Daniel P. Huttenlocher, Gregory Klanderman, and William J. Rucklidge. Comparing images using the Hausdor distance. IEEE Transactions on Pattern Analysis and Machine Intelligence, 15:850-863, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....already addressed: Preprocessing: sequence stabilization, histogram equalization. A general purpose method for image matching has been recently proposed [OTV] The method, inspired by the notion of Hausdor distance, extends to the grey level case a work on ecient matching of binary images[HKR93] which is well known in literature. The method leads to really promising results, even in presence of severe occlusions. This algorithms solves the following problem: given an image containing an object (or a part of an object) to recognize, and given a model image extracted from a description ....

D. P. Huttenlocher, G. A. Klanderman, and W. J. Rucklidge. Comparing images using the Hausdor distance. IEEE Trans. on Pattern Analysis and Machine Intelligence, 9(15):850-863, 1993.

....values of the other. Under certain assumptions, this provides a tight bound on the directed Hausdor distance of the two grey level surfaces. The proposed technique can be seen as an equivalent in the grey level case of a matching method developed for the binary case by Huttenlocher et al. [2]. The method ts naturally an implementation based on comparison of data structures and requires no numerical computations whatsoever. Moreover, it is able to match images successfully in the presence of severe occlusions. The range of possible applications is vast; we present preliminary, ....

....defect detection [1] gesture recognition [4] robot localization [7] range image analysis [5] and content based video and database indexing. Hausdor measures have been used in computer vision nearly exclusively to match binary patterns of contours or edges. The work by Huttenlocher et al. [2, 3, 6] is the most representative here, and an apt springboard to introduce the main points and innovations of our technique. Huttenlocher et al. used the Hausdor distance to implement an ecient search of a binary edge model M in a binary edge image I . They xed a (small) threshold , say = 1 pixel, ....

D. P. Huttenlocher, G. A. Klanderman, and W. J. Rucklidge. Comparing images using the hausdor distance. IEEE Trans. on Pattern Analysis and Machine Intelligence, 9(15):850-863, 1993.

....measures (such as Sum of Squared Di erence, normalized correlations etc. of misaligned faces do not re ect pose di erences well, since they are poor at re ecting the spatial di erences between distinctive feature points. On the other hand, feature based similarity measures (e.g. Hausdor measure [13]) capture geometric di erences between distinctive feature points, but completely ignore image intensity di erences. In the rest of this section, we rst introduce a feature based similarity measure(FBSM) to quantify structural(pose) variation in face images, and derive a feature texture ....

.... where S d (CEa E b ) is the root mean squared length of displacement vectors in the directed FPCM CEa E b : S d (CEa E b ) 1 N X i2Ea d i 2 (9) This similarity measure is in fact a modi cation of the classical Hausdor measure, which takes maximum of displacement vectors lengths [13][14] Note that this similarity measure is proportional to the average spatial distances, rather than intensity di erences between two sets of feature points. We argue that this property is crucial to pose alignment, since an optimization algorithm using this similarity (or dissimilarity) measure ....

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D. P. Huttenlocher, G.A.Klanderman, and W.J.Rucklidge, \Comparing Images Using the Hausdor Distance", IEEE Trans. on PAMI, vol. 15, pp. 850-863, Sept. 1993.

....classical recognition systems can bene t from learning techniques. In particular, we concentrate on recognizing objects using the Hausdor distance as a shape comparison measure. Comparing shapes using the Hausdor distance has proven to be a reliable and ecient method for object recognition (see [8, 15, 7]) In this context, shapes are sets of points obtained from images using edge detection. Some examples are shown in Figure 1. Typically, an object is represented in terms of an ideal shape, which is referred to as the model. A new shape is classi ed as an instance of the object if the Hausdor ....

D. Huttenlocher, G. Klanderman, and W. Rucklidge. Comparing images using the hausdor distance. PAMI, 15(9):850-863, September 1993.

..... 50 6 Chapter 1 Introduction The problem of object detection and recognition is central to the eld of computer vision. Classical computer vision methods concentrate on objects with xed or parameterized shapes or with known photometric information (see [17, 23, 30, 19, 25]) This was a good starting point for the eld, since it made the recognition problem well de ned, and allowed for the development of important mathematical and algorithmic tools. On the other hand, no arti cial system can recognize generic objects like a dog, a house or a tree. These objects ....

