Blotches detection

,)  
 ∀ ∈  ,ĥ ( )   
 , ,
  , 
and   . (3) 
 −  −, 
       ̌ , ,
 ( , )( )  ,  ĥ( , ) ( ) , 
 Since most of the reported statistical  tests require that analyzed  data be normally 
distributed, the set is firstly transformed by using the Box-Cox 
 −, −,
  (,)
transformation [9].  This transformation ℎ  give(, ) rise to the set 
 −, −,
  ̃(,)
normally distributed. Then, in order to locate the outliers within ,  itℎ is possible(,  to) 
apply one statistical test among the ones reported [10-11]. In this work, we− ,retain the Minimum 
 
52 
 Blotches detection 
Covariance Determinant (MCD) test for its efficiency and relatively low computational 
complexity [10]. The MCD test provides a set of a typical values of the illumination 
 −,(k) (k-1)
coefficient that are asssociated to candidate blocks in Aj and Aj and are more susceptible to 
  (k)
be blotched. The same procedure is carried out to detect suspicious blocks between Aj and 
 (k+1)
Aj . Only the blocks that are judged as suspicious in both the backward and the forward 
 (k-1) (k) (k+1) (k)
directions (by considering respectively the pairs (Aj , Aj ) and (Aj , Aj ) are retained for 
the final blotch detection step since blotches are considered as illumination variations occuring 
in both directions. 
2.2. Blotch detection 
 Given the positions of the suspicious regions at different resolution levels, it is necessary 
to deduce the positions of the retained candidate regions at the initial resolution level. Since 
the goal behind resorting to a multiscale analysis is to handle the different sizes of the 
blotches, we consider a block at the initial resolution level as suspicious if it has been judged 
as such at, at least one resolution level initial resolution level. Since the goal behind resorting 
to a multiscale analysis is to handle the different sizes of the blotches, we consider a block at 
the initial resolution level as suspicious if it has been judged as such at, at least one resolution 
level 
 The final step consists of detecting the corrupted pixels in each candidate region at the 
 ,∀1 ≤  ≤ .
initial resolution of . For this purpose, one of the reported heuristic detectors as the SDIa, 
the ROD, the SROD, or the AR based detectors is used between suspicious blocks in and 
their homologous in the motion compensated refrence frames. 
  
2.3. Blotch removal 
 We assume that the spots are identified and detected correctly in the previous step at this 
stage is a binary table, where the mottled pixel is color coded white and the rest black. This 
binary image is used to guide the recovery process. To remove blotches are detected, an 
approach based on the proposed inpainting. The performance of the solution is assessed 
subjectively or using some full reference image quality classical metrics like PSNR. In this 
work, we use hierarchical diagram similar to [12] and strategic global optimization. This 
approach introduces an effective performance and high quality output. 
 (a) A blotched image (b) bloctch detection map 
 (c) The initial priority map 
 Figure 1. An example of the priority map 
 53 
 Nguyen Thi Quynh Hoa 
 Firstly, a Gaussian pyramid was built from the original image to create hierarchical 
diagrams of input images. A set of images with different levels of detail can be created with 
 as the input or original image. Number of pyramid levels depending on the original size 
of the image and the minimum resolution allowed. Then, a strategy used to fill in missing areas 
with  the lowest resolution, . Athigher resolutions, inpainting problem are modeled as a 
graph optimization labels which help to show the selected label for each pixel unknown. It can 
be determined by optimizing  the energy function optimization algorithm by global, multi-
labeled graph cut [13]. A description of the algorithm removes spots is given in Figure 1. 
2.3.1. Correction of lowest resolution frame 
 At lowest resolution, a template-based approach is used to remove the blob by using 
priority based on the window and choose the patch. Recommended removal methods work 
repeated as follows: 
 - Detect spots: Identify spots and their boundaries based on the binary image. If no pixels 
in the spot, the algorithm is terminated due spots completely erased. 
 - Define priorities edit: Calculator and randomly select a pixel p with the highest priority 
and determines a patch, P, gathered at p. In this work, we used the model of the most common 
priorities proposed in [14, 15] Combine the patch: Find a patch is not blurred, , similar to 
with mean squared error of pixel squares is not blurred. 
  
 - Blotch removal: Fill in missing information in patch . 
 - Information update: Update the binary mask image and return the step 1. 
 
