3D Filtering of Colour Video Sequences Using ... - Semantic Scholar

3D Filtering of Colour Video Sequences Using Fuzzy Logic and Vector Order Statistics Volodymyr Ponomaryov, Alberto Rosales-Silva, and Francisco Gallegos-Funes National Polytechnic Institute of Mexico, ESIME, Av. Santa Ana, 1000, Col. San Fco- Culhuacan, 04430, Mexico-city, Mexico {Ponomaryov,vponomar}@ipn.mx

Abstract. Novel approach designed in this paper permits the suppression of impulsive noise in multichannel video sequences. It employs the fuzzy logic and vector order statistic methods to detect motion and noise presence during spatial-temporal processing neighbouring video frames, preserving the edges, fine details, as well as colour properties. Numerous simulation results have justified it excellent performance in terms of objective criteria: Pick Signal-toNoise Ratio (PSNR), Mean Absolute Error (MAE) and Normalized Colour Difference (NCD), as well as in subjective perception by human viewer.

1 Introduction Images and video sequences are acquired by sensor of different nature, so, the quality of data can be degraded because of non-ideality of a sensor or during transmission process where a noise is introduced. Standard processing operations: edge detection, image segmentation, pattern recognition in noise presence can present low quality results. So, the image pre-processing stage is a principal part in any computer vision application and includes reducing image noise without degrading its quality. There are known many algorithms that are employed for impulsive noise suppression in two dimensions (2D), for example some proposed in [1-6]. The aim of this work is to design a novel scheme that permits to realize the processing in 2D, as well as and in 3D, demonstrating better performance in terms of objective and subjective criteria. A novel filtering scheme employs fuzzy logic and vector order statistic theory in processing of video sequences, and as it is justified, proposed approach can efficiently suppress impulsive noise generated in communication channel, guaranteeing better edge and fine preservation and chromaticity characteristics. Novel scheme, named as 2D Fuzzy Two Step Colour Filter, gathering the fuzzy set theory and vector order statistics has demonstrated the ability to outperform existed filters as one can see analyzing the simulation results. There are other 2D algorithms that are also implemented and used in this paper as comparative ones: INR filter [1], AMNF, AMNF2 (Adaptive Non-Parametric Filters) [2]; AMNF3 (Adaptive Multichannel Non-Parametric Vector Rank M-type K-nearest Neighbour Filter) [3]; GVDF (Generalized Vector Directional Filter) [4]; CWVDF (Centred Weighted Vector Directional Filters) [5]; and, finally, VMF_FAS (Vector J. Blanc-Talon et al. (Eds.): ACIVS 2009, LNCS 5807, pp. 210–221, 2009. © Springer-Verlag Berlin Heidelberg 2009

3D Filtering of Colour Video Sequences

211

Median Filter Fast Adaptive Similarity) [6]. These techniques demonstrated the better results among a lot of other existed and are used as comparative ones. Developing mentioned novel 2D filter, we also present a novel 3D filtering approach employing a correlation between neighbour frames. Here, the information from previous or/and future frames can be also available, but the efficient employment of the several neighbour frames should be found during processing, taking into account a motion between frames. A lot of proposals have been presented in video denoising, in spatial, temporal and spatio-temporal denoising [7-15]. Let draw a brief review of several video denoising algorithms. Paper [7] exposes a motion-compensated 3D locally adaptive minimum mean squared error filter in processing the video sequences using the intelligent pixel aggregation algorithm. Novel video denoising algorithm for Gaussian noise in the wavelet transform (WT) domain is introduced in [8] permitting usage of local correlations between the wavelet coefficients of video sequence in space and time. The technique based on the transform in the local 3D variable-sized windows is designed in [9]. For every spatial position in each a frame, the block-matching algorithm is employed to collect highly correlated blocks from neighbouring frames. The final estimate is a weighted average of the overlapping local ones. An image sequence algorithm for noise suppression that is similar to before mentioned is proposed in [10]. Another technique [11] involves two low-complexity filters for Gaussian noise reducing. A new algorithm, in which the local variance of Gaussian noise is estimated in the homogeneous cubes for the 3-D video signal, is employed in paper [12]. Novel temporal denoising filter multihypothesis motion compensated filter is developed for removing of Gaussian noise in a video signal [13]. In the paper [14], the video denoising is realized in the WT domain, where the motion estimation/compensation, temporal filtering, and spatial smoothing are undertaken. Recently in [15], a new fuzzy-rule-based algorithm for noise suppression of video sequences corrupted with Gaussian noise is exposed. The method constitutes a fuzzy-logic-based improvement of a detail and the motion adaptive multiple class averaging filter. Proposed fuzzy motion and detail adaptive video filter (FMDAF) has shown excellent ability in suppression of Gaussian noise. In this paper, introducing 3D scheme in filtering the video sequences contaminated by impulsive noise, we also realize the adaptation of several 2D algorithms in filtering of 3D video data: MF-3F (Median Filter that exploits three frames); VGVDF, VVMF (Video Vector Median Filter) [16], which applies the directional techniques as an ordering criterion; VVDKNNVMF (Video Vector Directional K-nearest Neighbour Vector Median Filter) [16], where the ideas of vector order statistics are employed. Additionally, we have implemented the KNNF (K-nearest neighbour filter) [17]; VATM (Video Alpha Trimmed Mean) [17]; and VAVDATM (Video Adaptive Vector Directional Alpha Trimmed Mean) [18] that connects the directional techniques procedures with adaptive and order statistics techniques. First, in novel approach, during the spatial stage of processing for proposed algorithm, each a frame is filtered in every R, G, and B channel, employing fuzzy logic and vector order statistic methods together. Second, the filtered frames are processed in the next, temporal stage of the algorithm detecting the noise and movement levels by proposed fuzzy-directional method, employing the filtered spatial frame (t-1) and

