& Multi-resolution Blending and the Oraple Journey

## Partial derivative in \( x \) |
## Partial derivative in \( y \) |

## Gradient Magnitude Image |
## Original |

In this part, we apply a smoothing operator, i.e. the Gaussian filter, to create a blurred version of the original image. This allows us to compute the partial derivatives and gradient magnitude on less noisy images.

## Partial derivative in \( x \)## Computed from blurred image |
## Partial derivative in \( y \)## Computed from blurred image |

## Gradient Magnitude Image## Computed from blurred image |
## Gradient Magnitude Image## Previous version |

## Derivative of Gaussian filter \( D_x \) |
## Derivative of Gaussian Filter \( D_y \) |

## Blurred Taj Mahal image |
## Sharpened 0.5x |
## Sharpened 1x |

## Sharpened 1.5x |
## Sharpened 2x |
## Sharpened 2.5x |

## Mt. Tamalpais |
## Mt. Tamalpais (Blurred) |

Now, to sharpen the image again:

## Blurred Mt. Tam image |
## Sharpened 0.5x |
## Sharpened 1x |

## Sharpened 1.5x |
## Sharpened 2x |
## Sharpened 2.5x |

## Derek Picture |
## Nutmeg Picture |
## Hybrid Picture |

## Ed Sheeran |
## Nutmeg Picture |
## Hybrid Picture |

## Input Image: Ed Sheeran |
## Input Image: Squirrel |

## Filtered Image: Ed Sheeran |
## Filtered Image: Squirrel |

## Hybrid Image |

## Uncolored output |
## Colored low-pass filter |
## Colored high-pass filter |

Now, what if we used colors in both high-frequency and low-frequency components?

In this example, this is also a viable approach. However, I like the results that used colored high-pass filter better.

I think for different hybrid images, the visual output will be different each time you try different combinations of weights as well as choices of filters to retain color. It's quite challenging to definitively say which approach will always work the best.
## Porsche 911 |
## Frog |
## Hybrid Picture |

## Joker |
## Frog |
## Hybrid Picture |

## Apple |
## Orange |
## Apple (Masked) |
## Orange (Masked) |
## Blended |

To deliver the final result, we blend the corresponding levels of the Laplacian stacks of the two images using a Gaussian mask, and then collapse the final image.

## Result |

## Input |
## Output |

## Input 1 |
## Input 2 |

## Irregular mask |
## Result |