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Frontiers in Pathology and Genetics (FPG) Volume 2, 2014
Facial Pores in Melanin Layer and Genetic Algorithms for Human Face Characterization Carlos Villegas-Quezada*1, Joan Climent2 Engineering Department, Universidad Iberoamericana, Mexico City; Computer Engineering School, Universitat Politecnica de Catalunya, Barcelona, Spain carlos.villegas@ibero.mx; 2juan.climent@upc.es
*1
Abstract The characterization of a face is a vital element for its computational representation used for several applications such as: medical, dermatology, cosmetology, facial recognition, etc. Often, characterization has been performed by geometrical points, eigenface, binary patterns. This paper proposes two novelty methods for the characterization of a face. First of all, the main facial pores of a face are identified from the melanin layer of the skin by using a digital image of the face. Once the pores have been identified, nine characteristics are obtained from each of them. Such characteristics are considered as the dependant variable and the rest of them as the independent variables, in order to obtain a multivariable polynomial as an approximant of the point series. The solution of this polynomial is combinatorially hard and very difficult to tackle using traditional methods. Combinatory Optimization process is required for which an Genetic Algorithm is used to obtain and select the best coefficients and maximum degree to configure the approximation polynomial and characterize the face in an adequate way, allowing the polynomial to be used in more complex application that pattern recognition. Keywords Facial Pore Identification; Melanin Layer from RGB Images; Genetic Algorithms; Face Characterization
Introduction Feature extraction from a human face is a vital element for data preparation for face characterization and it is used for several applications such as face detection, face recognition, medical applications and cosmetics among others. For extracting human face features geometrical elements, principal components analysis (PCA), local binary patterns (LBP), texture appearance models, skin characteristics, etc. has been used. The skin pores is an element that has been recently under research as a unique feature. From a genetic point of view, the diverse elements that configure the skin are: colour, texture, pores, etc. They are formed from the embryo. Specifically, the skin is the juxtaposition of two main embryological elements: epidermis 12
prospective, which is located at the surface of the early gastrula; and the prospective mesoderm which is brought in contact with inner surface of the epidermis during gastrulation [McGrath, Eady and Pope, 2004]. Therefore, it is considered that the number of skin pores of each human being, its configuration, their measurements, is present a unique relationship for each human. Some features may vary due to weather, age and environmental elements. Overall, the composition and texture of the skin and the pores are distinctive elements in each individual. The process of characterization of an individual from different features of his face is rather interesting from the computer point of view. The difficulty of this problem stems from the fact that faces appear to be roughly alike and the differences between them are quite subtle. The characterization of a face is a vital element for complex pattern recognition processes required for several application such as: medical, cosmetology, face recognition, etc. The frontal face images form a very dense cluster in image space which makes it virtually impossible for traditional pattern recognition techniques to accurately discriminate among them. [McGrath, Eady and Pope, 2004]. This paper use facial pores as a feature, from which a face is characterized. From a machine learning point of view, the characterization of a face can be done based on the function-approximation paradigm. Allowing the characterization to be used in several pattern recognition application, using what it has specificall been named as supervised learning. Supervised learning attempts to learn đ?‘“đ?‘“ by examples. One observes the system under study both, inputs and outputs, and assembles a training set of observations. In the approach it is possible formulate from the perspective of function approximation. Where the data pairs (đ?‘Ľđ?‘Ľđ?‘–đ?‘– , đ?‘Śđ?‘Śđ?‘–đ?‘– ) are viewed as points in a (đ?‘?đ?‘? + 1)-dimensional Euclidean space. The goal is to obtain a useful
Frontiers in Pathology and Genetics (FPG) Volume 2, 2014