212

V. Ponomaryov, A. Rosales-Silva, and F. Gallegos-Funes

next one (t). As a final step, the present frame is filtered applying the fuzzy rules based on direction information, which realises the suppression of a noise in a current frame. Numerical simulations demonstrate that novel framework outperforms several mentioned above filtering approaches in processing the video colour sequences. It has been investigated the contaminated by impulsive noise test colour images: “Lena”, “Peppers”, “Baboon”. “Parrots” (320x320 pixels in RGB space, 24 bits), and video sequences: “Flowers” and “Miss America” (QCIF format, 176x144 pixels in each a frame).

2 Fuzzy Two Step Colour Filter Let introduce the absolute differences named as gradients and angle divergence (directions) that represent the level of similarity among different pixels. This permits the usage of its values in probe of two hypothesises: the central pixel is a noise one or it is noisy free pixel. To resolve this, let calculate in each a window for each a direction (N, E, S, W, NW, NE, SE, SW), in respect to the central pixel, the “gradient” xcβ ( i, j ) − x β ( i + k , j + l ) = ∇(βk ,l ) x ( i, j ) , where ( i, j ) = ( 0, 0 ) . Here, index β shows

different R, G, and B channels of colour frame, and ( k , l ) represent each one of the

eight mentioned directions with values: {−1, 0,1} (see Fig.1). Similar to [19, 20], let introduce not only one “basic gradient” for any direction, but also four “related gradient”, with ( k , l ) from values {−2, −1, 0,1, 2} . Function ∇γβ shows the gradient values for each a direction, and parameter γ marks any chosen direction. For example,

β for the “SE” direction (Fig.1), the gradients are as follows: ∇(β1,1) x ( 0,0 ) = ∇ SE ( basic ) , β β ∇(β0,2) x ( i − 1, j + 1) = ∇ SE ( rel1) , ∇( 2,0 ) x ( i + 1, j − 1) =

∇ βSE ( rel 2) ,

∇(β0,0 ) x ( i − 1, j + 1)

β β β = ∇ SE ( rel 3) , and ∇( 0,0 ) x ( i + 1, j − 1) = ∇ SE ( rel 4 ) .

