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摘要: 针对视觉词袋（Bag-of-visual-words，BOVW）模型直方图量化误差大的缺点，提出基于稀疏编码的图像检索算法.由于大多数图像特征属于非线性流形结构，传统稀疏编码使用向量空间对其度量必然导致不准确的稀疏表示.考虑到图像特征空间的流形结构，选择对称正定矩阵作为特征描述子，构建黎曼流形空间.利用核技术将黎曼流形结构映射到再生核希尔伯特空间，非线性流形转换为线性稀疏编码，获得图像更准确的稀疏表示.实验在Corel1000和Caltech101两个数据集上进行，与已有的图像检索算法对比，提出的图像检索算法不仅提高了检索准确率，而且获得了更好的检索性能.Abstract: In the BOVW (bag-of-visual-words) model, histogram quantization would result in a bigger error for image retrieval. Considering this shortcoming, a new image retrieval algorithm based on sparse coding is proposed. Most image features belongs to nonlinear manifold structure, but the traditional sparse coding uses vector space to measure image feature space, which must lead to an inaccurate sparse representation. Owing to the manifold structure of image features space, symmetric positive definite matrices are selected as feature descriptors to build a Riemannian manifold space. Through the kernel method, the Riemann manifold structure is mapped into the reproducing kernel Hilbert space, and nonlinear manifold is converted into linear sparse coding, so the image can acquire a more accurate sparse representation. Experiments are performed on the Corel1000 database and Caltech101 database. In comparison with the existing image retrieval algorithms, the new image retrieval algorithm largely improves the retrieval accuracy and has a better efficiency.1) 本文责任编委 贾云得
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图 1 Corel1000数据集字典大小对检索准确率的影响
Fig. 1 The influence of dictionary size on the retrieval accuracy on Corel1000 database
图 2 Caltech101数据集字典大小对检索准确率的影响
Fig. 2 The influence of dictionary size on the retrieval accuracy on Caltech101 database
图 3 Corel1000数据集两类算法检索对比图
Fig. 3 The retrieval accuracy contrastive figure of two algorithms on Corel1000 database
图 4 Caltech101数据集两类算法检索对比图
Fig. 4 The retrieval accuracy contrastive figure of two algorithms on Caltech101 database
图 5 Corel1000数据集各类算法 $F_{1}$ -measure对比图
Fig. 5 The $F_{1}$ -measure contrastive figure of different algorithms on Corel1000 database
图 6 Corel1000数据集各类算法检索结果示例
Fig. 6 A few retrieval examples on Corel1000 database by different algorithms
图 7 Caltech101数据集各类算法 $F_{1}$ -measure对比图
Fig. 7 The $F_{1}$ -measure contrastive figure of different algorithms on Caltech101 database
图 8 Caltech101数据集各类算法检索结果示例
Fig. 8 A few retrieval examples on Caltech101 database by different algorithms
表 1 Corel1000数据集各类算法MAP值对比
Table 1 The MAP contrastive results of different algorithms on Corel11000 database
各类算法 MAP (%) Error n-Grams算法 42.31 士0.0729 LTrPs算法 54.25 士0.0533 RMSC算法 54.25 士0.0468 
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表 2 Caltech101数据集各类算法MAP值对比
Table 2 The MAP contrastive results of different algorithms on Caltech101 database
各类算法 MAP (%) Error n-Grams算法 28.32 士0.0898 LTrPs算法 43.81 士0.0732 RMSC算法 51.31 士0.0539
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表 3 Caltech101数据集的图像类别
Table 3 The image classification on Caltech101 database
1~17类 18~34类 35~51类 52~68类 69~85类 86~101类 1 faces 18 camera 35 dragonfly 52 ibis 69 okapi 86 stapler 2 faces_easy 19 cannon 36 electric_guitar 53 inline_skate 70 pagoda 87 starfish 3 leopards 20 car_side 37 elephant 54 joshua_tree 71 panda 88 stegosaurus 4 motorbikes 21 ceiling_fan 38 emu 55 kangaroo 72 pigeon 89 stop_sign 5 accordion 22 cellphone 39 euphonium 56 ketch 73 pizza 90 strawberry 6 airplanes 23 chair 40 ewer 57 lamp 74 platypus 91 sunflower 7 anchor 24 chandelier 41 ferry 58 laptop 75 pyramid 92 tick 8 ant 25 cougar_body 42 flamingo 59 llama 76 revolver 93 trilobite 9 barrel 26 cougar_face 43 flamingo_head 60 lobster 77 rhino 94 umbrella 10 bass 27 crab 44 garfield 61 lotus 78 rooster 95 watch 11 beaver 28 crayfish 45 gerenuk 62 mandolin 79 saxophone 96 water」illy 12 binocular 29 crocodile 46 gramophone 63 mayfly 80 schooner 97 wheelchair 13 bonsai 30 crocodile_head 47 grand_piano 64 menorah 81 scissors 98 wild_cat 14 brain 31 cup 48 hawksbill 65 metronome 82 scorpion 99 windsor_chair 15 brontosaurus 32 dalmatian 49 headphone 66 minaret 83 sea_horse 100 wrench 16 buddha 33 dollar_bill 50 hedgehog 67 nautilus 84 snoopy 101 yin_yang 17 butterfly 34 dolphin 51 helicopter 68 octopus 85 soccer_ball
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