Assessing the Use of Similarity Distance Measurement

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					Short Paper
                      Proc. of Int. Conf. on Advances in Computing, Control, and Telecommunication Technologies 2011

 Assessing the Use of Similarity Distance Measurement
                in Shape Recognition
                Siti Salwa Salleh, Noor Aznimah Abdul Aziz, Daud Mohamad, and Megawati Omar2
                                       Faculty of Computer and Mathematical Science,
                                                  Research Management Institute
                            University Technology MARA, 40450 Shah Alam, Selangor, Malaysia

Abstract— Distance measure is one of the techniques widely               shape recognition recognizes reference shape from other
used to measure the similarity between two feature matrices              shape, and test whether the reference shape is applicable or
of objects. The objective of this paper is to explore researches         otherwise [20, 10]. This recognition technique is being used
on applied distance measures in shape-based recognition. In              in industries such as fashion, architectural, journalism,
distance measures computation, patterns that are similar will
                                                                         advertisement, education, and entertainment.
have a small distance while uncorrelated pattern in the feature
space will have a far a part distance. The search for effective              Among recognition techniques, similarity measure using
distance measures of shape recognition is always active as               distance measure techniques is one of the popular methods.
each measure suffers certain drawbacks and it must be selected           It works in the manner that small distances corresponding to
appropriately to handle chosen shape features of the objects.            large similarities and large distances corresponding to the
Thus in this paper, the Chord, Cosine, Euclidean,                        small. This approach is widely used for measuring the
Mahalanobis, Trigonometric and Jaccard distance were                     similarity between objects as reported in [3, 8, 9, 12, 14, 16].
reviewed and discussed in terms of their contributions,                  Generally, distance measures is extensively employed in
measures strengths and weaknesses. It was found that Jaccard             content-based image retrieval for shape-based trademark
and Mahalanobis have their strengths that they were selected
                                                                         retrieval, shape-based image retrieval, planar object
to guide in justifying and identifying appropriate distance
measures of our future work on two dimensional sketching                 recognition such as handwritten character recognition and
images. The new distance measure is expected to perform                  other. Likewise, various similarity measures techniques have
better and capable to obtain significance degree of accuracy             also been used to define appropriate distance function that
and recognition rate for real time recognition for automatic             provides the reasonable results for the images comparison.
classifier.                                                              They are Euclidean Distance [14], Mahalanobis Distance [3],
                                                                         Chord Distance [9] Cosine Distance [16], Trigonometric
Index Terms— Distance Measures, shape recognition,                       Distance [8] Jaccard Distance [12] and others. But among
recognition classifier, similarity measures, shape context.              those, not all distance measures work well on a sketch-based
                                                                         input and each distance measure have its own strength and
                       I. INTRODUCTION                                   also suffer from certain weakness.
    Over the years, object recognition has been employed in
several approaches. One of the approaches is a shape                                 II. PROBLEM STATEMENT AND OBJECTIVE
descriptor which covers shape space [15], chord context [9],                 A central problem in object recognition is to determine
shape context [13], Fourier descriptors [21] and more of its             proper distance measure for a particular object. Extensive
kind. Shape descriptor has been deployed to find the                     studies on shape recognition prove some significance
corresponding points or features between shapes [13, 1].                 progresses but current use of the recognition and shape
Previous shape recognition researchers widely use neural                 classification technique has yet to prove satisfactory. Since
network [17, 7], hidden markov model (HMM) [19], simple                  each distance measure has its own strength and weakness,
matching techniques or similarity measures [3, 8, 9, 12, 14,             researchers must be careful to choose the different ways of
16]. However, recognition using Neural Network and HMM                   measuring the distance, which is the chosen approaches
requires a large set of training database [18, 3], while simple          must conform to their needs and applications. It is important
matching technique does not return a promising recognition               to note that, there is no general distance measure that works
performance. Moreover, in certain application, large dataset             best for every kind of shape feature. Hence, the best way in
are not available, neither nor it practical. Shape is a dominant         selecting distance or similarity measure is by identifying and
feature of an object as it consist lines, contours, curves, and          considering the most minimum vector space values by the
vertices and it is normally presented by discrete set of points          use of simple function [8].
or set of pixels value sampled from region or internal and                   Another problem we may bear in mind is that however
external contour on the object [1, 5]. Generally, there are few          appropriate the distance function is, it still suffers from some
recognition techniques that based on object properties                   of kind of shortcomings. A survey by Wang et. al [14] men-
[5,6,10] which are shape, texture, color, and brightness. But            tioned that most of existing distance function encompasses
compared to other features, shape is the most unique where               a complexity of the computation measure. It also brings some
it is able to recognize objects more efficiently. Practically,           difficulty to combine or embed the metric proposed with the
© 2011 ACEEE
DOI: 02.ACT.2011.03. 19
Short Paper
                      Proc. of Int. Conf. on Advances in Computing, Control, and Telecommunication Technologies 2011