Fig. 1. Basic and related directions for gradients and angle divergence values


213

Let introduce the angle divergence for each a channel in such a way where we omit two of three channels in the case of each a colour frame. For example, in the “SE” direction, the “basic” and “related” vectorial (angular) values can be written as: β β β β β θ(β0,2) x ( i − 1, j + 1) = θ SE ( rel1) , θ( 2,0 ) x ( i + 1, j − 1) = θ SE ( rel 2 ) , θ( 0,0 ) x ( i − 1, j + 1) = θ SE ( rel 3) , β and θ(β0,0) x ( i + 1, j − 1) = θ SE ( rel 4 ) .The basic angle divergence in the “SE” direction

between pixels (0,0) and (1,1) for given channel β (Fig.1) is calculated as follows:

θ

β γ = SE ( basic )

⎡ 2(255) 2 + x(β0.0 ) ⋅ x(β1,1) ⎢ = arccos ⎢ 2(255 2 ) + x β 2 1 / 2 ⋅ 2(255 2 ) + x β ( 0, 0 ) (1,1) ⎣

(

))

(

(

(

⎤ ⎥ . (1) 1/ 2 ⎥ ⎦

)) 2

Figure 1 exposes the employed pixels in processing procedure in the chosen SE direction for the basic and related components. Let introduce fuzzy sets: BIG (B) and SMALL (S) that permit estimating the noise presence in a central pixel for window 5 × 5 . A big membership degree (near to value one) in the S set shows that the central pixel is free of noise, and large membership degree in the B set shows that central pixel is noisy one with large probability. The Gaussian membership functions are used to calculate membership degrees for fuzzy gradient and fuzzy angle values:

μ∇β

γ = SE ( basic )

( SMALL ,BIG )

⎧1, if ( ∇γβ < med 2, ∇γβ > med1) ⎪ 2 2 ⎪ ⎛ ⎧ β ⎛ ⎧ β ⎫⎞ ⎫⎞ ⎞ = ⎨⎛ ⎜ exp ⎜ − ⎪ ( ∇γ − med 2 ) ⎪ ⎟ , exp ⎜ − ⎪ ( ∇γ − med1) ⎪ ⎟ ⎟ , ⎪⎜ ⎨ ⎬ ⎨ ⎬⎟ ⎟ 2 2 ⎜⎜ ⎟ ⎜⎜ 2σ 1 2σ 1 ⎪⎜ ⎪⎩ ⎪⎭ ⎟⎠ ⎪⎩ ⎪⎭ ⎟⎠ ⎟ ⎝ ⎝ ⎝ ⎠ ⎩

where values med1 = 60,

μθγβ ( SMALL, BIG )

med 2 = 10,

med 4 = 0.1,

,

(2)

σ 12 = 1000 ;

⎧ 1, if (θ γβ ≤ med 4, θ γβ ≥ med 3) ⎪⎪ = ⎨⎛ ⎡ ⎧⎪ (θ γβ − med 4) 2 ⎫⎪⎤ ⎡ ⎧⎪ (θ γβ − med 3) 2 ⎫⎪⎤ ⎞ ⎜ ⎟ , exp ⎥ ⎢− ⎨ ⎬ ⎬⎥ ⎟, ⎪⎜ exp ⎢− ⎨ 2σ 22 2σ 22 ⎪⎭⎥⎦ ⎪⎭⎥⎦ ⎠ ⎢⎣ ⎪⎩ ⎢⎣ ⎪⎩ ⎪⎩⎝

and values med 3 = 0.615,

otherwise

otherwise ,

(3)

σ 22 = 0.8 . The values in equations (2)-(3)

were found during numerical simulations according to the best values for PSNR and MAE criteria.

3 Fuzzy Rules in Two Dimensions Let present novel fuzzy rules applied for gradient values and angular values in each a channel.

γ

β Fuzzy Rule 1_2D introduces the membership level of x(i , j ) in the set BIG for any β direction: IF ( ∇ γβ is B AND ∇γ ( rel1) is S, AND ∇γβ( rel 2) is S, AND

∇γβ( rel 3)

is B,

214


β β β β AND ∇γ ( rel 4) is B) AND (θγ is B AND θγ ( rel1) is S, AND θ γβ( rel 2) is S, AND θ γ ( rel 3) is

βF βF β B, AND θ γ ( rel 4 ) is B) THEN fuzzy gradient-angular value ∇γ θγ is BIG. The opera-

tor AND= min ( A, B ) outside of the parenthesis, and inside of the parenthesis A AND B =A ∗ B . Fuzzy Rule 2_2D presents the noisy factor gathering eight fuzzy gradientdirectional values that are calculated for each a direction as: IF fuzzy gradient-angular βF βF βF βF values ∇ βNFθ Nβ F is B OR ∇ βS Fθ Sβ F is B, OR ∇ E θ E is B, OR ∇W θW is B, OR βF βF βF βF ∇ βSWF θ SW is B, OR ∇ βNEFθ NE is B, OR ∇ NW θ NW is B, OR

