Furthermore, an appearance phase function is added for imposing unrelated structures into the grating images and controlling their appearances, making the target image more invisible in each of them. [sent-23, score-0.704]
19 Our method can be used for several applications such as creating moir e´ art, in which two seemingly unrelated grating images are superposed to reveal an unexpected target image. [sent-24, score-1.379]
20 Given “The Starry Night” and “The Scream” as the target images, our method generates two grating images L1 and L2. [sent-26, score-0.519]
21 When overlaying L1 over L2 with their top edges aligned, the occurred moir e´ pattern resembles “The Starry Night”. [sent-27, score-0.899]
22 In addition to inciting sense of wonder by moir e´ art, due to its information hiding nature, our method can also be used for steganography in which the message image is hidden and embedded, and can only be revealed with the key image. [sent-29, score-0.936]
23 Our grating images can be printed on separated transparencies and the decoding can be simply performed by overlaying them together. [sent-30, score-0.614]
24 11991122 targetimageI1targetimageI2gratingimageL1gratingimageL2superpositon#1superpositon#2 Figure 1: An example of moir e´ art created by our method. [sent-33, score-0.814]
25 Given two target images I1 and I2, we generate two grating images L1 and L2. [sent-34, score-0.532]
26 When overlaying L1 over L2 with their top edges aligned, the interference pattern incurred by the moir e´ phenomenon resembles I1. [sent-35, score-0.946]
27 By moving L1 downwards to align its bottom edge with L2’s, the moir e´ pattern looks like I2. [sent-36, score-0.865]
28 Related work Amidror’s book “The Theory ofthe Moir e´ Phenomenon” provides a comprehensive and thorough treatment of the theory behind moir e´ phenomenon [1]. [sent-38, score-0.829]
29 It applies Fourier domain approaches to give a detailed analysis for moir e´ phenomenon caused by periodic patterns and repetitive nonperiodic patterns. [sent-39, score-1.028]
30 Our method is built upon the fundamental moir e´ theorem described in this book. [sent-40, score-0.837]
31 Lebanon and Bruckstein [6] pioneered in studying synthesis of the desired moir e´ pattern caused by superposing two generated images. [sent-41, score-0.904]
32 Although both their method and our method build upon the fundamental moir e´ theorem, with the proposed smoothness term and appearance phase function, the results of our method are visually more promising. [sent-42, score-1.066]
33 Hersch and Chosson [3] proposed a moir e´ synthesis method for creating dynamic moving moir e´ patterns when shifting the base band stripe-like layer slowly. [sent-44, score-1.634]
34 Some focused on image hiding in time-averaged moir e´ [9, 10], the moir e´ pattern appeared on a fast oscillating image due to persistence of vision. [sent-45, score-1.725]
35 However, optical watermarking uses occlusion while our method uses moir e´ phenomenon. [sent-50, score-0.845]
36 Fundamental moir e´ theorem This paper takes the spectral approach for analysing the moir e´ phenomenon [1]. [sent-56, score-1.647]
37 In this paper, we consider the moir e´ pattern between repetitive non-periodic grating layers, called curvilinear gratings. [sent-66, score-1.322]
38 Here, the periodic function p determines the intensity behaviour while the bending function φ determines the geometric layout of the grating r. [sent-68, score-0.631]
39 In the superposition (c), some low-frequency, nearly horizontal moir e´ patterns are noticeable. [sent-76, score-0.975]
40 The two components close to the origin (f1−f2 and f2 −f1) correspond to the visible moir e´ patterns as they are o−f low-frequency and significant enough. [sent-80, score-0.86]
41 The fundamental moir e´ theorem [1] states that the periodic profile and the geometric layout of the moir e´ are completely independent to each other. [sent-81, score-1.856]
42 Mathematically, it says that the (k1, k2)-moir e´ component mk1 of the superposition r (here, k1, k2 are integers indicating the different moir e´ components, called moir e´ index) is given by ,k2 mk1,k2 (x, y) = pk1,k2 (φk1,k2 (x, y)). [sent-82, score-1.75]
43 The bending function φk1 brings moir e´ appearance and is given by ,k2 φk1,k2 (x, y) = k1φ1(x, y) The 1-D periodic profile function moir e´ is given by pk1 ,k2 into the (k1, k2)- + k2φ2(x, pk1 ,k2 (4) y). [sent-83, score-1.863]
44 With the fundamenFtal m{oiFr e{´ pthe}o(rkemu,) we can decompose the moir e´ pattern into several (k1, k2)-moir e´ components whose periodic profiles and bending phase functions can be treated independently. [sent-93, score-1.279]
45 Moir e´ pattern synthesis We attempt to solve the following problem: Given a target image I, find two curvilinear grating images L1 and L2 such that the moir e´ pattern of their superposition is close to I. [sent-96, score-1.587]