approximation to đ?‘“đ?‘“(đ?‘Ľđ?‘Ľ) for all đ?‘Ľđ?‘Ľ. Using a multivariate approximant to be solved with a combinatiorail optimization problem focus by a genetic algorithm will allow to obtain a possible way to characterize a human face from a training data set without overtraining risks. The problem is to find the proper form of the approximant as well as the adequate number and value of the coefficients of the multivariate polynomial. Arbitrarily, a polynomial form as an approximant is selected and, thereafter, an eclectic genetic algorithm [kuri] is used to find the coefficients and the degree of the approximation polynomials which minimize the fitness error for the data is used. These data set matrix of ( đ?‘›đ?‘› − đ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘&#x;đ?‘&#x;đ?‘&#x;đ?‘&#x;đ?‘&#x;đ?‘&#x; Ă— đ?‘?đ?‘? − đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??š ) are used for configuring the multivariate polynomial and are used to characterize the faces which form the training set. Identification of Skin Pores in Melanin Layer Marcelo Malpighi, Bolonia University professor, was the first one who studied the pores in 1686. He studied the pores of the fingers as well as the crest surfaces and pore morphology, using a microscope (McRoberts 2011). Later on, in 1823, Johannes Purkinje wrote a thesis about papillary crests and pores. Performing microscopic studies of the epidermis and proposed the possibility of identification of people from skin pores (Cummins and Wright 1940). However, it wasn’t until the beginning of the 20th Century when pores were studied in a much more scientific and practical way. In 1912, Professor Edmund Locard from Lyon University and founder of the criminalistics Lab of Lyon published a work name “Poroscopyâ€?, which established the scrutiny of sweat pores for identification system as complementary of the already known dactyloscopy (McRoberts 2011; Ashbaugh 1999). The purpose was not substituting, but complementing those that didn’t had enough crests in their fingerprints for identification. Locard, found that the pores presented elliptical, oval, squared, rhomboidal and triangular forms. Locard’s method took morphology, situation, dimensions and existing pore numbers on the papillary crests of the fingertips as a base. Locard in 1924 (McRoberts 2011), Ashbaugh (Champod 2009) and Busselaar (2011), showed that only by using 20 to 40 pores would be enough for establishing the identity of a person with their fingerprints. As stated, ridge characteristics, like pores, are permanent, immutable, and unique (Jain, Chen and Demirkus 2007). However, in Locard’s Era, it was very difficult to perform detailed studies of the pores
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due to lack of adequate equipment. To make pore study possible, it is necessary to use high-resolution sensors in order to visualize the pores in an optimal way and extract fine and detailed features (Level 3 features). In recent years, pore research has been done again, specially its application on fingerprint identification. Jain et al. (2007) researched about the use of pores and ridges using level 3 features for fingerprint matching. De Assis and Nilceu (2013), proposed a method based on pore identification to identify fingerprints when only fragments are available. Fingerprint pore identification using Scale Invariant feature transform and Fusion Techniques was proposed by Malathi and Meena (2012). Zhao et al. (2010) proposed a Dynamic anisotropic method (DAPM) which extracted the pores according to local ridge characteristics, as well as their orientation and frequency. Overall, the methods that extract pores from fingerprints use skeletonizationbased pore extraction and matching algorithms techniques or a combination of traditional image processing filters. Human face pore identification has been mostly used for dermatological and cosmetics applications. In dermatology, pores are studied in delimited face sections. It is necessary to use magnifying glasses, dermatoscope, spectrometers or macroscopic photography taken from a short distance from the face. For beauty and cosmetics applications, special image processing devices, taking three or more images in order to detect certain features in several face areas, including pores are used. However, to achieve that, special equipment was used (dermatoscope, spectrometer) or photography with great zooming. Pore Identification In Human Face Skin is the outermost tissue of the body. It has an area of approximately 16,000 đ?‘?đ?‘?đ?‘?đ?‘?2 and has a very complex and multi-layered structure. As skin is very complex, a hierarchical taxonomy can be obtained. Such taxonomy is based on physiology, anatomy, optical, and visual properties of the components of skin, configured in six layers (Igarashi, Nishino and Nyar 2005). Those six layers contain, from cellular level elements (first layer – Micro Scale) to visible body parts such as face and arms (layer 6 – Macro Scale). The pores, along with wrinkles, moles and freckles are describes as “skin featuresâ€? (layer 4 – Meso Scale). Some elements from layer 4 are visible to the human eye, their visual properties are mainly determined by