βF ∇ βSEFθ SE is B THEN noisy

β factor r is BIG. The operation OR in rule 2 is introduced as max ( A, B ) β

The noisy factor r is employed as a threshold to distinguish among a noisy pixel and a free noise one. So, if r β ≥ R0β , it is applied the filtering procedure employing the fuzzy gradient-angular values as weights, in opposite case, the output is formed as β

β

unchanged central pixel: yout = x( i , j ) . For r β ≥ 0.3 (the value R0β =0.3 was chosen in numerical simulations according to the best values for PSNR and MAE criteria), the fuzzy weights are used in the standard negator function ( ς ( x) = 1 − x, x ∈ [0,1] ) defined as ρ (∇ γβF θ γβF ) = 1 − ∇ γβF θ γβF , where ∇ γβF θ γβF ∈ [0,1] ; so, this value origins the fuzzy membership value in a new fuzzy set defined as “NO BIG” (noise free). Introducing the fuzzy weight for central pixel in NO BIG fuzzy set as follows: ρ (∇ (β0F,0 )θ (β0F,0 ) ) = 3 1 − r β , finally, the ordering procedure is defined in the spatial filtering algorithm as follows:

{

}

β β β (1) β (2) β (9) xγβ& = xSW ,K , x(βi , j ) ,K , xNE ⇒ , xγ& ≤ xγ& ≤ L ≤ xγ&

(1)

implies

ρ ( ∇γβ& Fθγ&β F ) ≤ ρ ( ∇γβ& Fθγ&β F ) ≤ L ≤ ρ ( ∇γβ& Fθγ&β F ) , ( 2)

(9)

where γ& = ( N, E, S, W, ( i, j ) , NW, NE, SE, SW) permitting to remove the values more outlying from the central pixel (i,j). So, the filtering algorithm, which applies the fuzzy gradient-angular values, selects one of the neighbour pixels from the jth ordered values or central component permitting to avoid the smoothing of a frame.

4 Three Dimensional Filtering 4.1 Fuzzy Colour Filter in Three Dimensions

Let introduce 3D procedure employing the above presented filtering procedure as a first step in the initial frame of a video sequence (spatial stage). After the temporal stage of the algorithm, the mentioned spatial algorithm should be used again to suppress non-stationary noise left during the temporal stage of the procedure. Employing


215

two neighbour frames (past and present) of a video sequence permits to calculate the movement and noise fuzzy levels of a central pixel. Here, a 5x5x2 sliding window, which is formed by past and present frames, is employed, and the difference values between these frames are calculated:

λ(βk ,l ) ( A ( i, j ) , B ( i, j ) ) = A ( i + k , j + l ) − B ( i + k , j + l ) ,

(4)

where A ( i, j ) are pixels in t-1 frame of video sequence, and B ( i, j ) show the pixels

in t frame, with indexes ( k , l ) ∈ {−2, −1, 0,1, 2} .

Using values λ(βk ,l ) in Eq. (4)) denominated as gradient difference values, we obtain an error frame. Now, let calculate the absolute difference gradient values of a central pixel in respect to its neighbour ones for a 5x5x1 window processing. The absolute difference gradient values are calculated in the next equation for the SE (basic) direction only. The same procedure should be repeated for all other basic and related values in any direction: β β β ′β ′β ∇′(1,1 ) λ ( 0,0 ) = ∇ SE ( basic ) , where ∇ SE ( basic ) = λ( 0,0 ) − λ(1,1) ,

(5)

As in 2D framework, let calculate the absolute difference angular values of a central pixel in respect to its neighbour ones as an angle divergence value among t-1 and t frames as follows: ⎡

φ(βk ,l ) ( A(i , j ), B (i, j ) ) = arccos⎢

(

2( 255) 2 + A(i + k , j + l ) ⋅ B (i + k , j + l )

⎣⎢ 2( 255 ) + ( A(i + k , j + l ) ) 2

) ⋅ (2(255 ) + ( A(i + k , j + l )) )

2 1/ 2

2 1/ 2

2

⎤ ⎥ (6) ⎦⎥

Using angle divergence value φ(βk ,l ) , we present the absolute angular divergence ones: ∇′′(1,1β)φ ( 0, 0 ) = ∇′′SEβ(basic ) , where ∇′′SEβ(basic ) = φ(β0,0) − φ(β1,1) ,

