The document provides an overview of the SIFT algorithm, detailing the key mathematical formulas involved in stages such as Gaussian filtering, difference-of-Gaussians, and keypoint descriptor computation. It explains concepts like scale-space construction, keypoint matching using methods like Euclidean distance and Lowe's ratio test, and highlights the use of the Histogram of Oriented Gradients for keypoint descriptors. The text emphasizes SIFT's applications in object recognition, image stitching, and 3D reconstruction.

1. THE SIFT
ALGORITHM
AND ITS
FORMULAS
An overview of the SIFT algorithm and the key
mathematical formulas used in its different stages,
including Gaussian filtering, Difference-of-
Gaussians, and keypoint descriptor computation.

2. GAUSSIAN FILTER

3. DIFFERENCE-OF-GAUSSIANS (DOG)
• Scale-Space Construction
• Difference-of-Gaussians
• Mathematical Formulation
• Purpose of DoG

4. KEYPOINT DESCRIPTOR (EXAMPLE: HOG)
Keypoint Descriptor
Formulas
HOG (Histogram of
Oriented Gradients)
HOG Descriptor Calculation
HOG Descriptor Formula Keypoint Matching

5. KEYPOINT MATCHING
Euclidean Distance
Lowe's Ratio Test
Feature Vector Similarity
Descriptor Comparison

6. SIFT ALGORITHM OVERVIEW
Gaussian Filter
Difference-of-Gaussians
(DoG)
Keypoint Descriptor
(Example: Histogram of
Oriented Gradients - HOG)
Keypoint Matching

7. KEY FORMULAS IN SIFT
Gaussian Filter
85%
Difference-of-Gaussians
(DoG)
90%
Histogram of Oriented Gradients
(HOG) Descriptor
80%
Keypoint Matching
75%

8. SIFT IN ACTION
Object Recognition Image Stitching 3D Reconstruction

9. SIFT'S MATHEMATICAL FOUNDATION
Gaussian Filter Difference-of-Gaussians (DoG) Keypoint Descriptor (Histogram of
Oriented Gradients)
Keypoint Matching Combination of Techniques