Gabor Wavelet-Based Appearance Models - IEEE Xplore

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Abstract—There has been considerable research in the last several years based on the principles of Active Appearance. Models (AAMs). AAM is a robust ...
Gabor Wavelet-Based Appearance Models Kha Gia Quach

Chi Nhan Duong

Khoa Luu

Hoai Bac Le

HCMUS Ho Chi Minh City, Vietnam [email protected]

HCMUS Ho Chi Minh City, Vietnam [email protected]

Carnegie Mellon University, USA [email protected]

HCMUS Ho Chi Minh City, Vietnam [email protected]

Abstract—There has been considerable research in the last several years based on the principles of Active Appearance Models (AAMs). AAM is a robust methodology for general image (object) descriptions that incorporates shape and texture information. In this work, we extend the basic AAMs by developing a new method for texture description for the application of human facial modeling and synthesizing. The premise is to develop a better texture based model for the face that incorporates specific facial information such as wrinkling, micro-features (e.g., moles, scares, freckles, etc.), and aging features (e.g., sagging, hollowing of checks, weight gain, etc.) This paper proposes a new improvement in texture synthesis--Gabor Wavelet-based Appearance Model. The experimental results demonstrate the potential of this approach for face-based applications. Keywords-component; Active Appearance Model; Principal Component Analysis; Wavelet Transform

I.

INTRODUCTION

Active Appearance Models (AAMs) [1] [2] is one of the most efficient techniques to analyze longitudinal facial images. AAMs generate a feature space that is capable of modeling the aging variations of the face. It has further been used to synthesize new “aged” faces based upon its model. Although AAMs are able to synthesize photo-realistic images of human faces, AAMs employ raw image intensity for texture model. Moreover, the global property of Principal Component Analysis (PCA) makes the synthesized faces look smoother and younger than usual. However, texture variations in the human face are more prominent after 30 years of age. During this period, the human face experiences soft-tissue changes such as fine wrinkling, formation of lines and creases, and some hyper-pigmentation changes to local coloration. Therefore, we address this problem by applying Gabor Wavelet Network (GWN) [3] in texture modeling of AAMs. Since GWNs provide the localization property and the ability of encoding almost all image information [4], this makes GWNs’ products appear better when compared with PCA as demonstrated in Section IV.B.2).a). Moreover, this also leads to a well reconstructed image without any blurring effect. This helps retain most of the facial information such as wrinkling, micro-features and aging features. In this paper, we focus on the reconstruction quality of AAMs which is essential to face-based applications such as age progression. The main contributions of this paper are to improve AAMs texture representation and to propose a fitting procedure by using

Gabor Wavelet Network (GWN) instead of PCA in texture modeling. We could prove our method is better than another approach [5], which also incorporated GWN with AAMs. II.

RELATED WORK

Texture modeling concerns have been present since the introduction of AAMs. There are many researchers who study the high-dimensional texture representation problem. When representing a high-resolution image, the problems of storage and computational requirements will be encountered. Two solutions are suggested to reduce the redundant information in the high-dimensional textures, including image compression using wavelet [6] and using local textures instead of global textures [7]. This paper extends the work of Changbo Hu et al. [5] which introduced the idea of using GWN to model face texture as an alternative to PCA in AAMs for face alignment and face recognition. They argued the global property of PCA caused a wide-spreading error in the texture part of AAMs, when occlusions appear in face images. This leads to a less accurate matching between the model and new images. To address this problem in face alignment, they used GWNs. There is no need for reconstructing images in face alignment or face recognition, so they did not focus much on the quality of the reconstructed images and no qualitative results were given for this. Recently, Su et al [8] addressed the problem with the intensity model of AAMs by combining Gabor wavelet and Local Binary Pattern (LBP) to represent textures in AAMs. The new texture representation improved the accuracy of model fitting, which resulted in a more accurate and reliable model parameter. However, the LBP operator cannot be inversed, so it will eliminate the capability of synthesizing face images of AAMs. As a result, it cannot be applied in age progression, since we have to synthesize face images from model parameters. Therefore, we propose a better approach using GWN for synthesizing photo-realistic face images in applications such as age progression. III.

