In this paper, we show that a multiplication operator on the Dirichlet space D is unitarily equivalent to Dirichlet shift of multiplicity n ＋ 1 （n ≥ 0） if and only if its symbol is c zn＋1 for some constant c. The...In this paper, we show that a multiplication operator on the Dirichlet space D is unitarily equivalent to Dirichlet shift of multiplicity n ＋ 1 （n ≥ 0） if and only if its symbol is c zn＋1 for some constant c. The result is very different from the cases of both the Bergman space and the Hardy space.展开更多
In this paper, we propose an automatic classification for various images collections using two stage clustering method. Here, we have used global and local image features. First, we review about various types of featu...In this paper, we propose an automatic classification for various images collections using two stage clustering method. Here, we have used global and local image features. First, we review about various types of feature vector that is suita-ble to represent local and global properties of images, and similarity measures that can be represented an affinity be-tween these images. Second, we consider a clustering method for image collection. Here, we first build a coarser clus-tering by partitioning various images into several clusters using the flexible Mean shift algorithm and K-mean cluster-ing algorithm. Second, we construct dense clustering of images collection by optimizing a Gaussian Dirichlet process mixture model taking initial clusters as given coarser clustering. Finally, we have conducted the comparative experi-ments between our method and existing methods on various images datasets. Our approach has significant advantage over existing techniques. Besides integrating temporal and image content information, our approach can cluster auto-matically photographs without some assumption about number of clusters or requiring a priori information about initial clusters and it can also generalize better to different image collections.展开更多
基金Supported by Tianyuan Foundation of China (Grant No. 10926143)Young Science Foundation of Shanxi Province(Grant No. 2010021002-2)+2 种基金the National Natural Science Foundation of China (Grant No. 10971195)the Natural Science Foundation of Zhejiang Province (Grant Nos. Y6090689 Y6110260)
文摘In this paper, we show that a multiplication operator on the Dirichlet space D is unitarily equivalent to Dirichlet shift of multiplicity n ＋ 1 （n ≥ 0） if and only if its symbol is c zn＋1 for some constant c. The result is very different from the cases of both the Bergman space and the Hardy space.
文摘In this paper, we propose an automatic classification for various images collections using two stage clustering method. Here, we have used global and local image features. First, we review about various types of feature vector that is suita-ble to represent local and global properties of images, and similarity measures that can be represented an affinity be-tween these images. Second, we consider a clustering method for image collection. Here, we first build a coarser clus-tering by partitioning various images into several clusters using the flexible Mean shift algorithm and K-mean cluster-ing algorithm. Second, we construct dense clustering of images collection by optimizing a Gaussian Dirichlet process mixture model taking initial clusters as given coarser clustering. Finally, we have conducted the comparative experi-ments between our method and existing methods on various images datasets. Our approach has significant advantage over existing techniques. Besides integrating temporal and image content information, our approach can cluster auto-matically photographs without some assumption about number of clusters or requiring a priori information about initial clusters and it can also generalize better to different image collections.
