Topological Triangular Spatial Relationship - Semantic Scholar

4th Indian International Conference on Artificial Intelligence (IICAI-09)

Topological Triangular Spatial Relationship D.S. Guru1 , S. Manjunath1 , and P. Punitha2 1

2

University of Mysore, Mysore, India University of Glasgow, Glasgow, United Kingdom

Abstract. In this paper, we present a novel scheme for archival and retrieval of symbolic images from a symbolic image database based on Triangular Spatial Relationship [1]. Conventionally, Triangular Spatial Relationship was designed to preserve only spatial relationship among the components in a symbolic image neglecting the topological relationship existing between them, where topological relationship plays a major role in preserving the structure of the symbolic image. Hence in this paper we extend the concept of Triangular Spatial Relationship to Topological Triangular Spatial Relationship. The proposed can handle both spatial as well as topological relationships existing among the components present in the image which is suitable for high level image archival and retrieval. Also, we propose a new similarity measure which takes care of both spatial as well as topological relation for similarity match retrieval and is invariant to image transformations. To study the efficacy of the proposed method we have conducted experimentation on video frames of cartoon film and on a set of personal photographs taken during outings.

1

Introduction

Widespread availability of images in digital form has created a growing interest in designing methods that can archive, search and retrieve images of desired content effectively and efficiently. An efficient image archival and retrieval system is characterized by its ability to retrieve relevant images based on their visual and semantic content rather than using simple attributes or keywords assigned to them [2]. An image archival and retrieval systems can be broadly classified into two categories viz., low level feature and high level feature based image retrieval systems. In low level feature based image retrieval system, low level features such as color, shape, and texture are extracted from the physical images and used for image archival and retrieval. In high level feature based image retrieval system, objects present in images are identified, their spatial and topological relationships is perceived, archived in the database and later used for retrieval. Studying the higher level features among objects abstracts the physical image and enhances the understandability of the content present in images. Hence, an image archival and retrieval system should allow adequate abstraction mechanism for capturing higher level semantics of images in order to support content addressability [3]. That is for two images to be similar not only color, shape and texture should be same but the arrangements of objects should also be similar. In fact, that is

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the strategy, which is being generally employed by human vision system most of the times. Hence, effectiveness of a method of representing images depends on the perception of knowledge embedded in images in terms of objects present in them along with their spatial and topological relationships. Spatial relationship gives the direction/ orientation in which two or more objects are scattered and topological relationship gives how two or more objects are topologically related i.e., overlap, disjoint, contained etc., in an image. Also, processing pixel level physical images in order to capture higher level semantics requires more time and space. So, the objects present in the physical images are identified (manually or semi-automatically) and each object is iconized by icons and placed at the centroid of the minimum bounding rectangle of each object. Figure 1 and Figure 2 show obtained symbolic images for a cartoon image and symbolic image created for the purpose of face recognition [4] respectively. These converted images are treated as symbolic images. Normally in the database, the objects present in the image along with their spatial, topological relationship , their corresponding labels and the physical images are stored. This database is termed as symbolic image database (SID). Given a test image it is converted into equivalent symbolic image, compared with those of the symbolic images present in the symbolic image database and labels of exact or similar images are retrieved. Once the labels are obtained from the system corresponding physical images are retrieved. Archival and retrieval of physical images based on symbolic images takes less time compared to conventional image retrieval systems which are developed using low-level features [5]. Also,symbolic based image archival ad retrieval system preserves the abstract high level features providing more satisfactorily answer the higher level user queries than low level feature based image retrieval.