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the optical phenomena which are inducted by very fine components (from micro taxonomy), which are subjacent to layer 4. Pores Nd Skin Surface Pattern A characteristic pattern is found in the surface of the skin due to the intersection lines of the skin. Such fine lines cross each other and form several shapes: squares, rectangles, triangles and trapezoids. Moreover, among those shapes are the pores conformed by the holes of the glands and hair follicles. The pores and skin surface lines, provide to each region of the body a unique topography and are unique for each individual. Such unique topography is established before birth and complements other lines appearing throughout life, such as wrinkles (Gherardi 2007). The analysis and pore quantification, especially in the face, has been done in dermatology processes, and recently in cosmetic processes (Francois, Maudet and McDaniel 2009; Demirli et al. 2007). Pores are found in different shapes (not only rounded) and sizes. Their size varies in average, from 50 đ?œ‡đ?œ‡đ?œ‡đ?œ‡ to 500 đ?œ‡đ?œ‡đ?œ‡đ?œ‡, but very specialized devices and analysis is required to observe them. Pores with a size of 100 đ?œ‡đ?œ‡đ?œ‡đ?œ‡ , represent the smallest size pore that can be observed by the human eye using a dermatoscope. Pores of 250 đ?œ‡đ?œ‡đ?œ‡đ?œ‡ are the ones that can be observed from images of digital cameras with controlled conditions and depending on the density of the pixels. The pores of 500 đ?œ‡đ?œ‡đ?œ‡đ?œ‡ are the ones that can be observed at simple sight and from high-resolution colour images of digital cameras in normal conditions of light (not controlled) at a larger distance [19]. An estimate number of approximately 30,000 pores are in the human face. In average, from the possible 30,00 pores that can be found in the human face, only 3,000 to 4,000 of them can be detected by images from digital cameras with non-controlled conditions. Pores are sweat gland terminations and according to expert forensic and genetic studies, their distribution is unique for each individual, constant throughout life; therefore pores are unique, permanent and invariant and can be used as elements that allow identification and recognition. However, its detection specially by using image digital cameras depends on the light that reflects on the skin. Pores And Light Reflection On Skin Layers From an optics perspective, human skin may be 14
Frontiers in Pathology and Genetics (FPG) Volume 2, 2014
described in terms of two different layers, absorption and scattering, the top layer reflects dermis collagens (Anderson and Parrish 1981; Dawson and Barker 1980; Wan, Anderson and Parrish 1981). Absorption in the skin over the visible spectrum is caused by two types of chromophores: melanin and hemoglobin; scattering is caused by fiber, cells or cellular organelles (Igarashi, Nishino and Nayar 2005). The primary chromophere absorption light from the infrared spectra near the skin is hemoglobin, which is located in the dermis. Epidermis absorption is dominated by melanin, which is a polymer constructed by the condensation of tyrosine molecules, which have large absorption spectra in short frequency wavelength. Part of the incident light is reflected at the surface of the skin, the rest of light penetrates into the skin layers. In the epidermal layer the light is absorbed by melanin (very little scattering), in dermal layer the light is scattered multiple times and absorbed by hemoglobin. Melanin absorption depends on the quantity of melanosomes per unit volume in the epidermis. Melanin provides the type of color of skin. According to Jacques (1998), around 1.6% to 6.3% of the epidermis volume is occupied by melanosomes in adults with light skin; for those with the skin moderately pigmented, the volume is around 11 to 16%. For adults with dark skin, the volume of melanosomes is between 18% and 43%. The above simplification of the skin optical transportation mechanism, allows the development of a three layer optical model (two uniform media layers –epidermis and dermis- over an ideal diffusive surface). This simplified skin reflection theory can be represented as (Sun and Smith 2013): 2 2 đ?‘…đ?‘…đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ = đ?‘‡đ?‘‡đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’ Ă— đ?‘‡đ?‘‡đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘ Ă— đ?‘…đ?‘…đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘
(1)
where đ?‘‡đ?‘‡đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’ and đ?‘‡đ?‘‡đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘ are the transmittance coefficients of the simulated epidermis and dermis layers, and đ?‘…đ?‘…đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘ is the diffusive reflectance coefficient of the deepest fat layer, and the transmittance through transparent layer satisfies the Lambert-Beer law: đ?‘‡đ?‘‡đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’ = đ?‘’đ?‘’ −đ?œ‡đ?œ‡ đ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘š đ?‘™đ?‘™đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’ đ?‘?đ?‘? đ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘š
đ?‘‡đ?‘‡đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘ = đ?‘’đ?‘’ −đ?œ‡đ?œ‡ â„Ž đ?‘’đ?‘’đ?‘’đ?‘’ đ?‘™đ?‘™đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘ đ?‘?đ?‘? â„Ž đ?‘’đ?‘’đ?‘’đ?‘’
(2) (3)
Where đ?œ‡đ?œ‡đ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘š and đ?œ‡đ?œ‡â„Žđ?‘’đ?‘’đ?‘’đ?‘’ are the wavelength absorptive coefficients of melanin and hemoglobin; đ?‘™đ?‘™đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’ and đ?‘™đ?‘™đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘ are the length of light paths within epidermis and dermis; and đ?‘?đ?‘?đ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘š , đ?‘?đ?‘?â„Žđ?‘’đ?‘’đ?‘’đ?‘’ are the concentrations of melanin and hemoglobin respectively. Several studies, have found that wavelength (đ?œ†đ?œ†) depend on the coefficient of absorption of melamine in the epidermis.
