# A Generic Framework for Enhancing Autonomous Driving Accuracy through Multimodal Data Fusion
## 4 Proposed Study
### Proposed Feature Extraction Models
#### 4.2.3 Proposed Hybrid Fusion Model
The pixel intensity of the 2D image is multiplied by the weighted intensity values of the 3D image pixels using Equation (4). This task is carried out to convert the 2D pixel intensity values to their corresponding 3D pixel intensity values. Advanced matrix and \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Meaning** \\ \hline A & No. of the wavelength of 2D image \\ B & No. of the wavelength of 3D image \\ \(N_{A}\) & No. of pixels in 2D image \\ \(N_{B}\) & No. of pixels in 3D image \\ \(N_{F}\) & No. of pixels in fused 3D image \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Notations used in proposed image fusion model. Figure 9: Functioning of hybrid fusion model. vector operations that are used for the above-mentioned transformations are discussed in the following paragraphs. Algorithm 3 describes the steps involved in the proposed hybrid image fusion algorithm. Before starting the main fusion operations, the wavelength intensities and the pixel intensities of the 2D sentinel images are represented as corresponding row and column items of the image matrix using the below-mentioned equation. \[I_{i}\times N_{j},j,k=I_{i},j,k \tag{5}\]

In the next stage, the multispectral 3D images are extracted from the 2D sentinel images by multiplying the wavelength frequencies \(A\) and \(B\) of panchromatic images with the pixels of the 2D images. This operation is carried out with the help of multiplying Equation (4) by the below-mentioned equation. By carrying out this operation, the pixel values of 2D sentinel images are normalized and converted to 3D image pixel values. \[E_{n}=\sum_{k=0}^{A-1}=A_{n,k}W_{k} \tag{6}\]

Using the new notations, Equation (4) can be rewritten as

\[E_{n}=AW^{t} \tag{7}\]

where \(W\) is the line vector of size \(A\) and components of \(W_{T}\) stand for the action of transposing the image matrix. Though the 2D image pixels are converted to 3D image pixels, the transformation only converts the values; advanced vector projections must be introduced to convert the 2D sentinel image to an actual 3D image. This task is accomplished using Equation (9). ```
1 Input 2D image
2 B:3D GF-3 image
3 Assign Variables
4 A: No of wavelength of 2D image
5 B: No of wavelength of 3D image
6\(N_{A}\): No of pixels in 2D image
7\(N_{B}\): No of pixels in 3D image
8\(N_{F}\): No of pixels in fused 3D image
9 Projection of 2D to 3D
10 For i = 1 to \(N_{A}\) do
11 Step 1: Compute \(w_{i}\) for 2D image matrix
12 Step 2: Compute projection of A on B using equation \(P_{B_{k}}(E)\)
13 End for
14 Transformation to vector
15 For j = 1 to \(N_{B}\)
16 Step 3: Compute \(E\) using equation
17 Step 4: Compute \(B^{\prime}\)using Equation (12)
18 Step 5: Compute S using \(\sigma^{\prime}\) and \(E^{\prime}\) with
19 End For For i = 1 to \(N_{A}\) do
20 Step 6: Compute \(B^{\prime}\) using equation End for for k = 1 to \(N_{F}\)
21 Step 7: Compute RGB intensities for the fused panchromatic
22 Step 8: image projected on a 3D image using Brovey fusion Equation (17)
23 Output
24 Step 9: B = Fused Image
```

**Algorithm 3**Proposed hybrid image fusion algorithm. The general projection of a vector, v, on vector u is performed using the equation

\[P_{v}=\frac{u.v}{u.u}u \tag{8}\]

\[PB_{k}(E)=\frac{B_{k}^{T}.B}{B_{k}^{T}B_{k}}B_{k}. \tag{9}\]

where \(B_{k}\) is a column of vector \(B\). From a statistical point of view, the multispectral image obtained is a combination of any 3D image format along with the weights of the pixel intensities, which are correlated to the pixels of 2D sentinel images [44; 45], thus using a projection operation on every pixel of a 2D image. This calculation with a single weight is really a projection onto a wavelength-specific picture, and the entire computation is identical to summing all projections onto all \((F)\) wavelengths.