Fig. 1. (a) Physical image (b) Intermediate image (c) Symbolic image with icons

Image archival and retrieval by high level features can be categorized into three categories viz., exact match retrieval, subimage retrieval and similar image retrieval. The purpose of exact match retrieval is to retrieve images from the database which are identical to the given query image, in subimage retrieval those images which contain query image as a part are retrieved. Similarity retrieval

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Fig. 2. (a) A sample image (b) Manual annotation of the selected dominant points on the face (c) Symbolic image of (a) (d) Symbolic image with labels

finds images from the database which have few/all objects with similar spatial and topological relationship with that of the query image. Detail presentation regarding types of content based image retrieval based on spatial constraints can be found in [6]. Image retrieval based on high level semantics has attained tremendous applications in medical image retrieval [7], line drawing retrieval [8], [9], video retrieval [10], [11], real estate marketing , interior design [5], biometric [4], etc., With these wide range of applications a new way for representing symbolic images in SID suitable for real time application is proposed in this paper. The rest of the paper is organized as follows. Related works are presented in section 2. In section 3 an extension to conventional Triangular Spatial Relationship (TSR) which can preserve both spatial as well as topological relationships among the components is presented. The efficacy of the proposed method is corroborated on a set of cartoon frames extracted from a cartoon movie and outdoor photographs collected at different instant of time is illustrated in section 4. The paper is concluded in Section 5.

2

Related Work

Retrieval by spatial similarity has received considerable attention from many researchers and various methodologies have been proposed. The insinuated methodologies can be broadly classified into two categories, the value oriented viz., Pixel based [12], Quadtree based [13], R-tree based [14], which are shown to be insufficient to deal with complicated operations in an intelligent, fast and flexible manner [15], as they work on low level image features, while other alternative object oriented models receive considerable attention. The object oriented methodologies can be further classified as string based ([16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29]), hash based ([30], [31], [32], [33], [34], [35], [36]), graph based ( [37], [38], [39], [7],[6], [40]), index based ( [7], [41],

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[42],[43], [44],[45], [46], [47]) and matrix based ( [48], [49], [50], [51], [33], [16], [52], [53], [54]; [55]) approaches. Most of the string based representation schemes are not invariant to image transformations. Moreover, they are computationally expensive. The methods claimed to be invariant to rotations are either sensitive to center of the image, or are computationally inefficient and sometimes two dissimilar images are misjudged as similar or two similar images are misjudged as dissimilar. In order to retrieve similar symbolic images from a SID, algorithms ([56],[57],[58]) based on longest common subsequence matching were proposed. However, [59] reported that the subsequence matching fails for some instances. To overcome such false drops,[60] devised an alternative algorithm. The process of string matching takes non-deterministic-polynomial time complexity thus making these algorithms inefficient in practice. The hash table methodologies seem to be efficient. However, even the best known algorithm for the construction of the perfect hash table itself is of exponential time complexity. Updating a static image database requires reconstruction of the entire hash table from the beginning, which is the real bottleneck. The graph based algorithms are model based and have quadratic time complexity in terms of total number of objects in both the database and the query image. In addition, the method gives an approximate match and may miss an actual match at certain times. Many methods focusing on spatial relationships assume sequential search of the entire database ([37],[5]). Thus retrievals can be inefficient as comparisons often involve time intensive operation such as graph matching ([61], [45]). Indexed search is many times faster than sequential scanning even for large answer sets (with more than 10 thousand images) ([45],[44]). Despite of its high complexity, the index based methods treat only special types of relationships and object properties. All the methods assumes that all images and queries are at a known scale and orientation. In addition, some index based methods cannot handle even translation. The index based methods require an expensive preprocessing step for building a tree index structure. In the matrix based models the spatial relationships existing among the m components present in an image are represented by the use of a matrix of order m × m. The memory requirement, even for a small number of images is very high and hence encumbers retrieval.Also most of the matrix based models are not invariant to image transformations. In addition, the method ignores the situations in which there are multiple instances of iconic objects stating that similarity retrieval problem is NP-hard when multiplicity of objects is allowed in picture matching. However, the matrix based approaches, specifically, the 9DLT matrix based approach suffer from considerable problems which are discussed in [62]. Motivated to alleviate the problems of the 9DLT approach, altogether a new concept called Triangular Spatial Relationship (TSR) [1] was proposed as an improved, invariant spatial relationship to take care of image transformations. However, TSR was developed to handle only spatial constraints among the identified objects where, in some cases the topological relationships may play a major role in understanding the image. For instance, consider two images S1 and

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S2 in Fig 3, the TSR treats both as one and the same as both will get the same set of quadruples. This is because TSR can preserve only spatial relationship neglecting topological relationship.