Frontiers in Pathology and Genetics (FPG) Volume 2, 2014
Equation (4) is another formula describing the coefficient of absorption in melamine (đ?œ‡đ?œ‡đ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘š ) described by Jacques (1998): đ?œ‡đ?œ‡đ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘š = 6.6 Ă— 1011 (đ?œ†đ?œ†âˆ’3.33 )
(4)
The Skin And Its Computational Representtion Reflection on human skin presents several applications; the main one is the automatic localization of humans from colour images. This has been used in areas such as recognition and identification, medicine, cosmetics, games, picture, etc. The most common schema is the one based on the conventional method named RGB (Red-Green-Blue). However, it has been found by several studies that such model includes various colour distortions and information loss. Most photographic cameras use tri-colour system RGB presenting a very common limitation, which is the inability for obtaining the reflecting spectrum of the image being photographed. Illumination and luminosity are defined slightly different as they depend in one another, therefore they can be referred together as one, with the function of responding to the flow of light incident to the brightness. As it has been mentioned in previous section, skin has many layers. From the point of view of layer modelling and their interaction with the reflection of light, models with seven, six, five and three layers have been proposed (Zhang et al. 2005; Andersen and Bjerring 1990; Douven and Lucassen 2000; Meglinski et al. 2008). However, in recent years, especially for computer process for medical and dermatologic applications, a model including two layers has been proposed, describing the epidermis as the first layer and dermis as the second layer (Mantis and Zonios 2009). In this model the upper layer of skin (epidermis) weakens the dominant light from melanin absorption. On the other hand blood vessels located under the epidermis, do not help light to weaken. Light weakening in epidermis occurs because of the absorption of melanin, and it can be described using de Beer’s Law (Born and Wolf 1999): đ??´đ??´đ?‘’đ?‘’ (đ?œ†đ?œ†) = đ?‘’đ?‘’ −đ?œ‡đ?œ‡ đ?‘’đ?‘’ (đ?œ†đ?œ†)đ?‘‘đ?‘‘ = đ?‘’đ?‘’ −đ?‘Łđ?‘Łđ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘š đ?œ‡đ?œ‡ đ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘š (đ?œ†đ?œ†)đ?‘‘đ?‘‘
(5)
Where đ??´đ??´đ?‘’đ?‘’ represents light weakening at the epidermis, đ?œ‡đ?œ‡đ?‘’đ?‘’ is the coefficient of absorption of the epidermis, đ?‘‘đ?‘‘ is the epidermis thickness. The equation can be rewritten considering that the coefficient of absorption of the epidermis is the product of the concentration of melanin (đ?‘Łđ?‘Łđ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘š ) multiplied by the coefficient of absorption of melanin described before. (đ?œ‡đ?œ‡đ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘š ).
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Methods To Identify Skin Layers From RGB Images Color representation of skin in a determined colour space (RGB, CIElab, etc) is not a genuine physical quantity, it is an abstract derive of the function of the human visual system. The color of skin is mainly determined by the absorption and scattering of skin derived from the characteristics of melanin, hemoglobin and carotene. Several studies have been developed in past years, to evaluate and obtain the main characteristics of the main layers of the skin in a non-invasive way; especially from traditional digital image (RGB Systems), without having to use specialized devices for skin analysis. These studies are mainly focused in obtaining melanin and hemoglobin layers from skin. Among the most important research to obtain melanin and hemoglobin layers from colour spaces, are: Tsumura et al. (2003), proposal to use independent components analysis (ICA) over a RGB image to split the average concentrations of melanin and hemoglobin. Tsumura’s method has also been used to observe additional factor to reduce external effects on skin, such as shadows (Madooei, Drew and Sadeghi 2012). It has also been proposed a complex multi-layer method, using Kubelka-Munk theory to extract melanin, blood and collagen from the epidermal and dermis layers (Claridge et al. 2003). On the other hand, Yamamoto (2008) has applied a much more simpler method, consisting of 3 layers, based on Lambert’s Law. This method discriminates melanin and hemoglobin concentrations. Another method proposes the extraction of chromopheres using bilateral decomposition, allowing removing external effects of images (Zhao and Zerubia 2013). This method is the one to be used in this work as part of pore identification of the face. In general, the extraction of the melanin and hemoglobin within skin surface from photographs across a large area is desired in several applications, as compared to conventional spectrometer approaches working only over a limited and small skin area. Computer Model for identification of Facial Pores in Melanin Layer In this paper a novel automatic facial pore skin detection system is proposed. This procedure allows to locate human facial pores in color images taken by digital cameras (RGB) from melanin layer, without having to do a major zoom to the face. A description is made of the main methods used; the transformation
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suffered by a certain face from the original image until the obtaining of the facial pores is shown as an example. Images from PUT database are used (Kasinski, Florek and Schmidt 2008). Pre-Processing Of An Image The digital images used in this Project, obtained from PUT database, must pass through a pre-processing stage, consisting of the following parts: Face localization, Initial cut of the face, Eyes and mouth localization, Image equalization, Final cut of the face. All the software programming has been done in MATLAB (version 12), using several tools from the environment (Image processing Toolbox, Vision, Statistics). From a digital image as shown in fig. 1 (in this case an image from PUT database), the first step consists on identifying and locating the face in the image. The localization of the face uses Viola technique (Viola and Jones 2001; Tanaka 2012) to identify and obtain a rectangle, which frames the area of the face, as it can be observed in figure 1. Once the face has been identified, the next step is to localize the eyes (pink color rectangles) and mouth (blue rectangle), as it can be observed in fig. 1. Those elements will not be used in the process of identifying pores. Face will now suffer a cut to obtain the image with the fewer elements outside the face (green rectangle). The image is cut to reduce the number of pixels to be analysed. From this image the equalization and other preprocessing are performed. Later on, the rectangles found to locate the eyes and mouth are added with the purpose of having masks with the lowest possible size covering eyes and mouth (fig. 5). And have a larger skin area for the process of localizing pores.
