562 J.Comput.Sci.Technol.,May 2009,Vol.24.No.3 Zero Level 0 goes up sharply compared with Fig.1(b),and that of .8 pores begins to attenuate.Finally,in Fig.1(d).while the NLE of pores drastically decreases,the NLE of the 0.6 300 distractions continues to grow.At this level,the dif- 0.4 50 ferentiation between pores and distractions are justi- 400 0.2 fied.According to NLE behaviors from the first to third 80 130180230280 level,all pixels in the image fall into three categories. 50 0.0 1)Pixels with NLE relatively large at all levels, (a) 0 mainly relate to some sharp imperfections,e.g.,pixels One Level Two Level in purple rectangles in Figs.1(b)~1(d). 2)Pixels with NLE from small to large mainly re- late to gently rolling distractions,e.g.,pixels in green 0.6 0.6 rectangles in Figs.1(b)1(d). 300 0.4 3)Pixels with NLE from large to small mainly relate 350 0.4 to skin details,e.g.,pixels in yellow rectangles in Figs. 02 0.2 1(b)1(d). 130180230280 50 80 10 130180230280 As the residual image of EMD is nearly constant. meaning that all the oscillatory modes of original im- g age have been picked out,it is reasonable to use NLE IPD of all IMFs to define pixels'imperfect degree.We de- fine an imperfect degree for every pixel z of I as the weighted sum of NLE of all IMF levels and their differ- ences between adjacent levels: 00 NLEk(), k=0 130180230280 K-1 B=>(NLEk()-NLEk()) k=0 Fig.1.(f)is an image patch cropped from (a)(green rectangle). IPD(z)=Xea+(1-)e-8. (6) (b)~(d)are the first,second and third NLE (=0,1,2)of (f). In the above formula,the first term rewards pixels Pixels in purple,green and yellow rectangle correspond to cases in case 1),and the second term punishes those pixels 1),2),3)respectively.(e)IPD of(f).In (e)and (f),the corre- in case 3)and rewards pixels in case 2).A is a weight spondences between pixels in IPD and the image are marked out to balance two terms and usually set between 0.2~0.5 with different colors The IPD defined as above quantitatively measures 4.2 Analyze the Normalized Local Property the imperfect degree of every pixel.The larger the IPD is,the more imperfect the facial skin is.As seen from Having extracted the NLE of every pixel at different Figs.1(e),1(f),while pixels with large IPD exactly cor- levels,in this subsection,we make an analysis of NLE respond to distractions as we have marked with green and then propose a function of every pixel to charac- and purple rectangles,pixels with small IPD directly re- terize the energy distribution of the facial image. late to image regions with fine scale details,see yellow From an overall view of Figs.1(b)~1(d),we can rectangles.The accurate correspondences show that clearly see:the pores and imperfections (bumps,scars) our IPD indeed delivers an intuitive measure of degree exhibit different characteristics from the first level to of visual imperfection. the third level.For the former,NLE decreases,and for 4.3 Adjust the Coefficient the latter,NLE increases.More specifically,in Fig.1(b) the NLE of the first level,both the pores and bumps all Once the IPD for every pixel has been calculated, have high levels of energy,especially the pores and some the next step is to adjust the coefficients of every IMF distractions.Note that,the part with most highest to meet our goal based on the hints of IPD.It is recog- NLE is on the upper right in Fig.1(f)where the pores nized that pixels with large IPD generally correspond can be clearly seen.In Fig.1(c),the NLE of distractions to imperfect skin such as large bumps which we intend562 J. Comput. Sci. & Technol., May 2009, Vol.24, No.3 Fig.1. (f) is an image patch cropped from (a) (green rectangle). (b)∼(d) are the first, second and third NLE (k = 0, 1, 2) of (f). Pixels in purple, green and yellow rectangle correspond to cases 1), 2), 3) respectively. (e) IPD of (f). In (e) and (f), the corre￾spondences between pixels in IPD and the image are marked out with different colors. 4.2 Analyze the Normalized Local Property Having extracted the NLE of every pixel at different levels, in this subsection, we make an analysis of NLE, and then propose a function of every pixel to charac￾terize the energy distribution of the facial image. From an overall view of Figs. 1(b)∼1(d), we can clearly see: the pores and imperfections (bumps, scars) exhibit different characteristics from the first level to the third level. For the former, NLE decreases, and for the latter, NLE increases. More specifically, in Fig.1(b), the NLE of the first level, both the pores and bumps all have high levels of energy, especially the pores and some distractions. Note that, the part with most highest NLE is on the upper right in Fig.1(f) where the pores can be clearly seen. In Fig.1(c), the NLE of distractions goes up sharply compared with Fig.1(b), and that of pores begins to attenuate. Finally, in Fig.1(d), while the NLE of pores drastically decreases, the NLE of the distractions continues to grow. At this level, the dif￾ferentiation between pores and distractions are justi- fied. According to NLE behaviors from the first to third level, all pixels in the image fall into three categories. 1) Pixels with NLE relatively large at all levels, mainly relate to some sharp imperfections, e.g., pixels in purple rectangles in Figs. 1(b)∼1(d). 2) Pixels with NLE from small to large mainly re￾late to gently rolling distractions, e.g., pixels in green rectangles in Figs. 1(b)∼1(d). 3) Pixels with NLE from large to small mainly relate to skin details, e.g., pixels in yellow rectangles in Figs. 1(b)∼1(d). As the residual image of EMD is nearly constant, meaning that all the oscillatory modes of original im￾age have been picked out, it is reasonable to use NLE of all IMFs to define pixels’ imperfect degree. We de- fine an imperfect degree for every pixel x of I as the weighted sum of NLE of all IMF levels and their differ￾ences between adjacent levels: α = X K k=0 NLEk(x), β = K X−1 k=0 (NLEk(x) − NLEk+1(x)), IPD(x) = λeα + (1 − λ)e −β . (6) In the above formula, the first term rewards pixels in case 1), and the second term punishes those pixels in case 3) and rewards pixels in case 2). λ is a weight to balance two terms and usually set between 0.2∼0.5. The IPD defined as above quantitatively measures the imperfect degree of every pixel. The larger the IPD is, the more imperfect the facial skin is. As seen from Figs. 1(e), 1(f), while pixels with large IPD exactly cor￾respond to distractions as we have marked with green and purple rectangles, pixels with small IPD directly re￾late to image regions with fine scale details, see yellow rectangles. The accurate correspondences show that our IPD indeed delivers an intuitive measure of degree of visual imperfection. 4.3 Adjust the Coefficient Once the IPD for every pixel has been calculated, the next step is to adjust the coefficients of every IMF to meet our goal based on the hints of IPD. It is recog￾nized that pixels with large IPD generally correspond to imperfect skin such as large bumps which we intend