Fig. 3. Two objects 1 and 2 having same spatial relation but different topological relations

Although many models have been proposed for archival and retrieval of symbolic images based on their spatial relationships, only string based methodologies and the matrix based methodologies address the issues of topological relations [48], where two objects can have topological relationships such as disjoint, meet, containing, contained in and overlap. However, the above discussions have revealed the drawbacks of the string based and matrix based methodologies. The problem therefore is to devise an efficient methodology, which is smart enough to take care of image transformations and can rejuvenate to be acceptable for real pragmatic situations supporting both spatial and topological relationships. Motivated by the work of [1], in this paper we extend the concept of Triangular Spatial Relationship towards Topological Triangular Spatial Relationship which can handle both spatial as well as topological relationship among the objects present in the image. We use the same concept of triangular relationship among the components to preserve the spatial relation and to preserve the topological relation among the objects we study the topological relationship among the bounding boxes of the components. Also we modify the concepts of quadruples used in [1] to preserve the spatial relationship among the components present in the image. Instead of quadruples we create triplets to preserve the spatial relationship and Topological relationship among components. These triplets are called as Topological Triangular Spatial Relationship keys (Topological TSR keys).

3

Proposed Methodology

The proposed methodology consists of two stages. Stage 1 corresponds to representation of symbolic image through creation of a set of triplets for a given image through the perception of triangular spatial relationship along with the

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topological relationship among the components in the image. The second stage corresponds to similarity match retrieval scheme for a given query image invariant to image transformation. The following subsections deal with the major steps involved in the proposed representation and retrieval scheme.

3.1

Computation of Topological TSR keys

 Let there be n symbolic images SI1 , SI2 , ..., SIn to be archived in the SID. Let L1 , L2 , L3 , ..., Lm be the labels of m distinct iconic objects present in the image. Here each Li is an integer and 1 ≤ Li ≤ m. Encoding each iconic object present in a physical image by the respective label produces the corresponding symbolic image [51]. Therefore, each symbolic image SIi , ∀i = 1, 2, 3, ...n is said to contain mi ≤ m number of labels. In order to preserve spatial relationship among the components present in the image we use TSR. Given a set of components label L1 , L2 , L3 , ..., Lm a set of quadruples are extracted as explained in Guru and Nagabhushan [1]. Let (La , Lb , Lc , θ) be the quadruple representing the spatial relationship among any three objects A, B, C, then the topological relationship between the objects AB, AC and BC is need to be perceived. The possible topological relationship considered in this work between any two components present in the symbolic image are disjoint, meet, overlap, contain, contained-in which are represented by integer values viz., 1,2,3,4,5 respectively. Using the minimum bounding rectangles of the objects A, B and C, the topological relationships between AB, AC and BC are decided, their respective representative values are obtained as r1 , r2 and r3 respectively. For instance let us consider three object ABC where A is disjoint to object B with and have contained relationship with object C. Let the object B has disjoint relationship with object C as shown in Fig. 4. Then the topological relationship among the objects AB, AC and BC is given as r1 = 1, r2 = 4 and r3 = 1. The values, r1 , r2 and r3 are then concatenated to form a single number, RABC i.e., (Rabc = 141) and inserted into quadruple to form a pentuple (La , Lb , Lc , Rabc , θ).