OUR PROPOSED METHOD

Due to the smoothing effect of the AAM technique on images, it still may not represent sufficient texture information for human faces. We propose a combination model of GWN and AAMs. Our scheme consists of two main steps: (1) modeling face images in the training set using AAM shape parameters and GWN as texture parameters; (2) fitting a new face image to find the best parameters modeling it. Currently,

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this scheme only takes grayscale images as the input and the output is model parameters. The following section gives more details about this combined model. A. Training model As mentioned above, Chango Hu’s method [5] which used GWN would require a high number of wavelets for image synthesis. However, our proposed method can synthesize photo-realistic face images with an acceptable number of wavelets. 1) Modified modeling steps

fit the face better, a procedure proposed by Milborrow [10] is employed. This initialization procedure is more efficient than the other two (i.e. simple placing mean shape at the top left of the image and brute-force searching for initial shape). To demonstrate this, we also perform an experiment on 800 images from FG-NET database [11]. We fit these images with various initial procedures, then compare the optimized shape with the manually landmarked shape using Mean Error – ME68 metric (i.e. Euclidean distance between 68 landmark points). The optimized shape with Milborrow’s initial procedure gets the best result. Therefore, we proved that using a better initial shape can avoid getting stuck in local minima.

Changbo Hu et al. [5] suggested using a single GWN

( Ψ , w ) consisting a set of n odd Gabor wavelet functions

{ }

Ψ = ψ nk

and n associated weights w = {wk} for

approximating the shape-free images in AAMs. In this way, PCA is omitted from the texture modeling steps. However, it required high number of wavelets to get a quite clear and recognizable reconstructed face image. To avoid increasing the number of wavelets and to achieve better image quality, we suggest using GWN to approximate the differences (denoted {vi , vi = g i − g },1 ≤ i ≤ N ) between each texture vector gi and the mean texture vector g . The images are reconstructed in two steps. First, we reconstruct the differences using the trained N

GWN vˆi = ∑ wiψ ni . Then, we regenerate the image by adding i =1

the mean texture with the differences. gˆ i = g + vˆi (1) Now the reconstruction error is limited to the error of the vector vˆi . The recreated face image will be recognizable as a human face and as clear as the mean face no matter how many wavelets are used; and the GWN reconstruction only decides how different the reconstructed faces and the mean face are. Meanwhile, Changbo Hu’s method may result in unrecognizable face images when the number of wavelets used in GWN is too low. 2) Using GWN

TABLE I.

COMPARING ME68 BETWEEN DIFFERENT INITIAL PROCEDURES

Initial procedure Mean shape Brute-force Milborrow

ME68 2.5 0.77 0.17

The gradient descent procedure is then applied to minimize the difference between the normalized image g sampled by parameters (x, p) and GWN reconstruction image gˆ .

δ g = g − gˆ Optimizing the shape based on texture as follows.

(2)

1) Sample the image by using current shape x (represented by model parameter b) and pose p to obtain g 2) Calculate texture differences v = g − g 3) Use GWN to compute texture difference’s parameters tk = v,ψ nk , where ψ nk = ∑ l ( A −1 ) ψ nl and A is the k ,l

wavelet interference matrix with Ak ,l = ψ nk ,ψ nl

which

can be pre-computed. 4) Reconstruct the texture differences vˆ = ∑ k =1 tkψ nk n

5) Reconstruct the texture gˆ = vˆ + g 6) Compute the residual δ g and the current error E = δ g

2

Having an improved approximation, GWN with a higher number of wavelets is better suited for image synthesis. Krueger [3] suggested using a Laplacian pyramid scheme for better reconstructed images. However, the author did not give any idea for finding the best configuration of this pyramid scheme. How many layers and how many wavelets per each layer should be chosen? In this paper, the conclusion is given through some experimental results (See section IV).

