Results obtained

Our image databases consists of 2660 24-bit color images. Database #1 consists of 2139 images of size adjusted to $1024 \times 1024$ acquired from two CDs obtained from The Visual Delights Inc. (http://www.visualdelights.net).

**Figure 5:** Retrieval by image query (Databases #1 & #2): A building facade.
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Figures 4 - 5 display examples of image retrieval by query from both databases #1 and #2 utilizing equation 19. First 16 images retrieved are shown in both figures. Tables 1 - 4 display results for retrieval by image classification obtained using a nearest neighbor classifier and using $\Phi_{\cal SHT}$ 's as patterns (equation 17). The image space is partitioned into three classes, Structure, Non-structure and Intermediate, based upon the measure of structure present in an image. Each class is represented by 10 training samples.

Table 1: Retrieval by image classification (Database #2): Overall retrieval rate. T = Total # of images, D = Effective # of images, C = Correct and RR = Retrieval rate.

Total	Training	Effective	Correct	RR
T		D	C	(C/D)
521	30	491	363	73.93%

Table 1 shows the overall retrieval rate. Table 2 displays class-conditional retrieval performance measured in terms of recall and precision. Recall is defined as the fraction of the total number of images that are correctly retrieved for a particular class. Precision is defined as the fraction of images retrieved for a particular class that are actually correct. The retrieval statistics are shown fully in the confusion matrix shown in Table 3. Table 4 shows the distribution of images that actually belong to a particular class within the ``best matches'' for that class, in intervals of 100 images, and the corresponding efficiency of the system. Efficiency is defined as the ratio of the number of images that actually belong to a particular class in the block of closest best matches, to the size of the block, where the block size is equal to the number of images corresponding to that class. The best matches were obtained by sorting images in ascending order based upon their distances from the training samples of each class.

Table 2: Retrieval by image classification (Database #2): Recall and precision. (Database # 2.) T = Total, R = Retrieved, C = Correct.

Class	T	R	C	Recall	Precision
				(C/T)	(C/R)
Structure	255	222	195	76.47%	87.84%
Non-structure	140	144	114	81.43%	79.17%
Intermediate	96	125	54	56.25%	43.20%

Table 3: Retrieval by image classification (Database #2): Confusion matrix. Enteries presented in rows, e.g., 195 Structure class images classified as Structure, 14 as Non-structure, and 46 as Intermediate.

Class	Structure	Non-structure	Intermediate
Structure	195	14	46
Non-structure	1	114	25
Intermediate	26	16	54

Table 4: Retrieval by image classification (Database # 2): Distribution of images actually belonging to a particular class in the ``best matches'' for that class, in intervals of 100 images, and the efficiency of the system. T = Total # of images belonging to a certain class, Q = # of images that actually belong to a certain class in the first T best matches for that class, and Eff. = Efficiency.

Class	1-100	101-200	201-300	301-400	401-500	501-521	T	Q	Eff.=Q/T
Structure	87	70	57	28	13	-	255	190	74.51%
Non-structure	79	43	11	7	-	-	140	108	77.14%
Intermediate	38	32	13	11	2	-	96	36	37.50%