You are given an image represented by an `m x n` integer grid `image` where `image[i][j]` represents the pixel value of the image. You are also given three integers `sr`, `sc`, and `color`.
Perform a **flood fill** starting from the pixel `image[sr][sc]`. To perform a flood fill, consider the starting pixel, plus any pixels connected 4-directionally to the starting pixel of the same color as the starting pixel, plus any pixels connected to those pixels (also with the same color), and so on. Replace the color of all of the aforementioned pixels with `color`.
Return the modified image after performing the flood fill.
**Example 1:**
```
Input: image = [[1,1,1],[1,1,0],[1,0,1]], sr = 1, sc = 1, color = 2
Output: [[2,2,2],[2,2,0],[2,0,1]]
```
**Example 2:**
```
Input: image = [[0,0,0],[0,0,0]], sr = 0, sc = 0, color = 0
Output: [[0,0,0],[0,0,0]]
```