....transform of B speci es for 25 each location in the grid, the distance to the closest point in the set, DB (x) min y2B d(x; y) In particular, DB is zero at any point in B, and is small at nearby locations. The distance transform is commonly used for matching edge based models (see [6, 19]) The trivial way to compute this function takes O(hjBj) time, where h is the number of locations in the grid. On the other hand, ecient algorithms exist to compute the distance transform in O(h) time, independent of the number of points in B (see [5, 21] These algorithms have small constants ....

D.P. Huttenlocher, G.A. Klanderman, and W.J. Rucklidge. Comparing images using the hausdor distance. PAMI, 15(9):850-863, September 1993.

....in most of the work on image classi cation. If the distances are metric, such embedding is feasible as discussed below. However, most recent work in computer vision compares images using measures of similarity that are complex and non metric, in that they do not obey the triangle inequality ([1, 7, 9, 11, 22, 23, 25, 32, 33, 35]) This can occur because the triangle inequality is dicult to enforce in complex matching algorithms that are statistically robust (see discussion in Section 2.1) Also, when matching is conceptualized as the comparison between two probability distributions, there may be strong reasons for using ....

....are robust to outliers or to extremely noisy data will typically violate the triangle inequality. One group of such functions is the family of image comparison methods that match subsets of the images and ignore the most dissimilar parts (see [1, 11, 2, 32] As one example, Huttenlocher et al. [22, 23] perform recognition and motion tracking by comparing point sets using Hausdor distance. They consider only a xed fraction of the points for which this distance is minimized. By not considering the most dissimilar parts of the images, these methods become both robust to image points that are ....

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Huttenlocher, D., G. Klanderman, and W. Rucklidge, 1993, \Comparing Images Using the Hausdor Distance," IEEE Transactions on Pattern Analysis and Machine Intelligence, 15(9):850-863.

....outliers in the data. This probabilistic formulation for image matching yields several bene ts. Perhaps most importantly, we can consider an arbitrary likelihood function for the matching error between edge or intensity features. As compared to Hausdor distance based measures for edge matching [1, 2], this allows us to eliminate the sharp distinction between matched and unmatched template features. In addition, this method allows a simple method for incorporating prior knowledge and uncertainty in the data. We describe methods to estimate the constants in the measure that allow precise ....

....of failure measure that is described in Section 5. In order to formulate the problem in terms of maximum likelihood estimation of the model position, we must have some set of measurements that are a function of the position of the model. Similar to methods based on the Hausdor distance [1], we use the distance from each template pixel (at the position speci ed by t) to the closest occupied pixel in the image as our set of measurements. We denote these distances D # (t) D# (t) In general, these distances can be found quickly for any t if we precompute the distance transform ....

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D. P. Huttenlocher, G. A. Klanderman, and W. J. Rucklidge, \Comparing images using the Hausdor distance", #### ############ ## ####### ######## ### ####### ############, vol. 15, no. 9, pp. 850-863, Sept. 1993.

....outliers in the data. This probabilistic formulation for image matching yields several bene ts. Perhaps most importantly, we can consider an arbitrary likelihood function for the matching error between edge or intensity features. As compared to Hausdor distance based measures for edge matching [1, 2], this allows us to eliminate the sharp distinction between matched and unmatched template features. In addition, this method allows a simple method for incorporating prior knowledge and uncertainty in the data. We describe methods to estimate the constants in the measure that allow precise ....

....of failure measure that is described in Section 5. In order to formulate the problem in terms of maximum likelihood estimation of the model position, we must have some set of measurements that are a function of the position of the model. Similar to methods based on the Hausdor distance [1], we use the distance from each template pixel (at the position speci ed by t) to the closest occupied pixel in the image as our set of measurements. We denote these distances D 1 (t) Dm (t) In general, these distances can be found quickly for any t if we precompute the distance transform ....

[Article contains additional citation context not shown here]

D. P. Huttenlocher, G. A. Klanderman, and W. J. Rucklidge, \Comparing images using the Hausdor distance", IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 9, pp. 850-863, Sept. 1993.

....contours are manually extracted from grey scale images (using snakes for example, 13] prior to the type of processing described here. Human beings nd it easy to recognize shapes from contours and this renders them interesting from a cognitive point of view as well. Other related work includes [4, 5, 6, 8, 10, 11, 12, 18, 19, 24, 26]. The grouping of contours into parts is also the subject of [9] hereafter referred to as LGK) and it is on this that the present work is built. They use a model of non rigid contour self matching that allows the derivation of a part structure for a contour that has with much in common with the ....