7) Update shape b → b + δb and pose parameters p → p + δp using δ b = Bδ g , δ p = Pδ g where the two regression matrices B and P are pre-computed. 8) Stop if E is small enough or reaching the maximum number of iterations; otherwise repeat from step 1 with the new parameters calculated in previous step. Noting that ψ nk can be pre-computed in training step, so the

B. Fitting model Similar to AAMs, the fitting steps are also needed to determine model parameters that best fit the model into the new images. A variation of AAMs, Shape-AAM method [9], is incorporated in these step. The major change here is the calculation of texture parameters and image reconstruction, based on the GWN model.

complexity of fitting procedure can be further reduced.

First, given a new face image, we start with an initial shape x and pose p – the position and direction of shape x. To make x

IV.

EXPERIMENTAL RESULTS

In this section, we compare our proposed method with previous works on two issues including: ability of (I) modeling human face and (II) synthesizing aged faces. Considering these issues, efficiency of the proposed method is compared with AAMs [1] and AWN [5]. In modeling human face experiments, we use images from the IMM face database [12], which are also used in [5] for training and testing. For synthesizing aged faces,

two other databases are used in our experiments. They will be discussed in the following sections. A. Face Aging Databases 1) FG-NET

Figure 2: Example images of an individual in FG-NET [11] FG-NET [11] is one of the most common databases used in many publications related to face aging. This database contains 1002 face images of 82 subjects with age ranges from 0 to 69 years. Each image was annotated with 68 landmark points characterizing the object’s shape features. These points are very useful for locating facial features, especially in Active Appearance Model.

reconstructed faces are just slightly changed. First, GWN was trained with three images and then a sample of reconstructed image from each GWN configuration is shown in TABLE II. To measure the quality of reconstruction of our proposed method, we use peak signal-to-noise ratio (PSNR). The signal in this case is the original image, and the noise is the error caused by reconstruction. We can determine which configuration is better based on this metric. TABLE II.

RECONSTRUCTED IMAGES OF GWN

1 Layer

2 Layer

3 Layer

7×7 = 49 PSNR = 23.35dB

4×4 + 5×5 = 41 PSNR = 25.05dB

3×3+4×4+5×5 = 50 PSNR = 26.33 dB

12×12 = 144 PSNR = 24.08dB

8×8 + 9×9 = 145 PSNR = 27.19dB

3×3+6×6+10×10 = 145 PSNR = 28.27dB

25×25 = 625 PSNR = 27.39 dB

15×15+20×20 = 625 PSNR = 26 dB

6×6+12×12+21×21= 621 PSNR = 30.55dB

2) Vietnamese Longitudinal Face (VLF) Database

Figure 1: Photos of an individual in Vietnamese database [13] In [13] a longitudinal database of Vietnamese faces was collected and used to evaluate age-estimation on a notoriously difficulty population of people. VLF contains 227 Vietnamese color face images of 28 subjects, 12 males and 16 females, with age ranges from 1 to 80 years. They were scanned with a capture resolution of 300 dpi and stored in a bitmap format from photo albums of four families. Each subject has about eight frontal images with provided ground truth information. Similar to FG-NET database, each face image was also annotated with 68 landmarks. Most of subject’s age range is from 1 to 30 years. Therefore, this database is suitable for facial studies in the growth and development stage. B. Face modeling results To demonstrate the ability of modeling human faces, we perform two experiments which compare our proposed method with AAMs [1] and AWN [5]. The first experiment reveals the effect of GWN configuration (number of wavelets and layers) on the regenerated images and shows how efficient the proposed method is in reconstructing the face images from model parameters compared with AWN using the same configuration. The second one exposes the effect of the global property of AAM on reconstructed images. Thanks to local property of GWN, the reconstruction and fitting results of the proposed method are improved. 1) Reconstruction results with various GWN configurations In general, there is tradeoff between complexity and reconstruction quality. However, in this section, we prove that there is no need to increase the number of wavelets (i.e. the complexity) because our approach is already good with a small number of wavelets. An experiment applied on various GWN configurations shows that although the number of layers and wavelets are increased which means the complexity goes up,

We also perform another experiment to compare our approach with Hu’s approach [5]. We use the GWN of one layer of 7×7 = 49 wavelets. The reconstructed face images from Hu’s method are still blurry and hardly recognizable while our approach gets a clearer and recognizable reconstruction result. The reason for these comparative results is that we maintain the mean face and only use GWN for modeling the differences between each face and the mean face. Therefore, our proposed model retains most of the important face information. The reconstruction results for both methods are shown as follows. TABLE III.