(7)

The same reasoning done for ∇′SEβ (basic ) in respect to ∇ βSE (basic ) is realized also for ∇′′SEβ(basic ) value. Let employ the same Gaussian membership functions for fuzzy values as in the equations (2)-(3) introducing the fuzzy gradient-angular difference values. The numerical experiments realized in this case have given the values for function in eq. (3): med 4 =0.01, med 3 =0.1 according to the best PSNR and MAE criteria results. 4.2 Fuzzy Rules in 3D Filtering

Fuzzy rules used to characterize the movement and noise levels in central pixel components are defined as follows: Fuzzy Rule 1_3D determines the FIRST 3D fuzzy gradient-angular difference value as ( ∇γ′β F ∇γ′′β F ) : IF ( ∇γ′β is B AND ∇γ′β( rel1) is S, AND ∇′γβ( rel 2) is S, AND FIRST

β

∇′γ ( rel 3)

is B, AND

β

∇′γ ( rel 4)

is B) AND ( ∇γ′′β is B AND

∇γ′′(βrel1)

is S, AND

∇′′γ (βrel 2)

is S,

216


AND

∇′′γ (βrel 3)

is B, AND

∇′′γ (βrel 4)

is B) THEN ( ∇γ′β F ∇γ′′β F )

FIRST

is BIG. This rule charac-

terizes the movement and noise confidence in a central pixel by neighbour fuzzy values in any γ direction. Operation AND= min ( A, B ) outside of parenthesis. Fuzzy Rule 2_3D defines the SECOND 3D fuzzy gradient-angular difference value as ( ∇γ′β F ∇γ′′β F ) : IF ( ∇γ′β is S AND ∇′γβ( rel1) is S, AND ∇′γβ( rel 2) is S) SECOND

OR ( ∇γ′′β is S AND

∇γ′′(βrel1)

is S, AND

∇′′γ (βrel 2)

is S) THEN ( ∇γ′β F ∇γ′′β F )

SECOND

is

SMALL. This rule characterizes the no movement confidence in a central pixel in any γ direction. Operation OR= max ( A, B ) ; also, the operation AND= A ∗ B inside of parenthesis for fuzzy rules 1 and 2 presented above. Fuzzy Rule 3_3D defines the fuzzy 3D noisy factor r β : IF

OR ( ∇′Sβ F ∇′′S β F )

FIRST

is B, OR, L , OR ( ∇′Nβ F ∇′′N β F )

FIRST

( ( ∇′

βF

SE

∇′′SEβ F )

FIRST

is B

is B) THEN r β is BIG.

This Fuzzy Rule permits to calculate the fuzzy noisy factor and estimate the movement and noise level in a central component using the fuzzy values determined for all directions. Fuzzy Rule 4_3D defines the no movement 3D confidence factor η β : IF

( ( ∇′

βF

SE

∇′′SEβ F )

SECOND

is S OR ( ∇′Sβ F ∇′′S β F )

SECOND

is S, OR L , OR ( ∇′Nβ F ∇′′N β F )

SECOND

is

S) THEN η β is SMALL. The parameters r β and η β can be effectively applied in the decision: if a central pixel component is noisy, or is in movement, or is a free one of both mentioned events. Fuzzy Rules from 1_3D to 4_3D determine the novel algorithm based on the fuzzy parameters. It should be chosen the j-th component pixel, which satisfies to proposed conditions, guaranteeing that edges and fine details should be preserved according to ordering criterion in the selection of the nearest pixel according to fuzzy measure matter to the central pixel in t-1 and t frames. Enhancement of noise suppression capabilities of the filter can be realized at the final step via application of the FTSCF-2D that permits decreasing the influence of the non-stationary noise left by temporal filter. Some modifications of the FTSCF-2D applied after the FTSCF-3D should be realized because of the non-stationary nature of noise.

5 Numerical Simulation Performance of the filters is measured under different commonly used criteria, such as: PSNR, MAE [21], and NCD [16, 22, 23]. Lena, Baboon, Peppers, Parrots, etc. colour images with different texture propertied were used to evaluate 2-D algorithms. Also, Miss America and Flowers video colour sequences were investigated to justify robustness of the designed 3D filtering scheme in varying texture of a video sequence. The frames of the video sequences were contaminated by impulsive noise with different intensity in each a channel.