46 We will impose some desired properties of the gratings for different applications in Section 5, but focus on the basic moir e´ pattern synthesis problem in this section. [sent-97, score-0.931]
47 This indicates that we only need to consider four moir e´ components, (1, 1), (−1, −1), (1, −1) and (−1, 1). [sent-105, score-0.796]
48 mNootier e´ eth caotm (p1,o n1)e natnsd, ((1−,11), −, (1−) 1m,−oir1 e´) are equivalent as they just swap (th1,e1 r)o alensd o (f− L11, −a1nd) mL2o ; esim ariela erq fuoirv (le1,n −t a1s) ahendy (−1, 1) moir e´ components. [sent-106, score-0.796]
49 Therefore, we only manipulate the (1, −1) moir e´ component and leave owtehe orn components efo trh efr (e1e, as they are loemssp visually ndo lteiacveeable because of high frequency or low magnitude. [sent-109, score-0.872]
50 )l iacnidty ,φ wme e( dx,e yfin) e≡ m φ1,−1 ()x ≡, y m) as the moir e´ component, intensity profile )a n≡d phase function for the (1, −1)nmeonitr, e´ ontfe ethnsei superposition S p respectively. [sent-115, score-1.183]
51 11991144 ( ca) L I1( db) LIˆ2(e) superposit on Figure 4: A simple example for moir e´ pattern synthesis. [sent-116, score-0.826]
52 When superposing L1 and L2 together, the generated moir e´ pattern (e) looks similar to the target image Iˆ. [sent-122, score-0.954]
53 t Hthaotwe thvee ar, p bpeecaaruasnec eth oef range 1o)f- fmuonicrt ´eio mn pm kiss usually smaller than [0, 1], the synthesized moir e´ cannot match the intensity range of I. [sent-129, score-0.89]
54 (10) Thanks to the fundamental moir e´ theorem, the periodic profile pm can be pre-determined by the Fourier coefficients of p1 and p2 using Equation 9. [sent-135, score-1.106]
55 Note that the target image is slightly visible (although very obscurely) in one of the grating images. [sent-149, score-0.524]
56 The most important factor is probably the range of the resulting periodic profile because it directly affects the range of the intensity of the hidden moir e´ pattern. [sent-155, score-1.094]
57 The periodic profile pm with a larger range potentially gives a moir e´ image with better contrast. [sent-156, score-1.088]
58 mIfo tihr´e e periodic profiles p1 fan hdig p2 contain high-frequency components, they will have more significant high-frequency Fourier coefficients and also significant amplitudes of pk1,k2 for high-order moir e´ (where |k1| > 1and |k2 | > 1). [sent-162, score-1.04]
59 Since we ignore high-order moir e´ |ink our fr 1am anedw o|krk|, significant high-order em hoigir eh´ components could inference the target moir e´ pattern and make it less noticeable. [sent-163, score-1.724]
60 When using square waves as periodic profiles, the amplitude of high-order moir e´ components are not negligible. [sent-164, score-1.007]
61 Thus, the superposition could contain undesired high-frequency moir e´ patterns. [sent-165, score-0.981]
62 On the other hand, cosine waves do not have high-frequency components and there is no high-order moir e´ components when using as profiles. [sent-166, score-0.892]
63 The periodic profiles also directly affects the appearance of the resultant grating images. [sent-168, score-0.72]
64 For example, some applications might require binary grating images and the square waves become more suitable. [sent-178, score-0.496]
65 We used two cosine functions f(x) = 12+21 cosx as the profiles for most cases because they contain less artifacts due to high-order moir e´ components and have an acceptable range to represent the hidden image with good contrast. [sent-179, score-1.008]
66 Applications and results The previous section introduces the basic method for synthesizing the moir e´ pattern so that it looks similar to the target image. [sent-181, score-0.935]
67 Note that we have the luxury to control grating images’ appearances by adjusting the phase functions as long as their phase difference satisfies the phase modulation constraint (Equation 12). [sent-182, score-1.001]
68 Figure 6(d) an+d E(e,) wshheowre that the smoothness term improves the visual appearance of the grating and superposed images. [sent-252, score-0.578]
69 (17) This property allows use to design the appearance of the grating images by adding an appearance phase function φA. [sent-255, score-0.689]
70 However, when the frequency of φA is too high, undesired moir e´ will become noticeable on the grating images due to gridded sampling pattern of image pixels. [sent-257, score-1.357]
71 Adding the appearance phase function could also distort the appearance of the grating images, making the target images even less noticeable. [sent-258, score-0.751]
72 Figure 7 shows an example for controlling the appearance of the grating images and better image hiding with a diagonal stripe pattern as the appearance phase function. [sent-259, score-0.819]