RECONSTRUCTED IMAGES OF EACH TRAINING IMAGES Image 1

Image 2

Image 3

PSNR = 16.81 dB

PSNR = 17.74 dB

PSNR = 18.19 dB

PSNR = 23.35dB

PSNR = 26.33dB

PSNR = 26.37dB

Changbo Hu’s method

Our method

2) Comparisons between our proposed model and basic AAM All experiments in this section use GWN with 145 wavelets divided into three levels (i.e. 3×3, 6×6 and 10×10). We choose this GWN configuration because it has been shown in TABLE II. that provide a reasonably good reconstruction result with an acceptable number of wavelets. In addition, for basic AAM implementation, we only choose PCA configurations which retained 95% of the shape and texture variations. We found that if a higher percentage of variations (e.g. 97%, 98% …) is

chosen, which means more model parameters are used; the model performance decreases accordingly. a) Local vs. global property In this section, we demonstrate the local property of GWN and the global property of PCA on the model parameters through the reconstructed image. We fit the models with two images: one without error, one with a black hole on the right cheek. Then we reconstruct the image using the corresponding model parameters.

FG-NET database for training and testing in this section, because IMM only consists of 40 images, which make it harder for evaluating the performance of fitting steps. After training as in section III.A with 800 images from FG-NET database, we then test with the rest of images in the database. We compare the fitting results of our proposed model with the basic AAM implemented by Stegmann [15]. The fitting results are shown in TABLE V. and TABLE VI. which illustrate the significant improvement of Gabor-based AAM. From TABLE V. , we can see that our optimized shape fit perfectly to face images while basic AAM gets some minor errors in the outer shape and the mouth and even major errors in some images. TABLE IV.

EXPERIMENTS TO DEMONSTRATE THE QUALITY OF RECONSTRUCTION IMAGES

Figure 3: (a) Test image (d) Test image with a black hole; (b) and (e) corresponding reconstructed images by basic AAM; (c) and (f) corresponding reconstructed images by our proposed method Due to the global property of PCA, the errors are spreading all over the reconstructed images. Therefore, the effect of a black hole placed on the face image can be seen clearly from the image in Figure 3 (e). Major changes which occurred in skins, nose, mouth and eyes created a totally different face. Meanwhile, only local changes on the right cheek appear in the image resulting from our proposed method. This shows some advantage of GWN over PCA in retaining the identity of the person and eliminating the effect of errors. Theoretically, this is mainly due to the Gabor wavelet functions Ψ which provide the best localization property in both frequency and spatial domain, and they are located in major features of the face image where each of them has various weights according to the features[4]. Meanwhile, PCA basis images display global properties in the sense that they assign significant weights to the similar pixels. It accords with the fact that PCA basis images are just scaled versions of global Fourier filters[14]. b) Reconstructing face images Furthermore, we conduct an experiment to evaluate face recognition (FR) algorithm performance on these reconstructed images. We implement the Eigenfaces algorithm for Face Recognition. The purpose of this experiment is to compare the reconstruction quality of two models. Moreover, we also use the PSNR metric for comparison. The evaluation used 120 face images of 40 people from the IMM database. Each person has three images: the original (org), the AAM reconstructed (r1) and our proposed method reconstructed one (r2). The PCA and Euclidean distance were used in all experiments. The results (See TABLE IV. ) of our proposed method are better than basic AAM in this experiment, which means our proposed method’s reconstructed images are more similar to original images than AAM reconstructed images. In TABLE IV. , we also calculate the mean PSNR of each image in r1 and r2. The signal in this case is the corresponding images in org. c) Fitting results Searching for best model parameters, which fit a new input image, is a very essential step which would influence the result of regenerated images dramatically. We use images from

Galleries org org TABLE V.

Probes r1 r2

Mean PSNR 11.57 dB 17.20 dB

FITTING RESULTS WITH ORIGINAL AAM AND OUR METHOD Original AAM

TABLE VI.