217

Table 1 presents PSNR criterion values for 2D designed algorithm against other existed ones exposing the better values in the case of low and middle noise intensity. The best performance is presented by designed algorithm until 15% of noise intensity for Lena and until 10% for Baboon and Peppers colour images guaranteeing the robustness of novel framework because of different texture and chromaticity properties of the mentioned images. Table 1. PSNR criterion values for Lena, Baboon, and Peppers images, accordingly (%) Noise FTSCF2D 0 37,12 2 35,55 5 33,99 10 31,50 20 26,86 0 29,19 2 28,64 5 27,85 10 26,60 20 23,72 0 38,06 2 35,61 5 33,64 10 31,09 20 26,07

AVMF

VMF

AMNF3

CWVDF

31,58 31,31 30,95 30,10 27,83 24,44 24,39 24,27 23,97 22,88 31,55 31,28 30,81 29,80 27,30

30,47 30,3 30,07 29,46 27,58 24,15 24,11 24,02 23,78 22,79 30,88 30,68 30,30 29,44 27,19

29,45 29,34 29,21 28,93 28,18 23,76 23,71 23,64 23,48 23,09 29,47 29,25 29,02 28,71 27,82

33,05 32,15 31,24 29,04 24,3 24,96 24,67 24,16 23,14 20,67 32,87 31,47 29,75 27,34 22,12

VMF_ FAS 36,46 34,88 31,85 28,80 24,8 30,14 29,27 27,22 25,29 22,47 35,49 33,39 31,19 29,01 24,45

INR 31,71 31,58 31,45 30,93 29,03 27,44 27,25 27,01 26,39 24,95 32,56 32,10 31,54 30,81 28,41

Table 2. MAE criterion values for Lena, Baboon, and Peppers mages, accordingly (%) Noise 0 2 5 10 15 20 0 2 5 10 15 20 0 2 5 10 15

FTSCF2D 0,41 0,62 0,91 1,48 2,17 3,11 2,14 2,42 2,87 3,67 4,63 5,83 0,31 0,52 0,82 1,38 2,16

20

3,13

AVMF

VMF

AMNF3

CWVDF

VMF_FAS

INR

1,89 2,09 2,39 2,97 3,63 4,41 6,97 7,1 7,36 7,87 8,59 9,49 1,51 1,68 1,97 2,49 3,13

4,08 4,17 4,29 4,57 4,92 5,41 8,55 8,59 8,701 8,96 9,43 10,11 2,86 2,96 3,14 3,49 3,95

4,84 4,92 5,04 5,22 5,46 5,74 10,46 10,57 10,73 11,02 11,36 11,75 4,17 4,27 4,42 4,66 4,92

2,63 2,83 3,10 3,82 4,87 6,38 5,42 5,82 6,42 7,65 9,17 10,99 1,32 1,63 2,15 3,20 4,82

0,26 0,54 1,19 2,35 3,709 5,0 0,94 1,4 2,54 4,06 5,83 7,69 0,2 0,56 1,14 2,07 3,7

4,35 4,37 4,41 4,53 4,7 4,98 7,54 7,63 7,77 8,09 8,50 8,99 3,62 3,68 3,75 3,9 4,18

3,92

4,53

5,26

6,92

4,84

4,47

218


Table 2 exposes that the best performance in preservation of the edges and fine details for mentioned images is demonstrated by designed method permitting to avoid the smoothing in wide range of noise intensity. Fig.2 exposes subjective perception for image Parrots showing better preservation for edges, fine details and chromaticity characteristics in the case when designed filter is employed.

a)

d)

b)

c)

e)

f)

Fig. 2. Zoomed image region of image Parrots a) original, b) contaminated by impulsive noise of 10% intensity, c) Designed FTSCF-2D, d) AMNF3, e) VMF_FAS, f) INR Table 3. Average NCD values for Flowers video colour sequence (%) FTSCF_ Noise 3D 0 0,003 5 0,004 10 0,006 15 0,007 20 0,009 25 0,010 30 0,012