73 11991166 Figure 6: The vertical smoothness term ES ensures appearance smoothness of the grating and the superposed images. [sent-260, score-0.63]
74 Given the portraits of Newton and Beethoven as targets (a), without ES (λ=0), both the grating images (b) and the superposed images (c) contain visually disturbing discontinuity. [sent-261, score-0.536]
75 Adding the smoothness term with λ=1 helps reducing the discontinuity as shown in the grating images (d) and superposed images (e). [sent-262, score-0.572]
76 However, when the frequency is too high, moir e´ effects could be observed in the grating images due to insufficient sampling limited by the image resolution. [sent-265, score-1.304]
77 The proposed method can also be used for hiding a secret image within two grating images. [sent-271, score-0.587]
78 For this application, it is important to hide the image well so that the secret image cannot be visible with only one of the two grating images. [sent-273, score-0.516]
79 For achieving this goal, in addition to using the smoothness term to spread the information into two gratings, we have also added noise appearance phase functions to make the grating images more difficult to decrypt. [sent-274, score-0.736]
80 We would like to generate a key image K and a set of information images L1 to LN such that, when superposing K on Li, the moir e´ pattern looks like the target image Ii. [sent-275, score-0.967]
81 In order to spread information to both K and Li so that the hidden information is not obvious in either, similar to moir e´ art, we add a smoothness term and have the following energy function: E = EA + λES + E, where the appearance term EA is given by: ? [sent-277, score-0.944]
82 2 A larger λ in the energy function helps hiding the target images better, but resulting in more blur moir e´ pattern as well. [sent-350, score-1.004]
83 Even with the smoothness term, the target image could still be slightly visible in the grating images as shown in Figure 8(b) especially when the secret image contains discontinuities. [sent-351, score-0.631]
84 Unlike moir e´ art, φA does not have the requirement in Equation 17 and can be an arbitrary phase function. [sent-353, score-0.949]
85 Optical superposition One advantage ofthe proposed approach is that the moir e´ superposition can be performed without computers. [sent-365, score-1.112]
86 Although in principle, grating images need to be perfectly aligned, in practice, we found that the hidden images are still recognizable with imperfect alignments. [sent-372, score-0.52]
87 For example, the sampling pattern of the color filter array (CFA) in a digital camera serves as a grating pattern G due to sampling. [sent-374, score-0.516]
88 Given a target image I and a known grating pattern G, we can find the image L = pL (φL (x, y)) by obtaining φL with φL (x, y) = φG (x, y) + Ψ(x, y) , (21) (Iˆ). [sent-375, score-0.536]
89 However, because one of the grating image is given, we do not have the freedom to add appearance phase functions. [sent-378, score-0.629]
90 We printed the two grating images ofFigure 6 on a transparency and a paper respectively. [sent-383, score-0.544]
91 (a)gratingmage(b)scre ncapturedbythecamera Figure 11: With the known Bayer pattern G of the RICOH R7 digital camera, we can obtain the grating image (a). [sent-386, score-0.486]
92 Note that the hidden image seems recognizable in the grating image because in this scenario we cannot add a noise phase function. [sent-388, score-0.647]
93 Because of the limited range of pm, our method can only generate moir e´ images with lower contrast. [sent-393, score-0.822]
94 However, in the cases when high-order moir e´ components become significant, they could disturb the appearance of the target images and make them less recognizable. [sent-399, score-0.955]
95 Finally, the resolution and frequency content of the hidden images are limited by the process of moir e´ phenomenon. [sent-400, score-0.882]
96 Conclusions This paper addresses the problem of designing moir e´ patterns. [sent-402, score-0.796]
97 In addition, we introduce the phase appearance function to further decorrelate the grating images and the target image, making target image invisible in the grating images. [sent-404, score-1.224]
98 Our optimization function is customized for each problem and the phase function can be controlled to decorrelate the target images and grating images. [sent-405, score-0.686]
99 While successful in many ways, the effective resolution of the synthesized moir e´ image is less than the resolution of the target image. [sent-407, score-0.858]
100 In addition, the moir e´ image has lower contrast and brightness. [sent-408, score-0.796]
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