Fundamentals of Machine Learning

Chenyi Chen

What’s learning? • Example problem: face recognition

Prof. K

Prof. F

Prof. P

Prof. V


• Training data: a collection of images and labels (names)

Who is this guy?

• Evaluation criterion: correct labeling of new images

What’s learning? • Example problem: scene classification






• a few labeled training images

What’s the label of this image?

• goal to label yet unseen image

Why learning? • The world is very complicated • We don’t know the exact model/mechanism between input and output • Find an approximate (usually simplified) model between input and output through learning • Principles of learning are “universal” – society (e.g., scientific community) – animal (e.g., human) – machine

A Taste of Machine Learning

True label

Estimated label We want to minimize the difference between them!

Artificial Neural Network

Fundamentals of Computer Vision

Chenyi Chen

What is Computer Vision? • Input: images • Output: information about the world

What is Computer Vision? Example: • What is in this image? • Who is in this image? • Where are they? • What are they doing?

What is Computer Vision? Other questions: • What camera settings were used? • Which pixels go with which objects? • What is the scene description in 3D?

Camera Projection

Camera Projection

Camera Projection

Dimensionality Reduction Machine (3D to 2D) 3D world

2D image

Point of observation

What have we lost? Slide by A. Efros Figures © Stephen E. Palmer, 2002

A Tale of Two Coordinate Systems v





Two important coordinate systems: 1. World coordinate system z 2. Camera coordinate system


o “The World”

Geometric Transformations

What is the geometric relationship between these two images?


Image alignment

Why don’t these image line up exactly?

What is the geometric relationship between these two images?

Very important for creating mosaics!

2D image transformations

These transformations are a nested set of groups • Closed under composition and inverse is a member

Projective Transformations / Homographies

Called a homography (or planar perspective map)

Image warping with homographies

image plane in front

image plane below black area where no pixel maps to


A Quick Application: Lane Detection

Lane Detection

Lane Detection

Stereo Vision

A Taste of Stereo Vision

Visual Odometry, Structure-from-Motion, 3D Street Scene Reconstruction

KITTI Datasets • • • • • •

Stereo images Grayscale Color Rectified 1382*512 10 FPS

Visual Odometry • Visual odometry computes the trajectory of the vehicle only based on image sequences (LIBVISO2)

Depth Map • Disparity map is computed from grayscale stereo image pairs (LIBELAS) • Depth map can be derived from disparity map and camera model

Lane Detection • Projecting lane markers on the road (Caltech Lane Detector)

3D Street Scene Reconstruction

+ +

3D Street Scene Reconstruction • Dense reconstruction on run_70

Reconstruction with Non-Stereo Images/Structure-from-Motion • Triangulation: tracking a same point in three (or more) frames, its spatial position can be determined

Figure courtesy of Jianxiong Xiao

Sparse Reconstruction with Non-Stereo Images • Sparse reconstruction on run_70

Sparse Reconstruction with Non-Stereo Images • run_1

Sparse Reconstruction with Non-Stereo Images • run_9

Other Demos for Structure-from-Motion • a8 • YoTg

Other Demos for Structure-from-Motion

Other Demos for Structure-from-Motion

Deep Learning

The end of all the fundamentals

Vision Based Self-driving Car - Princeton University

The world is very complicated. • We don't know the exact model/mechanism between input and output. • Find an approximate (usually simplified) model between input and output through learning. • Principles of learning are “universal”. – society (e.g., scientific community). – animal (e.g., human). – machine ...

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