powerful classifier. Therefore, this study will identify a dis-              First of all, Euclidean distance is the most commonly used
tance measure that fulfils the following criteria (listed based          in similarity measurement for its simplicity [8, 14] where it
on priority): i) A measure that works well on strokes which              computes the difference of points in magnitude and widely
work well on sketching; Invariant to object transformation;              applied in several applications such as character recognition,
ii) A measure that can be modified and added with guiding                face recognition, image retrieval and others. On the other
elements; iii) Low computation suitable for real time (auto-             hand, the images in Euclidean distance are not necessarily
matic) checking purpose.                                                 similar in all features. To overcome the shortcoming in
                                                                         Euclidean, Zou and Umugwaneza [16] implemented a distance
              III. ANALYSIS OF RECENT RESEARCH                           metrics Cosine distance to improve the formulation by
                                                                         multiplying the first and second coordinates and add the
     The analysis was conducted by way of examining the                  results from Euclidean distance dimensional profile data
strengths and shortcomings of each measure. To iterate,                  matrix.
works that applied the distance functions are generally used                 Another measure that contains a simple distance function
in the area of image retrieval, shape retrieval and handwritten          and requires minimum computation time is Jaccard Distance.
character recognition. They commonly focus on overcoming                 In this sense, Jaccard Distance is better that it outdoes
overcome certain problems such as computation time,                      Euclidean Distance in shape recognition. Jaccard Distance is
invariant of image transforms, computational complexity.                 basically employed to compare two objects in a binary format
Secondly, the focus is to increase its retrieval accuracy. In            and it also does not require a large set of data for training and
this paper, the most recent studies that applied five different          testing purposes. It works by measuring the asymmetric
distance functions were studied. The studies are conducted               information on binary variables, the comparison between two
by (i) Wang et. al [14] who presented new Euclidean distance             vector components. However, despite its strength and being
for images, called IMED which image metric can be embedded               used widely, Jaccard Distance’s disadvantage is its variant
in the existing image recognition methods for 2D image. ii)              to image transformations. This distance function is commonly
Nemmour and Chibani [12] who proposed new kernel for the                 applied on binary data where the similarity computation
support vector machine for handwritten digit recognition                 computes the values of 0 and 1. The input object must be in
based on the Jaccard negative distance. The computation of               binary form and therefore, Jaccard’s method cannot be used
Jaccard distance in their study determines the correlated or             if any transformations are employed to the object features.
uncorrelated pattern based on pixel-based description where              Another requirement is that the size of both binary object
it takes into account the number of pixels in foreground and             and shapes must be of similar size. But Jaccard’s limitation
background for both patterns that leads to similar or dissimilar         can be improved by adding a pre-processing taks prior to the
patterns. (iii) Chen et. al [3] comes out with the Progressive           computation.
Mahalanobis distance for financial hand-written Chinese                      At present, the Mahalanobis distance is one of the
character recognition. Mahalanobis distance derived by a                 commonly distance measures used in CBIR. However, its
probability density function of multivariate normal distribution         weakness is that Mahalanobis distance’s computation needs
or the key is the calculation of covariance matrix. (iv) Zou             sufficient training samples and long computation time in
and Umugwaneza [16] that proposed cosine distance function               recognition. Computation time is one of the important
for shape-based trademark retrieval for 2D images. (vi)                  distributions in character recognition and retrieval
Mingqiang et. al [9] who proposed shape descriptor based                 applications, therefore consuming long computation time will
on chord context use to measuring similarities between 2D                affect the recognition performance. Consequently,
two shapes And finally (vii) Li et. al [8] who proposed new              Mahalanobis distance function will be more time-consuming
similarity measurement method, an algorithm for object shape             on large database. Eventhough Chen et al. [3] conducted a
analysis based on Trigonometric distance.                                research to reduce the computation time of original
                                                                         Mahalanobis Distance by creating a Progressive
                        IV. DISCUSSION                                   Mahalanobis Distance to reduce computational loads at
    The performance of recognition effectiveness of different            satisfactory level, its computation time still consumes more
measures investigated theoretically based on the work                    time than the Euclidean Distance. But interestingly,
reported by researchers. We studied works conducted by                   Mahalanobis [3] performs reliable result on financial hand-
previous researchers who did some improvement on the                     written Chinese characters that involve variations of size and
following distance function: Chord Distance, Cosine Distance,            density; stroke translation; stroke length and width; broken
Euclidean Distance, Mahalanobis Distance, Trigonometric                  and connected stroke and others. These applicable methods
distance and Jaccard Distance. The objects that these                    contribute to the accurate automatic retrieving system in
researchers work with were in many forms such as                         trademark images [16] handwritten digit recognition [12]
photography, hand sketches, drawing and others. The                      automatic bank cheque processing [3], and texture (Chen and
researches analyzed were chosen due to their closest input               Chu, 2005). Another distance is a Cosine Distance of which
type with our intended research, having a grayscale format as            whose strength is its consideration of the correlation of the
the grayscale format can be computed in minimal time.                    features vector. This measure normalizes all feature vectors
Moreover, most of the input used contains strokes and tiny               to unit length, comparing the angle between two shape
lines.                                                                   features vectors. In [16] worked on trademark retrieval using
© 2011 ACEEE
DOI: 02.ACT.2011.03.19
Short Paper
                       Proc. of Int. Conf. on Advances in Computing, Control, and Telecommunication Technologies 2011