Results 60% 100%

Our proposed method

COMPARING ME68 BETWEEN ORIGINAL AAM AND OUR PROPOSED MODEL

Model Original AAM Gabor-based AAM

ME68 0.78 0.17

C. Face aging results We also employ Gabor-based AAM for age progression to demonstrate prominent in face synthesis. In [16] Support Vector Regression (SVR) and Monte-Carlo simulation are used to generate an aging table where each age is an average representation at that age created by the simulation process. This table is used to age progress the Gabor-based AAM parameters for synthesizing a new face image. 1) Performance measurement

Since there is no standard metrics for measuring the performance of the age-progression model, in this section, we used age estimation and FR system to evaluate the quality of our synthesized faces. The former system assesses the ability of synthesizing faces at the target age. And the latter decides whether aged faces have the same ID as the source faces. Eigenfaces representation and Euclidean distance are used for measuring the similarity between a pair of faces. Mean Absolute Error (MAE) returned from the age estimation system in [13] is used for comparing the age of synthesized faces with the target age. 2) Comparing aging results between Our Proposed Method and Basic AAM Face age-progression can be divided into two categories: growth and development, and adult aging [17]. Therefore, we do two experiments: pre-adult aging (below 20 year) and adult aging (above 20 year) on FG-NET database. Only images at some specific ages (e.g. 0, 2, 4, 7, 10, 12, 14, 16, 18, 23, 25, 30, 33, 35, 40 and 45) are used for testing because their quantity is higher than others in the database. We produce synthesized faces for each selected age from the rest of the images of a person. For example, if a person A has five images (at age 0, 7, 10, 11 and 12), we will use the images at 7, 10, 11 and 12 to synthesize faces at age 0. Thus, the person A will have four synthesized images at age 0. FG-NET database is split into two parts: part A included images of 41 subjects (ID: 001 – 041) and part B included images of 41 subjects (ID: 042 – 082). Images in part A are used for training and images in part B are used for testing. For pre-adult aging (below 20 year), the FR and MAE results are showed as follows. TABLE VII. FR

FR RESULTS OF SYNTHESIZED FACES (BELOW 20 YR)

Galleries (No. of image)

Probes (No. of image)

Results Gabor-based AAM 59% 66% 63% 64% 65% 75% 87% 76% 70% 69%

Age 0 Age 2 Age 4 Age 7 Age 10 Age 12 Age 14 Age 16 Age 18

26 27 28 22 28 24 17 14 17 Average

TABLE VIII.

MAE RESULTS OF SYNTHESIZED FACES (BELOW 20 YR)

True age Age 0 Age 2 Age 4 Age 7 Age 10 Age 12 Age 14

Original images 0.9 1.64 1.68 1.43 1.19 1.55 1.6

262 262 285 228 273 257 173 131 122

Original AAM 60% 69% 69% 71% 69% 78% 87% 77% 74% 73%

MAE AAM “aged” Gabor-based images AAM “aged” images 4.47 2.47 5.11 2.19 2.39 2.73 2.33 1.73 2.39 1.88 2.59 1.65 3.33 2.08

No. of image 262 262 285 228 273 257 173

2.69 2.2 1.65

Age 16 Age 18 Average

3.62 7.36 3.73

2.64 5.08 2.49

131 122

These results in TABLE VII. , TABLE VIII. , TABLE IX. and TABLE X. reveal improvements for Gabor-based AAM in terms of FR and MAE. A comparion of the two method shows that overall MAE results of Gabor-based AAM are smaller in both phases (before and after 20-year-old). Meanwhile, Gabor-based AAM only gets a good result on FR in the latter phase (after 20-year-old). In more detail, we can see that, at the below 20-year period, recognition rate of the original AAM is 4% higher than Gabor-based AAM. By contrast, the result of Gabor-based AAM is higher at the adult aging stage. As we know, the shape of human face changes much in the growth and development phase and in the adult aging phase, the primary changes are formation of skin texture. Moreover, Gabor-based AAM is capable of modeling texture better than AAM which usually has smoothing effect that causes face images look younger than usual. Therefore, FR and MAE results of AAM are not as good as the results of Gabor-based AAM for the generated images in the adult aging phase. As a result, this confirmed that Gabor-based AAM is more suitable for adult aging (above 20-year-old). Besides, there are different trends between FR and MAE results in the growth and development phase where MAE results of AAM is worse, but its FR results are higher than Gabor-based AAM. This is due to error retaining in FR system which is based on simple Eigenfaces algorithm. For adult aging (above 20 year), the FR and MAE results are showed as follows. TABLE IX. FR

