Pigments identification of paintings using subspace distance unmixing algorithm

2018 ◽  
Author(s):  
Shuqiang Lyu ◽  
Bin Li ◽  
Dafeng Zhang ◽  
Qinghao Dong
Keyword(s):  
Subspace Distance

Weighted Subspace Distance and Its Applications to Object Recognition and Retrieval With Image Sets

2009 ◽  
Vol 16 (3) ◽  
pp. 227-230 ◽  
Author(s):  
Fei Li ◽  
Qionghai Dai ◽  
Wenli Xu ◽  
Guihua Er
Keyword(s):  
Object Recognition ◽  
Subspace Distance

scholarly journals A Proposal-Based Approach for Activity Image-to-Video Retrieval

2020 ◽  
Vol 34 (07) ◽  
pp. 12524-12531
Author(s):  
Ruicong Xu ◽  
Li Niu ◽  
Jianfu Zhang ◽  
Liqing Zhang
Keyword(s):  
Video Retrieval ◽  
Structural Information ◽  
Retrieval Task ◽  
Query Image ◽  
Similar Activity ◽  
Triplet Loss ◽  
Subspace Distance

Activity image-to-video retrieval task aims to retrieve videos containing the similar activity as the query image, which is a challenging task because videos generally have many background segments irrelevant to the activity. In this paper, we utilize R-C3D model to represent a video by a bag of activity proposals, which can filter out background segments to some extent. However, there are still noisy proposals in each bag. Thus, we propose an Activity Proposal-based Image-to-Video Retrieval (APIVR) approach, which incorporates multi-instance learning into cross-modal retrieval framework to address the proposal noise issue. Specifically, we propose a Graph Multi-Instance Learning (GMIL) module with graph convolutional layer, and integrate this module with classification loss, adversarial loss, and triplet loss in our cross-modal retrieval framework. Moreover, we propose geometry-aware triplet loss based on point-to-subspace distance to preserve the structural information of activity proposals. Extensive experiments on three widely-used datasets verify the effectiveness of our approach.

scholarly journals On sets of subspaces with two intersection dimensions and a geometrical junta bound

2021 ◽  
Author(s):  
Giovanni Longobardi ◽  
Leo Storme ◽  
Rocco Trombetti
Keyword(s):  
Vector Space ◽  
Upper Bound ◽  
Subspace Codes ◽  
Constant Dimension ◽  
Subspace Distance

AbstractIn this article, constant dimension subspace codes whose codewords have subspace distance in a prescribed set of integers, are considered. The easiest example of such an object is a junta (Combin Probab Comput 18(1–2):107–122, 2009); i.e. a subspace code in which all codewords go through a common subspace. We focus on the case when only two intersection values for the codewords, are assigned. In such a case we determine an upper bound for the dimension of the vector space spanned by the elements of a non-junta code. In addition, if the two intersection values are consecutive, we prove that such a bound is tight, and classify the examples attaining the largest possible dimension as one of four infinite families.

Bounds on Subspace Codes Based on Orthogonal Space Over Finite Fields of Characteristic 2

2019 ◽  
Vol 30 (05) ◽  
pp. 735-757
Author(s):  
Gang Wang ◽  
Min-Yao Niu ◽  
Fang-Wei Fu
Keyword(s):  
Linear Programming ◽  
Positive Integer ◽  
Finite Fields ◽  
Sphere Packing ◽  
Singular Subspace ◽  
Subspace Codes ◽  
Orthogonal Space ◽  
Johnson Bound ◽  
Characteristic 2 ◽  
Subspace Distance

In this paper, the Sphere-packing bound, Wang-Xing-Safavi-Naini bound, Johnson bound and Gilbert-Varshamov bound on the subspace code of length [Formula: see text], size [Formula: see text], minimum subspace distance [Formula: see text] based on [Formula: see text]-dimensional totally singular subspace in the [Formula: see text]-dimensional orthogonal space [Formula: see text] over finite fields [Formula: see text] of characteristic 2, denoted by [Formula: see text], are presented, where [Formula: see text] is a positive integer, [Formula: see text], [Formula: see text], [Formula: see text]. Then, we prove that [Formula: see text] codes attain the Wang-Xing-Safavi-Naini bound if and only if they are certain Steiner structures in [Formula: see text], where [Formula: see text] denotes the collection of all the [Formula: see text]-dimensional totally singular subspaces in the [Formula: see text]-dimensional orthogonal space [Formula: see text] over [Formula: see text] of characteristic 2. Finally, Gilbert-Varshamov bound and linear programming bound on the subspace code [Formula: see text] in [Formula: see text] are provided, where [Formula: see text] denotes the collection of all the totally singular subspaces in the [Formula: see text]-dimensional orthogonal space [Formula: see text] over [Formula: see text] of characteristic 2.

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