FIG. 1. IMAGE ORIGINAL (FROM PUT DATABASE) AFTER PROCEDURE OF FACE LOCALIZATION (GREEN), AND IDENTIFICATION OF EYES (PINK), NOSE (YELLOW), AND MOUTH (BLUE).
Obtaining The Melanin Layer As it has been described in previous section, several
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researchers have found methods to separate from RGB images, melanin and hemoglobin. In this paper a combination of some of the techniques described are used and taking them on account an algorithm has been done which allows separating the melamine layer. The finding of this work is making the identification of the pores of the face more accurate from certain picture and moreover obtaining moles and face spots that the individual subject to the study may have. From the methods described for obtaining melanin, Tsumura’s (1999), is the one considered as the most accurate one, as it uses independent component analysis method (ICA), however it is relatively complex and requires more processing time. Especially if it is meant to obtain the melanin layer in every image of the face contained in the “training databaseâ€? in facial identification or recognition process. On the other hand, it is considered that the detail obtained from melanin is very useful, mainly for cosmetic or dermatological applications. Regarding the method to localize the pores in the face, it is not necessary to have as much accuracy as required for obtaining the melanin. One of the partial hypothesis presented in this work, proposes to obtain the melanin layer from RGB digital image, from this layer it would be much more easy and accurate to obtain the facial pores. In particular, considering that the picture has not been taken at a short distance from the face or using special devices for skin study. Tsumura’s ideas have been used as a foundation for other researchers, who have found from simulations and live experimenting, formulae and specific values for melanin and hemoglobin allowing melanin and hemoglobin layers to be obtained from RGB pictures. Therefore, in this project Liu and Zerubia’s proposal has been taken, with some modifications, to obtain a formula that applies to each RGB pixel of the image under analysis, in order to obtain its corresponding melanin and hemoglobin values. Skin layers form an intensity image in RGB channels can be expressed by (Zhao and Zerubia 2013): đ?‘&#x;đ?‘&#x; đ?‘&#x;đ?‘&#x; đ??źđ??źđ?‘&#x;đ?‘&#x;,đ?‘‘đ?‘‘đ?‘‘đ?‘‘ = đ?œ‡đ?œ‡đ?‘šđ?‘š đ?‘™đ?‘™đ?‘’đ?‘’đ?‘’đ?‘’ đ?‘?đ?‘?đ?‘šđ?‘š (đ?‘Ľđ?‘Ľ) + đ?œ€đ?œ€đ?‘Ľđ?‘Ľ đ?‘”đ?‘” đ?‘”đ?‘”
�� ��
đ??źđ??źđ?‘”đ?‘”,đ?‘‘đ?‘‘đ?‘‘đ?‘‘ = đ?œ‡đ?œ‡đ?‘šđ?‘š đ?‘™đ?‘™đ?‘’đ?‘’đ?‘’đ?‘’ đ?‘?đ?‘?đ?‘šđ?‘š (đ?‘Ľđ?‘Ľ) + đ?œ‡đ?œ‡â„Ž đ?‘™đ?‘™đ?‘‘đ?‘‘ đ?‘?đ?‘?â„Ž (đ?‘Ľđ?‘Ľ) + đ?œ€đ?œ€đ?‘Ľđ?‘Ľ đ?‘?đ?‘? đ?‘?đ?‘? đ?‘™đ?‘™đ?‘šđ?‘š đ?‘?đ?‘?đ?‘šđ?‘š (đ?‘Ľđ?‘Ľ) + đ?œ‡đ?œ‡â„Žđ?‘?đ?‘? đ?‘™đ?‘™â„Žđ?‘?đ?‘? đ?‘?đ?‘?â„Ž (đ?‘Ľđ?‘Ľ) + đ?œ€đ?œ€đ?‘Ľđ?‘Ľ đ??źđ??źđ?‘?đ?‘?,đ?‘‘đ?‘‘đ?‘‘đ?‘‘ = đ?œ‡đ?œ‡đ?‘šđ?‘š
(6) (7) (8)
Average melanin and hemoglobin values have been taken from several proposals (Jolivot, Benezeth and Marzani 2013; Zhao and Zerubia 2013; Kharkar and Ratnaparkhe 2013). Several experiments have been
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carried out with the proposals and values from the authors mentioned before, results have been obtained and formulas and average melanin and hemoglobin values have been selected under several experimentations in this work.