MF_3F VVMF 0,014 0,014 0,015 0,015 0,016 0,017 0,018

0,014 0,014 0,015 0,015 0,016 0,017 0,018

VVDKNN VGVDF VMF 0,015 0,016 0,016 0,016 0,017 0,016 0,017 0,016 0,018 0,017 0,019 0,018 0,020 0,020

VAVD ATM 0,011 0,012 0,012 0,013 0,014 0,015 0,017

VATM

KNNF

0,014 0,014 0,015 0,015 0,016 0,017 0,018

0,006 0,008 0,010 0,013 0,017 0,022 0,027

Table 4. Average MAE values for Miss America video colour sequence (%) Noise 0 5 10 15 20 30 40

FTS CF3D 0,04 0,37 0,74 1,18 1,76 3,58 6,91

MF_ 3F

VVMF

2,46 2,51 2,59 2,70 2,86 3,35 4,42

2,50 2,54 2,61 2,71 2,85 3,31 4,33

VVDKN N VMF 2,91 3,11 3,28 3,43 3,60 4,39 6,78

VGVD F 2,99 2,91 2,87 2,85 2,89 3,28 4,712

VAVD ATM

VATM

KNNF

0,82 1,11 1,41 1,71 2,044 2,85 4,35

2,52 2,57 2,65 2,76 2,92 3,44 4,73

1,49 1,91 2,67 3,84 5,47 10,11 16,22


219

The capabilities of the designed algorithm in 3D processing are also exposed in following tables and figures. NCD criterion values, which are presented in the Table 3, characterizes the preservation in the chromaticity properties, justifying that the best performance in wide range of noise corruption in Flowers video sequence was obtained by novel 3D framework. It is known that this video sequence is characterized by variable texture and high diversity in colour distributions, so, this confirms Table 5. Average NCD values for Miss America video colour sequence (%) Noise 0 5 10 15 20 30

FTSCF3D 0,000 0,002 0,003 0,005 0,008 0,016

MF_3F

VVMF

0,009 0,009 0,010 0,010 0,010 0,012

0,009 0,009 0,009 0,010 0,010 0,012

a)

VVDKNN VMF 0,011 0,011 0,012 0,012 0,012 0,015

VGVDF 0,011 0,011 0,010 0,010 0,010 0,012

VAVD ATM 0,003 0,004 0,005 0,006 0,007 0,010

b)

d)

KNNF

0,009 0,009 0,010 0,010 0,010 0,012

0,006 0,007 0,010 0,014 0,020 0,038

c)

e)

g)

VATM

f)

h)

Fig. 3. a) Zoomed image region of 10th Miss America frame contaminated by impulsive noise of 15% intensity, b) Designed FTSCF-3D, c) MF_3F; d) VVMF, e) VGVDF, f) VAVDATM; g) VATM; h) KNNF

220


the robustness of the proposed framework. Similar numerical results (Tables 4 and 5) in less detailed video sequences, such as Miss America show that the designed algorithm demonstrates the best filtering performance (MAE and NCD values) for low and middle noise levels until 20% of noise intensity. Subjective perception by human viewer can be observed in Figure 3 showing better performance of the designed 3D framework in comparison with known methods. This figure presents the zoomed filtered Miss America frame, where novel algorithm preserves better the edges, fine details, and chromaticity properties against other filters.

6

Conclusion

The proposed framework has demonstrated the better performance in noise suppression for multichannel video sequences in comparison with existed filtering techniques. Novel 3D filtering approach outperforms known 2D and/or 3D filtering techniques as numerous simulation results justify. Fuzzy set theory together with vector order statistics technique, which are exploited in the designed algorithm, have demonstrated the better preservation of the edges, fine details and chromaticity characteristics in multichannel images and sequences in terms of objective criteria, as well as subjective perception by human viewer.

Acknowledgements The authors would thank National Polytechnic Institute of Mexico and CONACYT (project 8159) for their support to realize this work.