Fig. 4. Illustration of topological relationship

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In [63], a given quadruple (La , Lb , Lc , θ) is mapped onto a unique a key using key mapping function and used for archival and retrieval. Similarly, here also obtained pentuples could have been mapped onto a unique key. However, mapping into a unique key does not preserve the details of component/object identifiers, their topological relation and spatial orientation (Rabc , θ) which is very essential for similarity matching. Hence, instead of mapping entire pentuple into a unique key we map only labels (La , Lb , Lc ) into a unique label identifier L as follows. L = (La − 1)m2 + (Lb − 1)m + (Lc − 1)

(1)

After generating unique label identifier the pentuple (La , Lb , Lc , Rabc , θ) will become a triplet i.e., (L, Rabc , θ). The same is carried out for other pentuples and are stored in SID as symbolic image representatives. 3.2

Similarity match Retrieval

Our similarity function takes a set of triplets generated for a given test image and set of triplets corresponding to database image stored in database and produces a real number R indicating their similarity. Formally the similarity function is defined as SimT T SR :



T 1, T 2



→R

(2)

Where T 1 represents the list of triplet of the test image and T 2 represents the list of triplets of the database image. Consider two symbolic images S1 and S2 , and we want to compute the similarity of S2 with respect to S1 . Let there be n1 number of components in image 3 3 S1 and n2 number of components in image S2 respectively with Cn1 and Cn2 number of triplets. The similarity between two images can be calculated as 3

SIMT T SR

Cn1 X (α × SimT P ) + (β × SimSpatial ) = 2 i=1

(3)

Where SimT P and SimSpatial are the similarity measures used to measure topological and spatial similarities between any two triplets. Topological and spatial similarities are given in eq. 4 and eq. 5, and (α , β) are the suitable constants used to assign weights for topological and spatial relationships. In this work equal weights are assigned to topological and spatial relationships i.e., α, β = 1

1 2 Given a triplet of a query image L1 , Rabc , Θ1 and L2 , Rabc , Θ2 be a triplet of database image , the similarity of topological and spatial relationship between the two triplets is calculated as follows.The topological relationships 1 2 1 1 1 2 Rabc and Rabc are split into individual relationship i.e., Rab , Rac , Rbc andRab , 2 2 Rac , Rbc which is concatenated during archival of triplets into the database. Then the topological similarity is given by

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  1 × (Numberofcorrespondingtopologicalrelationshipmatched) 3 (4) Similarly, given two spatial orientation theta values θ1 and θ2 obtained using TSR, the spatial similarity is computed using cosine similarity as follows.
!   1 + cos Θ1 − Θ2 100.00 (5) SimSpatial = 3 Cn1 2 SimT P =

4

Experimentation

In order to corroborate the efficacy of the proposed method we have conducted experimentation on a dataset created using frames of cartoon Jhai Hanuman and photographs taken during friend’s outings. Totally we have considered 71 images in which first 26 are cartoon frames and remaining 45 are taken during friends outing. In this dataset we have considered frames / photographs which have similar topological and spatial relationships and also we have considered the photographs which have zoom versions of same frame or components with rotation in order to check how the proposed method responses for geometrical transformations. The physical (original) images were converted manually into symbolic images with a Matlab interface, as converting a physical image to a symbolic image itself is a research issue and it is out of the scope of this paper. A few samples considered for experimentation are shown in Fig 5 We have considered 8 database images as query images and ground truth for those images was created with the help of three human experts. The ground truth created by the human experts along with the ranking of similar images is given in Table 1, Table 2 and Table 3. Table 4 corresponds to the retrieved result along with the ranking of the images obtained using the proposed method. Table 1. Ground truth created by an human expert E1 for the test images

Query Image Number 1 13 16 27 32 41 46 51

Similar Images 1 2 7 10 3 4 5 2 8 11 16 17 18 19 21 22 13 14 23 24 25 26 16 15 17 20 18 19 21 22 3 4 5 6 8 11 1 2 7 10 27 28 29 31 30 33 34 35 36 32 36 37 38 39 40 41 42 43 44 45 49 50 70 71 68 64 65 66 56 57 58 60 61 46 52 50 47 49 53 39 71 51 48 54 39 49 50 60 71