FIG. 2. MELANIN LAYER (RGB IMAGE)
Hemoglobin layer is not important for the method used for locating facial pores. This layer is very useful for medical application, and its usefulness should be explored for cosmetic, medical and recognition applications. From RGB image, melanin layer is decomposed in three different channels, known in this paper as (MLr, MLg, MLb) and the G layer selected (MLg). This layer which specifically contains melanin (fig. 4), is the one used for the face pore identification in this paper.
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melanin layer) the process for identifying pores is started. The hypothesis below, remarks that in the melanin layer is much more easier to identify the pores of the face. Specially when not having images with great zooming to the skin of the face, as it has been previously mentioned. The image representing the melanin layer (from RGB channel), is converted to grey scale with the purpose to perform further analysis. The rectangles covering the eyes and mouth are inserted in the face, as an ellipse, removing most part of the surrounding elements of the face which are not useless for the following process (fig. 5). In the algorithmic process for identifying pores in this paper, several ideas proposed by the research on the pores of the fingerprints have been used (Jain, Chen and Demirkus 2007; De Assis and Marana 2013; Malathi and Meena 2012; Zhao et al. 2010; Singh and Kanwal 2013; Parsons, Smith and Thonnes 2008). These proposals have been modified and adapted, as their use in fingerprints is through a dermatoscope or highresolution scanner, which uses the images of a finger with a great zooming; process which cannot be performed with the vast majority of images used for facial characterization. The processes described as follows are carried out to reduce noise, in order to remark the pores of the melanin image Gabor’s filter is applied
FIG. 3. HEMOGLOBIN LAYER (RGB IMAGE) FIG. 6. IDENTIFICATION OF THE CENTROIDS OF THE PORES IN THE FACE
FIG. 4. MELANIN G-LAYER FOR PORE LOCALIZATION (MLg)
Pore Localization In The Face From the melanin image obtained from (MLg -
This process is aimed to reduce noise and remark areas where pores can be found. Pixel level pores present high negative response frequencies and their intensity values change abruptly from white to black in the region where pores are found (Jain, Chen and Demirkus 2007). In order to detect what is described before and have a greater contrast of the pores, a wavelet applied to a transformed known as “Mexican hatâ€? is used. This transformed is a filter pass-band with a đ?‘†đ?‘† scale. Using all the processes before it is possible to make the image binary, as well as the 17
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mathematical morphological application to depurate the blobs of the pixels. As it has been previously mentioned, pores are presented in different configurations (circular, elliptical, etc.). Therefore for the required zones, the centroid area is obtained. In the fig. 6 shows the image in black and white of the centroids of the pores located in blue color. Besides the coordinates of the centroid of each facial pore, the algorithm used obtains the approximate diameter of the pore. The fig. 7 shows the original image of the face with the pores found overlapped. The mask of the eyes and mouth used is indicated to delimitate the area in which pores cannot be identified. Finally, the pores of the face are separated to configure the point cloud representing the geometrical configuration (fig. 8). Such structure and their numerical data are the base for the detection process of the facial pore. In fig. 8 is showed the point cloud of facial pores. The number of pores obtained for the face which has served as an example, was 3,200. The processing of every image of the PUT database was obtained for each face with an interval of 2,500 to 3,600 pores. It is worth mentioning, that the identification process is used to identify pores with size between 250 đ?œ‡đ?œ‡đ?œ‡đ?œ‡ to 500 đ?œ‡đ?œ‡đ?œ‡đ?œ‡, which are the size of the pore that have been found to be subject to simple sight recognition and in RGB digital image.