References 1. Schulte, S., Morillas, S., Gregori, V., Kerre, E.: A New Fuzzy Color Correlated Impulse Noise Reduction Method Trans. on Image Proc. 16(10), 2565–2575 (2007) 2. Plataniotis, K.N., Androutsos, D., Vinayagamoorthy, S., Venetsanopoulos, A.N.: Color Image Processing Using Adaptive Multichannel Filters. IEEE Transactions on Image Processing 6(7), 933–949 (1997) 3. Ponomaryov, V.I., Gallegos-Funes, F.J., Rosales-Silva, A.: Real-time color imaging based on RM-Filters for impulsive noise reduction. Journal of Imaging Science and Technology 49(3), 205–219 (2005) 4. Trahanias, P.E., Venetsanopoulos, A.N.: Vector Directional Filters. A new class of multichannel image processing Filters. IEEE Trans. on Image Processing 2, 528–534 (1993) 5. Lukac, R., Smolka, B., Plataniotis, K.N., Venetsanopoulos, A.N.: Selection Weighted Vector Directional Filters. Comput. Vision and Image Understanding 94, 140–167 (2004) 6. Smolka, B., Lukac, R., Chydzinski, A., Plataniotis, K.N., Wojciechowski, W.: Fast Adaptive Similarity Based Impulsive Noise Reduction Filter. Real-Time Imaging 9(4), 261–276 (2003) 7. Yin, H.B., Fang, X.Z., Wei, Z., Yang, X.K.: An Improved Motion-Compensated 3-D LLMMSE Filter With Spatio–Temporal Adaptive Filtering Support. IEEE Trans. on Circuits and Syst. for Video Techn. 17(12), 1714–1727 (2007)


221

8. Varghese, G., Wang, Z.: Video Denoising using a Spatiotemporal Statistical Model of Wavelet Coefficient. In: Proc. of the IEEE ICASSP Int. Conf., pp. 1257–1260 (2005) 9. Rusanovskyy, D., Dabov, K., Egiazarian, K.: Moving-Window Varying Size 3D Transform-Based Video Denoising. In: Proc. of IEEE Int. Conf. VPQM 2006, Scottdale, USA, pp. 1–4 (2006) 10. Protter, M., Elad, M.: Image Sequence Denoising via Sparse and Redundant Representations. IEEE Trans. on Image Procces 18(1), 27–35 (2007) 11. Sen, D., Swamy, M.N.S., Ahmad, M.O.: Computationally fast techniques to reduce AWGN and speckle in videos. IET Image Process 1(4), 319–334 (2007) 12. Ghazal, M., Amer, A., Ghrayeb, A.: A Real-Time Technique for Spatio–Temporal Video Noise Estimation. IEEE Trans. on Circuits and Syst. For Video Techn. 17(12), 1690–1699 (2007) 13. Guo, L., Au, O.C., Ma, M., Liang, Z.: Temporal Video Denoising Based on Multihypothesis Motion Compensation. IEEE Trans. on Image Proc. (2009) 14. Jin, F., Fieguth, P., Winger, L.: Wavelet Video Denoising with Regularized Multiresolution Motion Estimation. EURASIP Journal on Applied Signal Processing, Art. ID 72705 1–11 (2006) 15. Mélange, T., Nachtegael, M., Kerre, E.E., Zlokolica, V., Schulte, S., De Witte, V., Pižurica, A., Philips, W.: Video Denoising by Fuzzy Motion and Details Adaptive Averaging. Journal of Electron. Imaging 17 (2008) 0430051-19 16. Ponomaryov, V.: Real-time 2D-3D filtering using order statistics based algorithms. Journal of Real-Time Image Processing 1(3), 173–194 (2007) 17. Zlokolica, V., Philips, W., Van De Ville, D.: A new non-linear filter for video processing. In: Proc. of the third IEEE Benelux Signal Processing Symposium (SPS-2002), Leuven, Belgium, pp. 221–224 (2002) 18. Ponomaryov, V., Rosales-Silva, A., Golikov, V.: Adaptive and vector directional processing applied to video colour images. Electronics Letters 42(11), 623–624 (2006) 19. Schulte, S., De Witte, V., Nachtegael, M., Van del Weken, D., Kerre, E.: Fuzzy two-step filter for impulse noise reduction from color images. IEEE Trans. Image Processing 15(11), 3567–3578 (2006) 20. Zlokolica, V., Schulte, S., Pizurica, A., Philips, W., Kerre, E.: Fuzzy logic recursive motion detection and denoising of video sequences. Journal of Electronic Imaging 15(2), 23008 (2006) 21. Bovik, A.: Handbook of Image and Video Processing. Academic Press, San Diego (2000) 22. Prat, W.K.: Digital Image Processing, 2nd edn. Wiley, New York (1991) 23. Plataniotis, K.N., Venetsanopoulos, A.N.: Color Image Processing and Applications. Springer, Berlin (2000)