Cosine Distance function where it shows a weakness where                   However, in application that receives direct input using a
this measure is invariant with the scaling of the image content            pen input device faces some disturbances in recognizing the
and treating similar images in different ways. However so, the             object, where the pen device will show differences from the
Cosine Distance produces more accurate results compared to                 pen pressures. Different pressure between individuals [4, 11]
the Euclidean Distance in retrieval effectiveness.                         produces significance differences in the result of recognition.
    Chord Distance also shows a high degree of retrieval                   The summary of previous work is shown below (Table 1).
accuracy than the other measures on the MPEG-7 CE-1                                                   TABLE I.
database and the Kimia silhouettes datasets retrieval test.                                  EVOLUTION OF DISTANCE FUNCTIONS
The strength here is that it is robust to noise and occultation.
Another potency is that its capability to describe a frequency
distribution of chord lengths with different orientations.
Shape descriptor using Chord context [9] for shape
description in CBIR showed that the measure is invariant in
image translation, rotation and scaling. However, the propose
descriptor perform no special operations to resist affine
transformation. Furthermore, in most researches on chord
distance, it also provides poor recognition result if the input
consists of strokes and lines. Likewise, Trigonometric
Distance applied in the object shapes analysis for retrieval
application produced better recognition rate on similarity
images in different angles. Li et. al [8] uses Trigonometric
distances that normalize the distance of two points in image
similarity. Trigonometric’s forte is that it reduces the influence
of noise and produces better recognition rate than Euclidean
distance in image retrieval. However, it requires a well cleaned
input whereby any noise can easily affect the recognition
performance. Defining and filtering noises in real time
application require efficient noise removal algorithm and
involve a careful choice of feature extractions steps and which
may be involve another difficult study.
    Hence in a nutshell, it was found that that each distance
function posses its own strength weaknesses in the context
of strokes and line input as well as for a real time application.
In short, sigh sensitivity through small deformation may
result in a large Euclidean Distance. The individual distance
needs normalized distance to decrease the percentage of                                             CONCLUSIONS
missed images in the results for effective image retrieval [16].
                                                                               Comparison was made on the distance measures and
While the Mahalanobis Distance is time consuming when
                                                                           basically, each distance performs differently against common
tested on large database, and also, limited samples cause a
                                                                           essential properties such as noise resistance, affine
bad influence. Other distance functions do not resist affine
                                                                           invariance, occultation invariance, statistical independent,
transform, contributing to a major weakness in accuracy
                                                                           reliability, translation, rotation, scale invariance and others.
retrieved, for example, Chord Distance [9]. Considerable efforts
                                                                           Most of the distance functions mentioned above require basic
have been made to obtain intuitively reasonable. Although
                                                                           pre processing tasks on the noise removal, object scale and
there is a remaining setback, some methods have been evolved
                                                                           rotation which are important in recognizing shapes. In
for better achievement in recognition retrieval. The proposed
                                                                           conclusion, we chose Jaccard and Mahalanobis to be the
similarity measure using distance function contribute to
                                                                           main references for our future work. Jaccard outshines the
strengths in flexibility against handling various type of queries
                                                                           others by its simplicity but able to maintain higher accuracy.
and robust to noise and minor occultation.
                                                                           On the other hand, Mahalanobis is able to deal with strokes
    Therefore, the Chord Distance, Cosine, Jaccard,
                                                                           and lines which provide us likelihood to produce a more
Mahalanobis and Trigonometry are found to be better than
                                                                           promising equation that combines both distance equations.
the Euclidean distance in all courses. Unfortunately,
                                                                           Again, in spite of its simplicity that allows minimum
Euclidean Distance’s hitches are on scale properties where it
                                                                           computation time, Jaccard works efficiently on a binary image
produces far distances; no similarity although the objects
                                                                           and Mahalanobis’s invariant to object transform works best
are in the normalized scale images and computated base
                                                                           for real time application which will, in turn, perform automatic
magnitude. Therefore, Euclidean suffers from the most
                                                                           checking on the object. Hence, our future work will focus on
important drawback that makes it offer the lowest degree of
                                                                           two dimensional sketching inputs from pen device. This may
recognition. On the other hand, Cosine Distance works well
                                                                           improve one of the selected distance functions and may com-
on the objects without rotation, translation and scale.
                                                                           bine it with other distance functions to improve similarity
© 2011 ACEEE
DOI: 02.ACT.2011.03.19
Short Paper
                       Proc. of Int. Conf. on Advances in Computing, Control, and Telecommunication Technologies 2011