Frontiers in Pathology and Genetics (FPG) Volume 2, 2014
for the purposes of characterization of a human face thorugh an approximant polynomial. Therefore, it is possible to use such characterization in several pattern recognition applications, cosmetology and dermatology. Multivariate Approximation and Genetic Algorithms for Facial Characterization The characterization of a face starting a partir de las caracteristicas de poros facials may be formulated as a problem of supervised learning, consisting of the acquisition of classification functions from a set of examples. Experiments were done using a set of frontal images of faces from PUT database (Kasinski, Florek and Schmidt 2008). Several methods to approximate functions have been proposed. Such as: traditional statistical methods, neural networks, genetic programming techniques to obtain symbolic regression. However, all of these methods present several limitations and are not entirely automatic. From facial pores characteristics obtained from the melanine layer (using PUT face database) the samples of the form (đ?‘Ľđ?‘Ľđ?‘–đ?‘– , đ?‘Śđ?‘Śđ?‘–đ?‘– ) are generated. A learning function đ?‘“đ?‘“ such that đ?‘“đ?‘“(đ?‘Ľđ?‘Ľđ?‘–đ?‘– ) = đ?‘Śđ?‘Śđ?‘–đ?‘– may be assumed. The goal is to find a function đ?‘“đ?‘“ such that the given function captures the general patterns present in the training data and we may apply the determined function to predict the values of đ?‘Śđ?‘Ś when đ?‘Ľđ?‘Ľ is given. The function may be generalized to a đ?‘›đ?‘› − đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘đ?‘‘ space. The values used for the function that identifies the face may be attributes of the pixels (such as levels of gray or color, entropy, high pass, etc.). Using this approach, it is capable to characterize a face holistically found a polynomial approximant, using a Eclectic Genetic Algorithm (Kuri and Villegas 1998). The approximant has the form of:
FIG. 7. LOCALIZATION OF THE PORES IN A FACE IMAGE
It is estimated that the number of pores can be detected by digital images in a certain face is between 3,000 to 4,000 pores, reason for which it is considered that the number of pores obtained with the proposed algorithms is enough for the purpose of the project presented in this paper. In fig. 9, it can be observed a zoom of a part of the point cloud, where the pore configuration can be observed with greater detail. From the results obtained, it has been considered that obtaining the pores from a melanin layer is adequate
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(
g1
gp
) ∑... ∑ Ci ...i V1i ...V pi
f V1,..., V p =
1
1
i1 = 0
i p =0
p
p
(1)
This approximation problem has been pretty much solved except for certain practical issues. The usual numerical methods with which these approximations are normally tackled imply the solution of systems of linear equations of similar order. Such systems lead to numerical instability which renders the said methods ineffectual. Also, the approximation of a relatively large set of data under the traditional least square
Frontiers in Pathology and Genetics (FPG) Volume 2, 2014
error measure leads to Hilbert matrices which are known to be particularly sensitive to rounding errors. In other words, even though it is theoretically possible to solve the approximation problem even for large samples, in practice it is both impossible and impractical to do so with the usual methods. Therefore, a genetic algorithm is used to fin the form of the approximant polynomial.
