Null-Space representation for view-invariant motion trajectory classification-recognition and indexing-retrieval

Abstract

This paper presents a novel classification/ retrieval system for motion events based on a perfect view invariant representation of motion trajectories and a linear classifier algorithm. Specifically, Null Space Invariant (NSI) matrix representation for motion trajectories has been derived. The proposed view invariant representation based on the NSI operator is invariant to affine transformations and preserves the null space matrix. We use principal component null space analysis (PC-NSA) for indexing and classification of the NSI operator for recognition and retrieval of motion events. We rely on PC-NSA to determine the distance of the query trajectory to the centroid of each class, which is a statistical information vector in the PCNSA algorithm representing the corresponding motion class. Our results show that NSI provides a powerful approach to motion event recognition and retrieval that is invariant to affine transformations due to camera motion.

Trajectory-based sign language recognition using Discriminant Analysis in higher-dimensional feature space

“…It is a popular benchmark dataset in the recent years [8,5,9,10,11]. It contains trajectory samples of 95 ASL signs performed by 5 persons.…”

“…In the past researches, much of prior work in motion trajectory recognition only utilizes 2D trajectories, e.g., ( , ) coordinates of a subject's hand position [8,5,9,10]. However, the -coordinate can tell us whether a signer's hand is moving forward or backward.…”

Vision‐based road slope estimation methods using road lines or local features from instant images

“…CB classification is a supervised learning technique, which learns from known road lines to create its training information set. The algorithm is also called as PCNSA, which is a powerful tool to classify many objects in a test group [23–25]. In this paper, we use this method which was originally designed for classification problems, for road slope estimation.…”

“…Here, LFB method does not need the road lines and it estimates the road slope when the vehicle first experiences the change in road structure. As a third method, we call principal component null space analysis (PCNSA) as the covariance‐based (CB) method, which first constructs a covariance matrix between left and right road lines as in [23–25]. Then, principal component analysis (PCA) is used for dimension reduction of covariance matrix by suppressing noisy components and for finding the null space after dimension reduction.…”