Bag of Visual Words for Image Representation & Visual Search Jianping Fan Dept of Computer Science UNC-Charlotte

1. Interest Point Extraction & SIFT 2. Clustering for Dictionary Learning 3. Bag of Visual Words 4. Image Representation & Applications Bag-of-Visual-Words

Interest Point Extraction Scale-space extrema detection –Uses difference-of-Gaussian function Keypoint localization –Sub-pixel location and scale fit to a model Orientation assignment –1 or more for each keypoint Keypoint descriptor –Created from local image gradients

Scale space Definition: where Interest Point Extraction

Scale space Keypoints are detected using scale-space extrema in difference-of-Gaussian function D D definition: Efficient to compute

Relationship of D to Close approximation to scale-normalized Laplacian of Gaussian, Diffusion equation: Approximate ∂G/∂σ: –giving, When D has scales differing by a constant factor it already incorporates the σ 2 scale normalization required for scale-invariance

Interest Point Extraction

Difference-of-Gaussian images … first octave … … second octave … … third octave … fourth octave … …

Finding extrema Sample point is selected only if it is a minimum or a maximum of these points DoG scale space Extrema in this image

Localization 3D quadratic function is fit to the local sample points Start with Taylor expansion with sample point as the origin –where Take the derivative with respect to X, and set it to 0, giving is the location of the keypoint This is a 3x3 linear system

Localization Derivatives approximated by finite differences, –example: If X is > 0.5 in any dimension, process repeated

Filtering Contrast (use prev. equation): –If | D(X) | < 0.03, throw it out Edge-iness: –Use ratio of principal curvatures to throw out poorly defined peaks –Curvatures come from Hessian: –Ratio of Trace(H) 2 and Determinant(H) –If ratio > (r+1) 2 /(r), throw it out (SIFT uses r=10)

Orientation assignment Descriptor computed relative to keypoint’s orientation achieves rotation invariance Precomputed along with mag. for all levels (useful in descriptor computation) Multiple orientations assigned to keypoints from an orientation histogram –Significantly improve stability of matching

Keypoint images

Descriptor Descriptor has 3 dimensions (x,y,θ) Orientation histogram of gradient magnitudes Position and orientation of each gradient sample rotated relative to keypoint orientation

Descriptor Best results achieved with 4x4x8 = 128 descriptor size Normalize to unit length –Reduces effect of illumination change Cap each element to 0.2, normalize again –Reduces non-linear illumination changes –0.2 determined experimentally

PCA-SIFT Different descriptor (same keypoints) Apply PCA to the gradient patch Descriptor size is 20 (instead of 128) More robust, faster

Interest Points & SIFT Features

Summary Scale space Difference-of-Gaussian Localization Filtering Orientation assignment Descriptor, 128 elements

Dictionary Learning

Quantization for Identification

28 Sparse Coding & Dictionary Learning Dictionary learning and sparse coding Sparse factor analysis model (Factor/feature/dish/dictionary atom) Indian Buffet process and beta process

Dictionary Learning

Image Representation via Bag-of-Visual-Words Dictionary

Application for Visual Search

How to do database indexing?

Application for Visual Search Visual Phrases & Contexts?

Multi-Resolution SIFT