measures performances. It deems that new distance function                  [9] Y. Mingqiang, K. Kidiyo, and R. Joseph, “Shape Matching
will perform better on sketching images where it will be able               and Object Recognition Using Chord Contexts”, Proceedings of the
to obtain better significance degree of accuracy and recogni-               International Conference on Visualisation,Washington, DC, USA,
tion rate for real time recognition for automatic classifier.               pp. 63-69, 9-11 July 2008.
                                                                            [10] Y. Mingqiang, K. Kidiyo, and R. Joseph, “A Survey of Shape
                                                                            Feature Extraction Techniques”, Pattern Recognition Techniques,
                       ACKNOWLEDGMENT                                       Technology and Applications, pp.43-90, 2008.
   This work was supported by the FRGS Grant, Ministry of                   [11] M. Nakai, T. Sudo, H. Shimodaira, and S. Sagayama, “Pen
Higher Education, Malaysia (600-RMI/ST/FRGS 5/3 Fst (98/                    Pressure Features for Writer Independent On-Line Handwritting
                                                                            Recognition Based on Substroke HMM”, Proceedings of the 16th
                                                                            Internaional Conference on Pattern Recognition, pp. 220-223, 2002.
                                                                            [12] H. Nemmour, and Y. Chibani, “New Jaccard-Distance Based
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DOI: 02.ACT.2011.03.19

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