1. GEOMETRIC TRANSFORMATIONS
• It is the conversion of existing digital map or images into GIS projected co-
ordinated system
• Map to Map transformation: Transforming a digital map into a GIS
projected co-ordinated system
• Image to map transformation: Transforming a satellite image into a GIS
projected co-ordinated system
2. g(x) = f (h(x))
• h(x) is the inner function, which first transforms x.
• f( )
⋅ is the outer function, which then acts on the result of h(x).
• g(x) is the final result after applying both functions.
So, instead of applying f(x) directly, we first transform x using
h(x), then apply f to the result.
3. • Parametric transformations apply a global deformation to an image,
where the behavior of the transformation is controlled by a small number
of parameters
Parametric transformations
• These transformations are widely used in computer vision, image
processing, and computer graphics for tasks like image warping,
registration, and augmentation.
4. GEOMETRIC METHODS
• Euclidean Transformation: Allows rotation but preserves shape and
size of existing map
• Similarity transformation: Allows rotation but preserves shape of
map but not size
• Affine transformation: Allows angular distortion but preserves
parallelism of map. That is parallel sides remain parallel even after
transformation
• Projective transformation: Allows angular distortion and length
distortion
7. Forward Warping (Forward Mapping)
• A transformation method where each pixel in the source image is
mapped forward to a new location in the destination image using a
transformation function.
x′ = h(x)
• x is the pixel in the source image.
• x' is the transformed pixel location in the destination image.
• h(x) is the transformation function that determines where each
source pixel moves.
8. Forward warping algorithm: (a) a pixel f (x) is copied to its corresponding
location x′
= h(x) in image g(x′
); (b) detail of the source and destination pixel
locations.
9. • Successive transformations applied step-by-step instead of a single operation to
improve accuracy and quality.
Multi-pass transforms
• Reduces artifacts (blurring, aliasing, noise).
• Enhances image quality and feature extraction.
• Improves accuracy in object detection and motion tracking.
10. Multi-pass transforms
(a) sparse control points −→ deformation grid; (b) denser set of
control point corre- spondences; (c) oriented line
correspondences; (d) uniform quadrilateral grid.
11. Feature-based morphing
• Feature-based image morphing is a method where the transformation
between two images is driven by aligning and blending specific features
(such as edges, corners, or points of interest) from both images.
• Image morphing is a technique used to smoothly transition between two
images by applying geometric warping and blending
• If two images are directly blended, ghosting artifacts appear because
features (e.g., eyes, nose, mouth) do not align.
12. • Feature Matching – Identify corresponding control points (e.g.,
facial landmarks).
• Intermediate Warping – Both images are warped towards a
common intermediate shape (e.g., 50% transition).
13. • Blending – The warped images are then combined using a
weighted sum
where t controls the transition between images.
