**4. Performance analysis**

In this, the outcome of fusion transformation is evaluated with different parameter, may be quantitatively & qualitatively and compared the results with the other algorithms, to check efficiency of the hybrid algorithm. Some of the quantitative parameters are listed below:

**Entropy:** Entropy is a measure of the information content in an image. An image with high information will have high entropy.

$$H = -\sum\_{i=0}^{L-1} p\_i \log \left( p\_i \right) \tag{4}$$

Where L is the number of grey levels in an image; Pi is the probability of occurring ith grey level.

**Standard Deviation:** Standard Deviation is used to measure the contrast in the fused image. It consists of both signal and noise, an image with more information would have high standard deviation.

$$\sigma = \sqrt{\sum\_{i=0}^{L-1} \left(i - \overline{i}\right)^2 h\_{fl}(i)}\tag{5}$$

Where hIf(i) is the normalized histogram of the fused image; L is the number of grey levels in an image.

**Mean Squared Error:**

was existing within the large set. As medical image knowledge is large, to cut back these knowledge PCA methodology is important. The strategy of principal element analysis permits USA to make and use a weakened set of variables, that area unit referred to as principal vectors. A reduced set is way easier to research and interpret. The foremost simple thanks to build a amalgamate image of many input pictures is playing the fusion as a weighted superposition of all input images [14]. The best coefficient coefficients, with relevancy info content and redundancy removal, is determined by a principal element analysis (PCA) of all input intensities. By computing PCA of the variance matrix of input intensities, the weights for every input image area unit obtained from the eigenvector comparable to the most important chemist price. PCA is that the simplest of verity eigenvector-based statistical procedure. Often, its operation is thought of as revealing the interior structure of the information in a very means that best explains the variance within the data [19]. If a variable knowledge set is envisioned as a collection of coordinates in a very high-dimensional data area (1 axis per variable), PCA will offer the user with a lower-dimensional image, a "shadow" of this object once viewed from its most informative viewpoint. This can be done by mistreatment solely the primary few principal parts in order that the spatial property of the remodeled knowledge is reduced. The amount of principal parts is a smaller amount than or capable the

• Transform the info into column vectors. Confirm the mean on every column

• Compute the eigenvectors V and Eigen|chemist} price D of C and kind them by

• Consider the primary column of V that corresponds to larger Eigen price to

The input images (images to be fused) I1(x, y) and I2(x, y) are arranged in two column vectors and their empirical means are subtracted. From the resulting

corresponding to the larger eigen value are obtained. The normalized components P1 and P2 (i.e., P1 + P2 = 1) are computed from the obtained eigenvector. The fused

In this, the outcome of fusion transformation is evaluated with different parameter, may be quantitatively & qualitatively and compared the results with the other

*IF*ð Þ¼ *x*, *y P*<sup>1</sup> ∗ *I*1ð Þþ *x*, *y P*<sup>2</sup> ∗ *I*2ð Þ *x*, *y* (3)

vector, compute the eigenvector and Eigen values and the Eigenvectors

amount of original variables [20].

*Multimedia Information Retrieval*

decreasing Eigen price

• P1 = V(1)/ΣV and P2 = V(2)/ΣV

figure P1 and P2 as

**4. Performance analysis**

image is

**66**

• Subtract the empirical mean vector.

• Mean of expectation = covariance(X).

• Compute the variance matrix C of X i.e. =XXT

Where P1 and P2 are the principal components.

PCA Algorithm:

$$\text{MSE} = \frac{\sum\_{i=0}^{M-1} \sum\_{j=0}^{N-1} [R(i,j) - F(i,j)]}{\text{MXN}} \tag{6}$$

**Root Mean Square Error (RMSE):** The error between fused image F and reference image R is given by,

$$RMSE = \sqrt{\frac{\sum\_{i=0}^{M-1} \sum\_{j=0}^{N-1} [R(i,j) - F(i,j)]^2}{M \text{XN}}} \tag{7}$$

Where R is reference image and F is fused image.

### **Peak Signal-to-Noise Ratio (PSNR):**

PSNR is the ratio between the maximum possible power of a signal and the power of corrupting noise that affects the fidelity of its representation.

