**3. Image fusion**

### **3.1 DWT image fusion**

Image fusion process is used to associate the two or more images in to a single image. The resultant fused image obtained will be more explanatory than the distinct source images. The wave remodel may be a mathematical tool which will be wont to discover native options in an exceedingly signal method. It can also be wont to decompose two-dimensional (2D) signals like second grayscale image signals into totally different resolution levels for multiresolution analysis. Wave remodel has been greatly utilized in several areas, like information compression, texture analysis, feature detection, and image fusion.

Wavelet transforms offer a framework within which a picture is rotten, with every level equivalent to lower band and better frequency bands. The DWT may be a spatial-frequency decomposition that provides a versatile multiresolution analysis of a picture. In general, the essential plan of image fusion supported ripple remodel is to perform a multiresolution decomposition on every supply image; the coefficients of each the low-frequency band and high-frequency bands are then performed with a definite fusion rule [13]. The wide used fusion rule is most choice rule. This straightforward theme simply selects the biggest absolute ripple constant at every location from the input pictures because the constant at that location within the united image [15]. After that, the united image is obtained by playacting the inverse DWT (IDWT) for the corresponding combined ripple coefficients. The elaborated fusion steps supported ripple remodel will be summarized below.

Step 1. the pictures to be amalgamated should be registered to assure that the corresponding pixels square measure aligned.

Step 2. These pictures square measure rotten into riffle remodeled pictures, severally, supported riffle transformation. The remodeled pictures with K-level decomposition can embrace one low-frequency portion (low-low band) and three high-frequency parts (low-high bands, poker game bands, and high-high bands).

Step 3. The remodel coefficients of various parts or bands square measure performed with an explicit fusion rule.

Step 4. The amalgamated image is built by acting associate inverse riffle remodel supported the combined remodel coefficients from Step 3 [16].

The overall fusion processing goes through the preprocessing and image registration followed by wavelet decomposition. The input images must be of same size for fusion. For easy computation and to abstract data, the image has got to be born-again into a grey scaled image from color image. Bar chart standardisation provides tonal distribution of the complete image. Preprocessed pictures square measure split in to four frequency sub bands like LL, LH, HL and HH. A general fusion rule is to select, the coefficients whose values are higher and the more dominant features at each scale are preserved in the new multi-resolution representation [17]. The fused image is constructed by performing an inverse wavelet transformation. The main objective of an image fusion is combining complimentary, as well as redundant data from multiple pictures to make one image that provides a lot of complete and correct description. This amalgamated image is a lot of appropriate for human visual, machine

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

perception or additional image process and analysis tasks. Another advantage of image fusion is that it decreases the cupboard space and price by storing solely the one amalgamated image, rather than storing totally different modality pictures [14]. within the space of medical imaging, combining the photographs {of totally different| of various} modalities of same scene offers numerous benefits it should be fusion of image taken at different spatial resolution, intensity and by totally different strategies helps medical practitioner/Radiologists to simply extract or acknowledge the options or abnormalities that will not be typically visible in single image [18] (**Figure 1**).

#### *3.1.1 Simple averaging rule*

• When the image region containing a pixel's neighbourhood that is uniform, its bar graph are going to be powerfully peaked, and therefore the transformation perform can map a slender vary of constituent values to the complete vary of the resultant image [14]. This causes AHE to over amplify the little amounts of

Image fusion process is used to associate the two or more images in to a single image. The resultant fused image obtained will be more explanatory than the distinct source images. The wave remodel may be a mathematical tool which will be wont to discover native options in an exceedingly signal method. It can also be wont to decompose two-dimensional (2D) signals like second grayscale image signals into totally different resolution levels for multiresolution analysis. Wave remodel has been greatly utilized in several areas, like information compression, texture

Wavelet transforms offer a framework within which a picture is rotten, with every level equivalent to lower band and better frequency bands. The DWT may be a spatial-frequency decomposition that provides a versatile multiresolution analysis of a picture. In general, the essential plan of image fusion supported ripple remodel is to perform a multiresolution decomposition on every supply image; the coefficients of each the low-frequency band and high-frequency bands are then

performed with a definite fusion rule [13]. The wide used fusion rule is most choice rule. This straightforward theme simply selects the biggest absolute ripple constant at every location from the input pictures because the constant at that location within the united image [15]. After that, the united image is obtained by playacting the inverse DWT (IDWT) for the corresponding combined ripple coefficients. The elaborated fusion steps supported ripple remodel will be summarized below. Step 1. the pictures to be amalgamated should be registered to assure that the

Step 2. These pictures square measure rotten into riffle remodeled pictures, severally, supported riffle transformation. The remodeled pictures with K-level decomposition can embrace one low-frequency portion (low-low band) and three high-frequency parts (low-high bands, poker game bands, and high-high bands). Step 3. The remodel coefficients of various parts or bands square measure

Step 4. The amalgamated image is built by acting associate inverse riffle remodel

The overall fusion processing goes through the preprocessing and image registration followed by wavelet decomposition. The input images must be of same size for fusion. For easy computation and to abstract data, the image has got to be born-again into a grey scaled image from color image. Bar chart standardisation provides tonal distribution of the complete image. Preprocessed pictures square measure split in to four frequency sub bands like LL, LH, HL and HH. A general fusion rule is to select, the coefficients whose values are higher and the more dominant features at each scale are preserved in the new multi-resolution representation [17]. The fused image is constructed by performing an inverse wavelet transformation. The main objective of an image fusion is combining complimentary, as well as redundant data from multiple pictures to make one image that provides a lot of complete and correct description. This amalgamated image is a lot of appropriate for human visual, machine

supported the combined remodel coefficients from Step 3 [16].

noise in for the most part uniform regions of the image [4].

