Chapter 1 Introduction
4.5 Parameter Tuning Details
4.5.5 Min-Hash
Here we have similar parameters pertaining to the dictionary: number of words and how the dictionary is generated. In addition, we have two more parameters: T the number of hash tables andH the number of hash functions. We try 1, 5, 25, and 100 tables with 1, 2, and 3 hash functions. Based on the results in Figure 4.16, which show these combinations with different dictionary sizes and dictionary generation, we chose to go ahead with AKM dictionary with 1 M words and using 25 and 100 tables with 1 hash function. Figure 4.17 shows the results of these combinations on the four scenarios, after which we chose (T,H) = (100,1)for the benchmark. We notice the following:
• Min-Hash performance is generally worse than Inverted File. This is expected, as it is just an approximation that works best for near identical images, and not for images with large distortions [12, 13].
• Geometric consistency checks are crucial for Min-Hash, as the first step provides very poor performance.
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ivf−none−l1−l1 ivf−none−l2−l2 ivf−tfidf−l2−cos ivf−bin−l1−l1 ivf−bin−l2−l2
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bow−akmeans−100k
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ivf−none−l1−l1 ivf−none−l2−l2 ivf−tfidf−l2−cos ivf−bin−l1−l1 ivf−bin−l2−l2
102 103 104 105
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bow−akmeans−1M
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bow−akmeans−1M
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102 103 104 105
10−2 10−1 100 101 102
bow−akmeans−1M
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ivf−none−l1−l1 ivf−none−l2−l2 ivf−tfidf−l2−cos ivf−bin−l1−l1 ivf−bin−l2−l2
102 103 104 105
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bow−hkm−1M
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ivf−none−l1−l1 ivf−none−l2−l2 ivf−tfidf−l2−cos ivf−bin−l1−l1 ivf−bin−l2−l2
Figure 4.14: Quick Tuning for Inverted File. Rows correspond to dictionaries: akm- 10K, akm-100K, 1km-1M, and hkm-1M, where the number corresponds to the number of words. First column depicts the recognition performance before geometric checks, second column shows the search time through the inverted file, third column shows the recognition performance after geometric step, while the fourth column shows the geometric check time.
Based on the results, we chose AKM dictionaries with 1 M visual words and the three combinations {tf-idf,l2,cos}, {bin,l2,l2}, and {none,l1,l1} for the full tuning in Figure 4.15.
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ivf−none−l1−l1 ivf−tfidf−l2−cos ivf−bin−l2−l2
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Scenario 4
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Figure 4.15: Full Tuning for Inverted File. Plots the results for the parameters chosen based on Figure 4.14.
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minhash−t1−f1 minhash−t1−f2 minhash−t1−f3 minhash−t5−f1 minhash−t5−f2 minhash−t5−f3 minhash−t25−f1 minhash−t25−f2 minhash−t25−f3 minhash−t100−f1 minhash−t100−f2 minhash−t100−f3
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bow−akmeans−1M
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bow−hkm−1M
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Performance (before)
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bow−hkm−1M
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bow−hkm−1M
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bow−hkm−1M
Number of Images
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Figure 4.16: Quick Tuning for Min-Hash. Rows correspond to dictionaries: akm-10K, akm-100K, akm-1M, and hkm-1M, where the number corresponds to the number of words.
First column depicts the recognition performance before geometric checks, second column shows the search time through the inverted file, third column shows the recognition per- formance after geometric step, while the fourth column shows the geometric check time.
We triedT =1, 5, 25, and 100 tables withH =1, 2, and 3 hash functions. Based on these results, we chose AKM dictionaries with 1 M visual words, T =25 and 100 tables with H=1 for full tuning in Figure 4.17.
102 103 104 105 0
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minhash−t25−f1 minhash−t100−f1
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Figure 4.17: Full Tuning for Min-Hash. Plots results for the four scenarios for the param- eters chosen in Figure 4.16. Based on these results, we choseT =100 tables withH =1 hash function.
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