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Figure 6. (a1), (a2), (a3), (a4), (a5), (a6), (a7) and (a8) watermarked image is degraded respectively through JPEG2000 compression, JPEG compression, median filtering, adding Salt&Pepper noise, rotating, center cropping, surrounding cropping and scaling. (b1), (b2), (b3), (b4), (b5), (b6), (b7) and (b8) The corresponding extracted watermarks.-Discrete Wavelet Transform Method: A New Optimized Robust Digital Image Watermarking Scheme

This paper has described a scheme for digital watermarking of still images based on discrete wavelet transform. In the proposed method, the embedded logo watermark can be extracted without access to the original image. It has been confirmed that the proposed watermarking method is able to extract the embedded logo watermark from the watermarked images that have degraded through compression, filtering, cropping and scaling. Although this algorithm is not robust against rotation, it can completely extract the watermark from watermarked images that lose about 35% of their areas by cropping attack.

Figure 1. (a) Original watermark (b) extracted watermarks after compression(c) merged watermark-Discrete Wavelet Transform Method: A New Optimized Robust Digital Image Watermarking Scheme

Therefore, each bit of the logo watermark is stored in one coefficient of a sub-block to keep the capacity of watermarking fixed. When a region of the watermarked image is destroyed; the whole watermark can be extracted using other regions of the watermarked image by merging extracted watermarks. Figure 1 shows result of merging logo watermarks that were extracted from a compressed (with JPEG2000 algorithm) watermarked image.

Figure 4. (a) The original "Hookah" image (b) Watermarked "Hookah" with Q=35 (c) The original "Baby" image (d) Watermarked "Baby" with Q=35-Discrete Wavelet Transform Method: A New Optimized Robust Digital Image Watermarking Scheme

A set of distortions is applied to the watermarked image and the watermark is extracted from the distorted image. We used bit correct rate (BCR) to evaluate our proposed algorithm and it is calculated from the following equation [6].

Figure 2. LL2 sub-band is divided into sub-block-Discrete Wavelet Transform Method: A New Optimized Robust Digital Image Watermarking Scheme

In the following experiments, two gray-level images with size of 512 by 512, “Baby” and “Hookah” are the test images. The binary image “IAU” with size of 32 by 32 is used in our simulations as a watermark. Figure 3 shows the watermark. In the experiments Haar wavelet filter was used for discrete wavelet transform. The level of wavelet decomposition (n) and the number of sub-blocks (K) were also assumed to be 2 and 16 respectively. The proposed watermarking algorithm is evaluated from the point view of embedded watermark transparency and robustness; the result of each is shown in next two sections.

BRAIN Journal-ANNSVM: A Novel Method for Graph-Type Classification by Utilization of Fourier Transformation, Wavelet Transformation, and Hough Transformation-Figure 10. Detailed accuracy separated by classes and a confusion matrix which belongs to the dataset of Coiflet 1 applied by our main method (ANNSVM)

With regard to accuracy values of each class as presented in Figure 10, we observed that the accuracy of the two-dimensional chart class was the lowest (i.e., 0.875), while others were over 0.9. Results here suggested that both the bar and pie classes have their own unique characteristics, as opposed to the 2Dchart class. For example, the graph images that contained some rectangles were individually categorized in the bar graph class. A similar phenomenon occurred for circles in the pie chart class. In contrast, the 2Dchart class contained mixed types of graphs; hence, the graph characteristics belonging to the 2Dchart class varied.

BRAIN Journal-ANNSVM: A Novel Method for Graph-Type Classification by Utilization of Fourier Transformation, Wavelet Transformation, and Hough Transformation-Figure 8. Simulation of Coiflet 1 (PyWavelets discussion group, 2008), analyzing as one-dimensional images

Using only the wavelet coefficients was inadequate for classification. For example, for the pie chart, we obtained large wavelet coefficients located in the low-frequency domain; however, if we changed a circle in the pie chart to other shapes, such as a radar chart, the wavelet transformation gave results that were similar to those of the original pie chart. The Hough transformation can solve this problem since it detects the shapes of objects

BRAIN Journal-ANNSVM: A Novel Method for Graph-Type Classification by Utilization of Fourier Transformation, Wavelet Transformation, and Hough Transformation-Figure 7b. Results from SVM, ANN, SVMANN, and ANNSVM that used WLHT

From the results of ANNSVM_WL and ANNSVM_HT, we found that wavelet coefficients had a larger impact on classification than the Hough transformation data because the results from our proposed method applied to WL were more accurate than those of HT. The wavelet coefficients can capture the dominant characteristics from the graphs better than the Hough transformation. The one-dimensional image represented in the frequency domain had oscillations with different amplitudes depending on the graph types. For example, a dominant part of a pie chart should be in the low-frequency domain, because there is a large island of concatenated pixels in a onedimensional image, and it has only a few changes. Conversely, since the scatter plot contains many widely spread points, its dominant part should be located in the high-frequency domain. Performing the wavelet transformation, if a mother wavelet and a part of the wavelet function have a close match, the wavelet coefficient will be large. Assuming we use a suitable wavelet family with the example pie chart case, the wavelet coefficients in the low-frequency domain should be large as compared to other parts of the domain.