Huttenlocher, D., G. Klanderman, and W. Rucklidge, 1993, \Comparing Images Using the Hausdor Distance," IEEE Transactions on Pattern Analysis and Machine Intelligence, 15(9):850-863.

....the distance from a point in A to B: h k (A; B) k th a2A min b2B d(a; b) The partial Hausdor distance is not a metric since it fails the triangle inequality. Deciding whether there is a translation plus scaling that brings the partial Hausdor distance under a given threshold is done in [21] by means of a transformation space subdivision scheme. The running time depends on the depth of subdivision of transformation space. The subdivision of transformation space is generalized to a general framework by [18] Here the optimal transformation is approximated. The matching can be done ....

Daniel P. Huttenlocher, Gregory A. Klanderman, and William J. Rucklidge. Comparing images using the hausdor distance. IEEE Transactions on Pattern Analysis and Machinen Intelligence, 15:850-863, 1993.

....is aligned to a point set A with respect to a transformation group G (e.g. rigid, similarity, linear, ane) if D(A; B) cannot be further decreased by applying to B a transformation from G. The main di erence between various alignment approaches is in the distance function used: Huttenlocher et al. [8] use the Hausdor distance, Sclaro and Pentland [9] use strain energy , Ton and Jain [10] use support functions , and Horn [11] Besl and McKay [12] Gold et al. 13] and the statistical shape community [2] use a least squares type (Procrustes 1 ) distance. Other di erences are the types of ....

D. Huttenlocher, G. Klanderman, and W. Rucklidge, \Comparing images using the Hausdor distance," IEEE Trans. Pattern Anal. and Machine Intelligence, vol. 15, no. 9, pp. 850-863, 1993.

....[6] registration of SPOT images is based on segmentation : a rst edge detection followed by a connectivity algorithm is applied to each channel yielding regions. Then a distance energy between segmentations is minimized by simulated annealing to obtain a global matching of the three channels. In [8], instead, edge maps obtained by a standard Canny type edge detector of two images are compared by using a Haussdor semidistance. Another variant is [5] where contours are obtained as zero crossings of the Laplacian of a gaussian and edge comparison is based on maximal correlation along closed ....

D.P. Huttenlocher, G.A. Klanderman, W.J. Rucklidge. Comparing Images Using the Hausdor Distance. IEEE Trans. on Pattern Analysis and Machine Intell., IEEE-PAMI(15), 9:850-863, 1993

....matching with partial Hausdor distance (lower left) and matching with the a ne invariant metric from [HV99b] lower right) 4. 6 Transformation space subdivision Matching of nite points, from images, under homotheties (translation and scaling) is done by subdividing the transformation space by [HKR93] Rather than the Hausdor distance itself, the partial Hausdor distance is used, which is the maximum of the two directed partial Hausdor distances d k (A; B) and d k (B; A) d k (A; B) maxf d k (A; B) d k (B; A)g; d k (A; B) k th q 2 A min t2B d(a; b) The partial ....

Daniel P. Huttenlocher, Gregory A. Klanderman, and William J. Rucklidge. Comparing images using the hausdor distance. IEEE Transactions on Pattern Analysis and Machinen Intelligence, 15:850-863, 1993.

....function m i (I ; l) measures how well the part matches the image I when placed at location l. The examples in this paper use fairly simple template matching for this cost function. Other possibilities would be to use more 2 complex apperance models (e.g. 18] or edge based techniques (e.g. [13]) The connections between parts indicate relationships between their locations. For each connection (v i ; v j ) there is a deformation cost function d ij (l i ; l j ) measuring how well the locations l i of v i and l j of v j agree with the object model. For instance, in the person model in ....

D.P. Huttenlocher, G.A. Klanderman, W.J. Rucklidge. Comparing Images Using the Hausdor Distance. PAMI, Vol. 15, No. 9, September 1993, Pages 850-863.

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Daniel P. Huttenlocher, Gregory Klanderman, and William J. Rucklidge. Comparing images using the Hausdor distance. IEEE Transactions on Pattern Analysis and Machine Intelligence, 15:850-863, 1993.

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