The PSNR measure is given by

$$PSNR = 10 \* \log\_{10} \frac{\left(L - 1\right)^2}{MSE} \tag{8}$$

The higher the PSNR value, better the fusion process.

## **5. Results and discussion**

The proposed algorithms are tested and compared with different fusion techniques. The testing data sets are of two medical modality images like, CT and MRI of size 480X403. The original MRI image of set 1 is shown in **Figure 2(a)** and also the CT image of set 1 is shown in **Figure 2(b)**.

**Figure 3** shows an image resulting from DWT simple averaging fusion technique. DWT maximum selection rule is applied on data set 1 and resulting image is shown in **Figures 4** and **5** shows an image which is obtained from PCA fusion method.

**Figure 3.** *Fused image of data set 1 in DWT. Simple Averaging method.*

**Table 1** shows the values of different quality parametric measures like Entropy, Standard Deviation, Mean Squared Error and Root Mean Squared Error for various fusion algorithms. Values for the proposed PCA is resulted better than other w.r.t the quality parametric measures.

**Figure 5.**

**Figure 4.**

**Table 1.**

**69**

*Fused image of data set-1 in PCA.*

CT 4.5208 74.0343 MRI 5.6829 73.4328

*Fused image of data set 1 in DWT. Maximum selection Rule method.*

*A Hybrid Image Fusion Algorithm for Medical Applications*

*DOI: http://dx.doi.org/10.5772/intechopen.96974*

*Comparison parameters of the output images of fusion algorithm of Dataset-1.*

**DWT Simple Averaging Entropy Standard Deviation MSE RMSE PSNR**

DWT Simple Average 5.8438 71.2463 91.2320 9.5515 47.3835 DWT Maximum Selection Rule 6.2348 69.3433 94.0791 9.6994 53.3932 PCA **7.0439 67.3869 95.2059 9.7573 58.6465** Existing [20] 6.9253 66.8564 96.6523 9.3254 56.3254

The testing data sets are of two medical modality images i.e., CT and MRI of size 410X388. The original MRI image of set 2 is shown in **Figure 6(a)** and the CT image of set 1 is shown in **Figure 6(b)**.

DWT maximum selection rule is applied on data set 2 and resulting image is shown in **Figures 7** and **8** shows an image resulting from DWT simple averaging fusion technique and **Figure 9** shows an image which is obtained from PCA fusion method.

**Table 2** shows, the values of different quality parametric measures like Entropy, Standard Deviation, Mean Squared Error and Root Mean Squared Error for various fusion algorithms. Values for the proposed PCA is resulted better than other w.r.t the quality parametric measures.

*A Hybrid Image Fusion Algorithm for Medical Applications DOI: http://dx.doi.org/10.5772/intechopen.96974*

**Figure 4.** *Fused image of data set 1 in DWT. Maximum selection Rule method.*

**Figure 5.** *Fused image of data set-1 in PCA.*


#### **Table 1.**

*Comparison parameters of the output images of fusion algorithm of Dataset-1.*

**Table 1** shows the values of different quality parametric measures like Entropy, Standard Deviation, Mean Squared Error and Root Mean Squared Error for various fusion algorithms. Values for the proposed PCA is resulted better than other w.r.t

The testing data sets are of two medical modality images i.e., CT and MRI of size 410X388. The original MRI image of set 2 is shown in **Figure 6(a)** and the CT image

**Table 2** shows, the values of different quality parametric measures like Entropy, Standard Deviation, Mean Squared Error and Root Mean Squared Error for various fusion algorithms. Values for the proposed PCA is resulted better than other w.r.t

DWT maximum selection rule is applied on data set 2 and resulting image is shown in **Figures 7** and **8** shows an image resulting from DWT simple averaging fusion technique and **Figure 9** shows an image which is obtained from PCA fusion

the quality parametric measures.

*Fused image of data set 1 in DWT. Simple Averaging method.*

of set 1 is shown in **Figure 6(b)**.

the quality parametric measures.

method.

**68**

**Figure 3.**

**Figure 2.**

*Data set-1 of the brain. (a) MRI scan image. (b) CT scan image.*

*Multimedia Information Retrieval*

**Figure 6.** *Data set-2 of the brain. (a) MRI scan image. (b) CT scan image.*

**Figure 7.** *Fused image of data set 2 in DWT. Maximum selection Rule method.*