BRAIN Journal-ANNSVM: A Novel Method for Graph-Type Classification by Utilization of Fourier Transformation, Wavelet Transformation, and Hough Transformation-Figure 7c. Results from SVM, ANN, SVMANN, and ANNSVM that used WLHT

BRAIN Journal-ANNSVM: A Novel Method for Graph-Type Classification by Utilization of Fourier Transformation, Wavelet Transformation, and Hough Transformation-Figure 7. Results from SVM, ANN, SVMANN, and ANNSVM that used WLHT

BRAIN Journal-ANNSVM: A Novel Method for Graph-Type Classification by Utilization of Fourier Transformation, Wavelet Transformation, and Hough Transformation-Figure 9. Illustration of three different wavelets with three waves that have high amplitude values, as indicated by the dashed red circles

The mother wavelet of Coiflet 5 contained triple-high oscillation amplitude (i.e., Figure 9a). We considered that this mother wavelet was inappropriate for our data because overall our data possibly contained only a few matches with the mother wavelet of Coiflet 5. Moreover, the Symlet 10 (i.e., Figure 9b) and 20 (i.e., Figure 9c) also provided supportive results that were lower than others in ANNSVM_WLHT because their mother wavelets also had a similar shape as that of Coiflet 5. For similar reasons, the Haar wavelet was not proper because it is a step function.

BRAIN Journal-ANNSVM: A Novel Method for Graph-Type Classification by Utilization of Fourier Transformation, Wavelet Transformation, and Hough Transformation-Figure 6. Results from ANNSVN that used WL and HT

To identify which features of data influentially impacted data separability, we conducted experiments for ANNSVM with WL and HT (i.e., Figure 6). The WL contained only wavelet coefficients, whereas HT included only results of the Hough transformation. We found that, again, results obtained via the linear kernel were not significant; however, using the RBF kernel, accuracy for WL was higher than that of HT, indicating that wavelet coefficients provide influential features that make data separable.

BRAIN Journal-ANNSVM: A Novel Method for Graph-Type Classification by Utilization of Fourier Transformation, Wavelet Transformation, and Hough Transformation-Figure 3. Demonstrating the process of classification by applying the ANN, then the SVM

Essentially, if the number of nodes in the hidden layers increases, processing time increases, and the resultant ANN will suffer from over-fitting. Conversely, too small of a number of hidden layers will cause under-fitting for the ANN. In our setting, the number of hidden layers and the number of nodes in each hidden layer were fixed at five. Concerning the learning rate and momentum settings, these impact sensitive training performances are set to optimal values obtained via a grid search technique. The number of nodes in the output layer was three because there are three different class labels (i.e., 2Dchart, bar, and pie) in our datasets. We used the ANN here because our datasets have nonlinear separation, and the ANN is also highly applicable to nonlinear modeling. Thus the ANN with multiple hidden layers was an optimal candidate; however, since the ANN is a black box learning approach, it is difficult to interpret implicit relationships between inputs and outputs.

RAIN Journal-ANNSVM: A Novel Method for Graph-Type Classification by Utilization of Fourier Transformation, Wavelet Transformation, and Hough Transformation-Figure 4. Processes of all experiments:

In this study, accuracy values of each dataset showed the performance of each method. These values represent are the proportion of the total number of predictions that were correctly classified. Initially, we classified training instances into three classes, with approximately 300 images per class. The graphs had been selectively gathered from the Web. We manually normalized the collected images by eliminating unused areas, such as unnecessary text. Moreover, we evaluated the experiments with 10 folds cross-validation because such an approach can mitigate the problem of over-fitting.

BRAIN Journal-ANNSVM: A Novel Method for Graph-Type Classification by Utilization of Fourier Transformation, Wavelet Transformation, and Hough Transformation-Figure 5. Results from CNN and ANNSVM that used 1Dimg and 2Dimg

We compared the results of CNN_1Dimg, CNN_2Dimg, ANNSVM_1Dimg, and ANNSVM_2Dimg to confirm the validity of ANNSVM when applied to images. The 1Dimg represented the dataset of one-dimensional images, while 2Dimg represented the dataset of twodimensional images. Results are shown in Figure 5.

BRAIN Journal-ANNSVM: A Novel Method for Graph-Type Classification by Utilization of Fourier Transformation, Wavelet Transformation, and Hough Transformation-Figure 2. Illustrating the core process of one-dimensional image construction by applying a DFT

First, we collect graph images as raw data, which contain different scales and sizes, and therefore need to be normalized. We clean the images by omitting irrelevant areas. For example, we omit unnecessary text that has nothing to do with our classification procedure. Moreover, to standardize the sizes and shapes of the images, we resize and reshape them to be 64 x 64 squares. Second, we examine each image pixel, each of which contains one color value. After each pixel is projected along the x- and y-axes, we count the number of projected pixels with a color value greater than zero to reduce image dimensionality. We, therefore, obtain two one-dimensional images from the x- and y-axes.

BRAIN Journal-ANNSVM: A Novel Method for Graph-Type Classification by Utilization of Fourier Transformation, Wavelet Transformation, and Hough Transformation-Figure 1. Example displaying two scatter plots with different characteristics and patterns

In addition to this introductory section, the remainder of this paper is organized as follows. In Section 2, we present previous work related to our present study. In Section 3, we describe details regarding the methodology used in this study. In Section 4, we describe our experiments and results, then discuss our findings. Finally, we summarize the key content of our study in Section 5.