FR RESULTS OF SYNTHESIZED FACES (ABOVE 20 YR)

Galleries (No. of image)

Age 23 Age 25 Age 30 Age 33 Age 40 Age 45

TABLE X.

7 7 4 4 2 4 Average

Probes (No. of image) 29 26 24 21 14 27

Results Original Gabor-based AAM AAM 72% 79% 77% 73% 58% 71% 80% 76% 35% 36% 92% 96% 69% 72%

MAE RESULTS OF SYNTHESIZED FACES (ABOVE 20 YR)

True age

Original images

Age 23 Age 25 Age 30 Age 33 Age 40 Age 45 Average

8.66 5.12 1.24 0.90 1.74 9.59 4.54

MAE AAM “aged” images 3.41 4.4 3.42 4.22 8.39 13.07 6.15

Gabor-based AAM “aged” images 8.34 6.56 1.77 1.61 3.60 9.60 5.25

No. of image 29 26 24 21 14 27

Because of lacking sufficient number of face images above 20-year-old, we only perform pre-adult aging on VLF database. For per-adult aging, we choose age 2, 4, 9 and 13 for testing.

Experimental results in TABLE XI. and TABLE XII. also show prominent of the Gabor-based AAM. Although the results are not as high as the results achieve with images in FG-NET, they also show improvement on MAE and FR results when using Gabor-based AAM. TABLE XI.

FR RESULTS OF SYNTHESIZED FACES ( BELOW 20 YR)

Galleries (No. of image) 14 10 12 18 Average

FR Age 2 Age 4 Age 9 Age 13

TABLE XII.

Probes (No. of image) 47 86 88 29

Original AAM 68% 33% 57% 72% 58%

Results Gabor-based AAM 79% 38% 59% 72% 62%

MAE RESULTS OF SYNTHESIZED FACES ( BELOW 20 YR)

True age

Original images

Age 2 Age 4 Age 9 Age 13 Average

2.52 2.36 1.40 2.90 2.29

MAE AAM “aged” images 6.41 2.30 2.93 5.35 4.25

Gabor-based AAM “aged” images 3.16 2.74 1.54 3.55 2.75

No. of image

V.

In this paper, we have pointed out the disadvantage of AAM’s texture representation. We then proposed combined method using a Gabor wavelet network for texture modeling, and we also looked into some improvement in training and fitting step. We proved that our method does not need a high number of wavelets for better reconstruction results and fitting the new image with a better initial shape will get more accurate model parameters. Some experimental results of face recognition and age progression are presented to show how it works on improving texture representation of AAM. REFERENCES [1]

[2]

[3] [4]

47 86 88 29

[5] [6]

[7]

3) Synthesized images Some synthesized images are shown in TABLE XIII. The results presented some representative images for pre-adult and adult aging reveal feasible in modeling shape and texture to demonstrate age-related changes. Moreover, age regression is also possible using our proposed model which can remove age-related changes such as lines under the eyes, around the mouth, as well as general textural changes. Despite difficulties in comparing quantitatively to other works, we believe that the quantitative results above and these images show potential of this work for age progression. TABLE XIII. Original image at age t1

SOME SYNTHESIZE “AGED” FACES Original image at age t2

Synthesized image at age t2 with head and facial hair

[8]

[9]

[10] [11] [12]

[13]

[14]

t1 = 1 yr

t2 = 11 yr

t2 = 11 yr

[15] [16]

[17] t1 = 47 yr

t2 =23 yr

t2 =23 yr

t1 = 33 yr

t2 = 40 yr

t2 = 40 yr

CONCLUSIONS

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