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Table 2. Ground truth created by an human expert E2 for the test images

Query Image Number 1 13 16 27 32 41 46 51

Similar Images 1 2 7 3 4 5 6 8 11 10 16 17 18 19 21 22 13 14 23 24 25 26 16 17 18 19 21 22 15 20 3 4 5 6 8 11 1 2 7 10 27 28 29 30 31 34 35 32 37 36 41 42 57 58 38 70 71 39 40 45 49 50 56 60 61 64 65 66 68 46 52 53 49 50 39 71 47 51 54 49 50 61 60 71 39

Table 3. Ground truth created by an human expert E3 for the test images

Query Image Number 1 13 16 27 32 41 46 51

Similar Images 127 13 16 17 27 29 32 38 39 46 52 51 54

10 3 4 5 6 8 11 16 17 18 19 21 22 14 23 24 25 26 18 19 21 22 15 20 3 4 5 6 8 11 1 2 7 10 28 30 31 35 34 36 37 40 41 42 43 44 45 49 50 70 71 68 64 65 66 56 57 58 60 61 49 50 52 39 47 71 39 48 49 50 60 71

Table 4. Rank of the images obtained by the proposed method

Query Image Number 1 13 16 27 32 41 46 51

Similar Images 1 13 16 27 32 41 46 51

2 7 10 22 17 18 15 8 4 6 16 3 19 11 24 23 14 26 25 18 19 17 22 21 6 20 11 4 5 15 3 1 10 8 7 2 29 28 31 34 35 30 37 36 42 60 70 44 71 58 43 39 66 45 64 49 57 65 38 51 40 68 56 61 39 71 53 47 50 49 52 39 48 54 50 71 49 61 60

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Fig. 5. Sample of dataset used in our experimentation

In order to measure the performance of the proposed method we use RN orm measure as defined in [64]. In order to calculate RN orm two rank orderings are required. The rank ordering provided by the system and the rank ordering provided by the expert is considered to compute RN orm . We calculate the average RN orm obtained between the system and Expert1, Expert2, Expert3 and are tabulated in Table 5. From Table 5 it is clear that the proposed method has high RN orm values with the individual experts ranking. The average RN orm and standard deviation of individual experts with systems are provided in Table 5. The average RN orm is high having minimum standard deviation indicating that the proposed method is good.

5

Conclusion

In this paper we have taken the work of extending the concept of Triangular Spatial Relationship towards Topological Triangular Spatial Relationship. Triangular Spatial Relationship was limited only to study spatial relationships among the objects present in an image neglecting topological relationship. Hence we incorporated topological relationship along with the spatial relationship in TSR. Also in TSR the obtained quadruples were mapped onto unique key which in turn lost the details of individual objects and their spatial orientation. Hence triplets were used to store the object details, spatial orientation and topological relationship among them.

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Table 5. RN orm based comparative performance between the rank ordering provided by the system and the experts Query Image Number

System V/S Experts E1 E2 E3 1 0.7035 0.7528 0.6854 13 0.8077 0.6538 0.6538 16 0.8000 0.8103 0.8084 27 0.8000 0.9118 0.7353 32 0.7500 0.7500 1.0000 41 0.5273 0.5273 0.6056 46 0.3269 0.3846 0.4808 51 0.6515 0.6061 0.6061 Average RN orm 0.67086 0.67458 0.69692 Standard Deviation 0.16848 0.16792 0.15631

We have proposed our own similarity measure which can take care of topological relationship and spatial orientation while matching. While retrieving similar images we have assumed that spatial, topological relationships will have equal weights, where as studying the variation by assigning different weights to spatial and topological relationships is an interesting work. This has not been addressed till now in the literature and this will be taken as our future work. In order to study the performance of the proposed method we have conducted experimentation on a dataset containing 71 images. We compared the rank ordering of the retrieved images obtained by the proposed method with the rank ordering provided by three different experts and the results are encouraging.

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