 Correction priority: So good priorities is essential because it directly affects the quality of 
the output. In this work, we used the model of the most common priorities proposed in [15] and 
it is defined as in Equation 4 
 (4) 
where C(p) and D(p) denote confidence and data terms, respectively and they are defined as follows: 
  
 (5) 
 ∑∩ 
   || (6) 
 
 During the initialization process, the values  of+ reliability, C(p) is set to 0 for each pixel in 
blotched and 1 for others. is very small positive value, which ensures that terminology is 
always dominate the other. and are two positive eigenvalues ( ≥ ) determine the 
local changes of pixel intensities∈ in each window Wp, gathered at p and is characterized by the 
following matrix:  2  2
  2   (7) 
   
  
   ∑  ,      2
where is a Gaussian window function calculates  a total weight. The term data including 
structural features depends on the variation of two separate values. Figure 1 illustrates a 
 
preferred map said pixels will be restored first. 
 Patch selection: The next step in the optimization algorithm is searching for patches 
matching the blurred area. In our work, a suitable patch is determined using similar 
54 
 Blotches detection 
measurements on all pixels not faded in patches. Therefore, it is determined based on the 
difference of color and gradient as below: 
 (8) 
 2 2
where I , I are the corresponding CIELab vectors;   represent the image gradient 
 p q (Ψ,Ψ)  ∑ ( ) (∇  ∇) 
vectors. is a user defined weight balancing the two terms. In our experiments, we used 
  
 . The patch with minimal distance to the source patch,∇ ,∇  , is the chosen one and given 
below:   
 
0.5  (9) 
2.3.2. Correction for higher resolution frame 
 ̂  ∈Φ{(Ψ,Ψ)}
 When finished creating images lowest resolution, compensation map is generated and 
used to reconstruct a higher resolution. Map offset determine the relationship between the pixel 
needs to be removed and the pixels in the region are not blurred are given below 
 (10) 
 Compensation map obtained from the lower∆ ,∆resolution,∈Ω is interpolated to higher resolution. 
   ,
However, the output image is derived directly from this map which contains annoying artifacts 
affect the nature of the images obtained. The authors of [16] the data and smoothness to refine 
compensation map. Energy function is defined as follows: 
 (11) 
 −∗ ∗     −, − −, − 2
 (, ) Ḃ ′ ′ ∈ ∈   (,)     (,)
 Ḃ   , , ∑ , ( ) ℎ Ǎ   ( )  
 (12) 
   ∑ () 1  ∑,∈ , 
where is a data term related to external requirements and is a smoothness term defined 
over a set of neighbouring pixels, N B. The parameter a is a user defined weight balancing the 
twoterms settoα=0.5inourexperiment.The detail of the data term and smoothness term are 
given by equation (12), (13): 
 (13) 
 ∞+∆,+∆∈Ω
whereβandγareweightsbalancingthesetwoterms,settoβ=l,γ=2inourexperiment.There 
    
are many approaches for minimizing this function. In the proposed method, a global 
optimization based on graph-cuts is developed because of the efficient implementation and the 
available source code. The alpha parameter is to determine the importance, or the balance 
between two operands. In this case, Ed and Es are chosen as 0.5 because these two operands are 
considered to have the same role, so they are equal. 
2.4. Experiment results 
 This section is dedicated to the performance evaluation of the proposed framework. 
 The performance of blotch detector scheme is evaluated in three round of simulation. The 
first round shows the benefits of versatile analysis versus monochrome case as in [7]. The 
second round presents a visual assessment using SROD detection in locating the damaged area 
candidates. And the last round is to evaluate the performance in comparison with the proposal in [17]. 
 (14) 
  =
 A sequence of thirteen frames,  has been used( for) +testing. Frames  are 720 × 576 pixels and 
encoded, which shows some typical frames to provide a visual demonstration of our proposal. 
 55 
 Nguyen Thi Quynh Hoa 
The first line contains some corrupted frames and the blotch detection is detected and 
represented by binary mask frames of the second line. The blotch removal frames are shown in 
the last line. In order to evaluate of performance the blotch removal algorithm, we compared 
with some state-of-the-art inpainting methods such as A. Criminisi et al. [14], Wu et al. [18] and 
Dang et al. [15]. The image quality of the proposed method has been objective evaluation with 
unclear quality indicators [19] and shown in Table 1. The higher the result are, the better the 
quality of the propose approach is. 
 Table 1. The blotch removal quality metric 
 Method 
 Our proposal [15] [14] [18] 
 Frame ID 
 18 0.2159 0.199 0.2118 0.2182 
 20 0.1987 0.2 0.2022 0.2032 
 32 0.1178 0.1105 0.1234 0.1095 
 37 0.1391 0.1248 0.1286 0.1321 
 46 0.1078 0.1075 0.1102 0.1135 
 50 0.1735 0.1724 0.1705 0.1773 
 68 0.1711 0.1591 0.1577 0.1727 
 85 0.1928 0.182 0.1825 0.1844 
 94 0.1934 0.1934 0.1946 0.1939 
 102 0.2382 0.2436 0.242 0.2367 
 103 0.3363 0.3456 0.3422 0.3227 
 111 0.2382 0.2436 0.242 0.2367 
 118 0.1429 0.1399 0.1395 0.1418 
3. Conclusions 
 The article has proposed a framework to detect and restore spots. The framework consists 
of two main stages: detection and recovery. For spot detection, a simple rank order difference 
(SROD) detector is proposed. Next, spots will be restored based on improved dimming printing 
techniques. The test results show an outstanding performance and expected results. The overall 
execution time of the schema is completely acceptable. In the future, we will improve and 
upgrade the framework to make it better with larger resolution videos. 
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