Explain Inverse warping algorithm for creating an image g(x) from an image f(x) using the parametric transform x= h(x)

Explain Inverse warping algorithm for creating an image g(x) from an image f(x) using the parametric transform x= h(x)

Answer:-

In image processing and computer vision, geometric transformations are used to change the spatial layout of an image. The inverse warping algorithm is a technique where we generate the output image g(x) by mapping each output pixel back to a corresponding position in the source image f(x) using the inverse of a given transformation function.

The given forward transformation is:

x' = h(x)

In inverse warping, we use the inverse of this transformation:

x = h⁻¹(x')

Algorithm Steps

1. Loop over each pixel x' in the output image g(x'):
   • Apply inverse mapping: x = h⁻¹(x')
   • Sample the source image f(x) at the location x
   • Assign: g(x') = f(h⁻¹(x'))
2. Repeat for all output pixels

Interpolation

Since x = h⁻¹(x') may not fall exactly on integer coordinates in the source image f(x), interpolation is required to estimate the value at non-grid locations.

Common interpolation methods:

• Nearest neighbor: fast but low quality
• Bilinear: better accuracy with smooth results
• Bicubic: higher-quality interpolation

Advantages Over Forward Warping

• No holes: Every pixel in g(x') is filled because we compute it explicitly.
• More accurate control: Output resolution and sampling are determined by the output grid.
• Preferred in practice: Especially in vision tasks like image alignment, morphing, and registration.

Example Use Cases

• Image alignment and registration
• Panorama stitching using homographies
• Geometric rectification
• Video stabilization

Pseudocode (Optional)

for each output pixel x':
    x = inverse_transform(x')   // x = h⁻¹(x')
    g(x') = interpolate(f, x)
  

Comparison with Forward Warping