www.seipub.org/fpg
and values” of the coefficients of the approximation polynomial in a way that the maximum absolute error between the data and the approximant is minimized. The polynomial is of the form presented in (1). The multivariate approximant genetic algorithm founds the configuration desired by the polynomial according to the facial pores features. For the original face example (fig 1) and the characteristics of its facial pores (fig 7), the multivariate approximant polynomial found has the form presented next: poliRface2 =
Feature1 a(1,1) a( 2,1) • • • a (10304,1)
Feature2 a(1, 2) • • • • a(10304, 2)
•••
Feature-p
••• • • • a(10304,10) a(1,10) • • • •
FIG. 8. MATRIX OF FACIAL PORE FEATURES
The main issue relies on the number of coefficients (C ) from equation 1 grows exponentially with the number of independent variables and the maximum degrees of polynomial. For example, for 10 variables and degree 6, the number of coefficients is approximately 710 ≈ 282.475 × 106 . Is a combinatory optimization problem, non-linear and NP-complete. And is very difficult to tackle using traditional methods [19]. The problem may be solved if we apply a Genetic Algorithm whose bits in the genome correspond to each coefficient of the variables in the equation (1). Also another genome is using to search the best powers of the independent variables. The goal is to find the form (coefficients and maximum degree) of a polynomial which better characterizes the relations between a set of independent variables and the dependent variable. To perform the optimization mentioned before, we used a method proposed in [42]. It allows us to find the “form
6.51764057623220722040071068409e-56*X1^27*X4^2*X5 + 5.18467952126471433055289809595e-59*X1^26*X3^3*X5 + 1.65279790439284320647488576377e-52*X1^26*X3*X4^3 + 1.80757659510743353384367440391e-59*X1^26*X4*X5^3 2.46341124230331352786048338149e-59*X1^24*X2*X3*X4*X5^3 + 3.91489809689599756338202324356e-51*X1^22*X2^2*X4^2*X5*X6^3 + 4.74909815754044223045623460821e-50*X1^22*X3*X4^5*X5^2 5.8406065022654855775174406455e-46*X1^21*X2*X4^4*X5*X6^3 2.17841821139547547309487781448e-45*X1^21*X3*X4^5*X5*X6^2 + 5.2148532788075010951764739133e-46*X1^21*X4^7*X5^2 + 1.87302930048996571351669659772e-65*X1^20*X2*X5^8*X6 + 4.35727015635736944379806881879e-39*X1^20*X4^10 1.65266603762361796591882573714e-36*X1^18*X3*X4^11 2.21365799599327675178373811447e-46*X1^16*X4^3*X5^5*X6^6 + 1.1371582746132310439366118433e-37*X1^14*X2^4*X3*X4^11 1.11753823676637228999503284247e-62*X1^13*X2^13*X3^4 + 1.22506884220498698812048665741e-50*X1^10*X2^5*X3^3*X4^6*X5^5 + 1.15071076317683229993096779039e-37*X1^10*X3*X4*X5^5*X6^12 + 3.99429223694557673056491977622e-53*X1^8*X2*X3^7*X5^7*X6^6 1.3513166768998766144179189133e-59*X1^5*X2^20*X3^2*X4*X6^2 + 9.70581787304005218746885977219e-58*X1^5*X2^12*X3^10*X4*X6^2 0.0000000000000000000000164792795408795929808449794432*X1^5*X 2^3*X3^2*X6^19 + 6.31862900304610654608325335761e54*X1^4*X3^19*X4^3*X5^2*X6 - 2.91725640994517722526501971319e66*X1^3*X2^12*X5^11*X6^4 + 0.0000000000238425346333799765822374635113*X1^2*X2*X3*X4^2*X 6^21 0.00775088916660480152509560269891*X1^2*X4^28 2.00664073895547880648641038591e-68*X1*X2^28*X4 6.31875250600758913577271769944e35*X1*X2^4*X3^3*X4^3*X5^6*X6^7 + 1.86654016450031079397097594484e-54*X1*X2^3*X4^3*X5^15*X6^8 0.000000000000000634605138465532871645608787733*X1*X2^2*X3^2* X4^2*X5*X6^18 1.71095187226456014444176694024e35*X1*X3^5*X4^12*X5^8*X6^3 + 5.17261445124154317760321734053e58*X2^25*X4^5 0.00000000000000000000000000192017071276839692377825776552*X2 ^12*X4^18 + 0.0000000000000000000000106782989544482559771782694766*X2^6*X 3*X4^3*X5^2*X6^18 0.000000000000000000160792208866728476495291202825*X2^4*X4^22 *X5^4 - 8.06623863460531831632164341237e-64*X2^3*X3^23*X5^3*X6 1.29010164929891725126367542329e-67*X2*X3^21*X4*X5^7 + 1.26939396511528515307465727615e-61*X3^27*X4*X6^2 + 63.6853190169448311053201905452*X4^30 + 0.00000649204116229648257868764180123*X6^30
This polynomial is the characterization of the face and allows to be used for other applications such as
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Frontiers in Pathology and Genetics (FPG) Volume 2, 2014
pattern recognition. This novelty method, programmed using MATLAB Genetic Algorithms toolbox, Image Processing, and Statistics.
343-356. Dawson, J., and D. Barker. “A theoretical and experimental study of light absorption and scattering by in vivo skin.” Phys. Med. Biol. 25 (1980): 695-709.
Conclusions Face characterization method by identifying it main facial pores and some of its characteristics, allows the development of a matrix from which an approximant polynomial can be created in order to characterize the face. The genetic algorithm used to obtain the configuration and form of the polynomial, decreases the approximation error obtained when using the traditional statistics methods. The polynomial of a characterization which is obtained, is considered to be a basic element to be used for more complex applications in facial recognition area, dermatology, medical, etc. As a future proposal from this paper, a genetical approximation polynomial will be generated for facial recognition, dermatology and cosmetics.
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