**3. Image fusion**

**3.1 DWT image fusion**

*Multimedia Information Retrieval*

analysis, feature detection, and image fusion.

corresponding pixels square measure aligned.

performed with an explicit fusion rule.

**64**

In remodel primarily based fusion formula an easy "averaging rule" is adopted to fuse the low frequency coefficients. Low-frequency coefficients contain define data associated with the image rather than specific major details, ANd therefore an averaging technique is applied to provide the composite low-frequency coefficients [18]. The computation is performed as follows:

$$F(\mathbf{x}, \mathbf{y}) = \frac{F\_1(\mathbf{x}, \mathbf{y}) + F\_2(\mathbf{x}, \mathbf{y})}{2} \tag{1}$$

where F(x, y) are the low frequency coefficients of the fused image IF, f1(x, y) and f2(x, y) are the low frequency coefficients of the source images.

#### *3.1.2 Maximum selection rule*

Maximum selection rule is used in high frequency coefficients. Two images wavelet coefficients are compared and select the maximum value coefficient for fusion process as shown in Eq. (2)

$$W(\mathbf{x}, \boldsymbol{y}) = \begin{array}{ll} W\_1(\mathbf{X}, \mathbf{Y}) & \text{if} \ I\_1(\mathbf{x}, \boldsymbol{y}) > I\_2(\mathbf{x}, \boldsymbol{y}) \\ W\_2(\mathbf{X}, \mathbf{Y}) & \text{if} \quad I\_1(\mathbf{x}, \boldsymbol{y}) < I\_2(\mathbf{x}, \boldsymbol{y}) \end{array} \tag{2}$$

W1 (x, y) – Image l wavelet coefficient. W2 (x, y) - Image 2 wavelet coefficient.

#### **3.2 Principal component analysis**

Principal element analysis is performed that aims at decreasing giant an outsized an oversized set of variables into a little set that also containing most of the data that

**Figure 1.** *Fusion Process using Wavelet transforms.*

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 amount of original variables [20].

algorithms, to check efficiency of the hybrid algorithm. Some of the quantitative

*i*¼0

Where L is the number of grey levels in an image; Pi is the probability of

X*<sup>L</sup>*�<sup>1</sup>

**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

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

*hIf*ð Þ*i*

*<sup>j</sup>*¼<sup>0</sup>½ � *R i*ð Þ� , *<sup>j</sup> F i*ð Þ , *<sup>j</sup>*

2

*<sup>i</sup>*¼<sup>0</sup> *<sup>i</sup>* � *<sup>i</sup>* � �<sup>2</sup>

Where hIf(i) is the normalized histogram of the fused image; L is the number of

*MXN*

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

<sup>2</sup> s

*MXN*

*<sup>j</sup>*¼<sup>0</sup>½ � *R i*ð Þ� , *<sup>j</sup> F i*ð Þ , *<sup>j</sup>*

ð Þ *<sup>L</sup>* � <sup>1</sup> <sup>2</sup>

*MSE* (8)

P*<sup>N</sup>*�<sup>1</sup>

**Root Mean Square Error (RMSE):** The error between fused image F and

P*<sup>N</sup>*�<sup>1</sup>

PSNR is the ratio between the maximum possible power of a signal and the

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

**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

*<sup>H</sup>* ¼ �<sup>X</sup> *L*�1

*σ* ¼

*MSE* ¼

*RMSE* ¼

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

the CT image of set 1 is shown in **Figure 2(b)**.

The PSNR measure is given by

**5. Results and discussion**

method.

**67**

Where R is reference image and F is fused image.

The higher the PSNR value, better the fusion process.

r

P*<sup>M</sup>*�<sup>1</sup> *i*¼0

> P*<sup>M</sup>*�<sup>1</sup> *i*¼0

power of corrupting noise that affects the fidelity of its representation.

*PSNR* ¼ 10 ∗ log <sup>10</sup>

**Entropy:** Entropy is a measure of the information content in an image. An image

*pi* log *pi*

� � (4)

(5)

(6)

(7)

parameters are listed below:

occurring ith grey level.

grey levels in an image. **Mean Squared Error:**

reference image R is given by,

would have high standard deviation.

with high information will have high entropy.

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

*A Hybrid Image Fusion Algorithm for Medical Applications*

PCA Algorithm:


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 vector, compute the eigenvector and Eigen values and the Eigenvectors 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 image is

$$I\_F(\mathbf{x}, \mathbf{y}) = P\_1 \ast I\_1(\mathbf{x}, \mathbf{y}) + P\_2 \ast I\_2(\mathbf{x}, \mathbf{y}) \tag{3}$$

Where P1 and P2 are the principal components.
