A.J. Baddeley, An error metric for binary images, in: W. Forstner, S. Ruwiedel (Eds.), Proceedings of Robust Computer Vision, 1992, pp. 59 -- 78.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....proposed by Swain and Ballard [10] The overall misclassification error (logical XOR) is given by: D xor (C Q ; C I k ) j( C Q n C I k ) C I k n C Q ) 11) D xor is sensitive to both false positives and false negatives. An important property of D xor is that it is a metric [1]. In the next section, similarity functions are discussed which take into account the distance of each misclassified hixel to the nearest correct set. 3.2 Geometry based similarity functions Because a hixel represents a hue hue edge, the distance between hue values is to be defined first. ....

.... hixel difference: Dmax (C Q ; C I k ) max a2C Q fd( a; C I k )g (16) Furthermore, the Hausdorff distance is defined by: D haus (C Q ; C I k ) maxfmax a2C Q d( a; C I k ) max b2C I k d( b; C Q )g (17) An important property of D haus ( is that it is a metric [1]. Except for D haus ( the above defined similarity functions are all sensitive to false positives and insensitive to false negatives. In the next section, the various similarity functions are evaluated in practice. 4 Experiments To evaluate the various similarity functions, the criteria 1 6 ....

Baddeley, A. J., An Error Metric for Binary Images, In Proceedings of Robust Computer Vision, W. Forstner and S. Ruwiedel (eds.), Karlsruhe, pp. 59 - 78, 1992.

....space subdivision scheme. The running time depends on the depth of subdivision of transformation space. For pattern matching, the Hausdorff metric is often too sensitive to noise. For finite point sets, the partial Hausdorff distance is not that sensitive, but it is no metric. Alternatively, [7] observes that the Hausdorff distance of ## # # # , # having a finite number of elements, can be written as ###### # ### ### ##### ##########. The supremum is then replaced by an average: # # ### ### # # ### # ### ##### ## # #### ### # # ### ,where#### ## # ### ### #### ##, ....

A. J. Baddeley. An error metric for binary images. In Robust Computer Vision: Quality of Vision Algorithms, Proc. of the Int. Workshop on Robust Computer Vision, Bonn, 1992, pages 59--78. Wichmann, 1992.

....or ane transformations (translation, rotation, scaling, and shear) 3.6 p th Order Mean Hausdor Distance For pattern matching, the Hausdor metric is often too sensitive to noise. For nite point sets, the partial Hausdor distance is not that sensitive, but it is no metric. Alternatively, [7] observes that the Hausdor distance of A; B X, X having a nite number of elements, 6 Figure 5: Polygonal curve and turning function. can be written as H(A;B) sup x2X jd(x; A) d(x; B)j. The supremum is then replaced by an average: p (A; B) 1 jXj P x2X jd(x; A) d(x; B)j p ....

....positive constant c. If d(A; B) is a metric, then so is d(A; B) w(d(A; B) With some of these functions, an unbounded metric d can be mapped to a bounded metric. For the cut o function min(x; c) the maximum distance value becomes c, so that property (14) above does not hold. It is used in [7] for comparing binary images. The log(x) function is used in the Banach Mazur distance log ( A; B) Without the logarithm it would not satisfy the triangle inequality, and therefore not be a metric. 4.2 Normalization Normalization is often used to scale the range of values of a ....

A. J. Baddeley. An error metric for binary images. In W. Forstner and S. Ruwiedel, editors, Robust Computer Vision: Quality of Vision Algorithms, Proceedings of the International Workshop on Robust Computer Vision, Bonn, 1992, pages 59-78. Wichmann, 1992.

....L) jL n Lj jLj ; fi 2 [0; 1] 8) ffl misclassification error for binary sets (L; L) j( L n L) L n L)j jSj = 1 Gamma r) ff r fi; 9) r = jLj jSj ; 2 [0; 1] In the optimal case, the quantities are zero. Advantages and disadvantages of these quantities are e.g. given in Baddeley 1992. In order to overcome the drawbacks related to these measures, Baddeley 1992 proposed a metric to measure the discrepancy between two binary sets: ffl Baddeley metric Delta p w (L; L) 1 jSj X x2S jw(d(x;L) Gamma w(d(x; L) j p # 1 p (10) with w(x) min(x; c) and c: ....

....sets (L; L) j( L n L) L n L)j jSj = 1 Gamma r) ff r fi; 9) r = jLj jSj ; 2 [0; 1] In the optimal case, the quantities are zero. Advantages and disadvantages of these quantities are e.g. given in Baddeley 1992. In order to overcome the drawbacks related to these measures, Baddeley 1992 proposed a metric to measure the discrepancy between two binary sets: ffl Baddeley metric Delta p w (L; L) 1 jSj X x2S jw(d(x;L) Gamma w(d(x; L) j p # 1 p (10) with w(x) min(x; c) and c: cutoff distance If there is no discrepancy between the binary sets, Delta = 0. ....

Baddeley, A. J. (1992): An Error Metric for Binary Images. In: Forstner, W.; Winter, S. (Eds.), Robust Computer Vision, pages 59--78. Wichmann, Karlsruhe, 1992.

....labels are as a triangle, two circles and an ellipse. If a point estimate is required rather than a sequence of typical realisations, Rue and Hurn (1997) describe a point estimator for the number of objects together with their locations, shapes and labels, based on Baddeley s delta metric (Baddeley, 1992). Finally, notice that it is possible to extend the template models to deal with the problem observed in fitting the ellipse in the lower right corner. The difficulty here is that the fluorescent material is not uniformly distributed over the surface of the cell; as a result, part of the cell s ....

Baddeley, A. J. (1992). An error metric for binary images. In Forstner, W. and Ruwiedel, S., editors, Robust Computer Vision: Quality of Vision Algorithms, pages 59--78. Wichmann Verlag.

....and have good theoretical properties. From a theoretical point of view, it is preferable to have a distance measure which is a metric, however other non metric measures of similarity between two images will still be of interest if their visual performance is good, see also the discussion in [1, 2]. Metrics for binary or black and white images are of basic interest in imaging. The most widely used metric is simply the percentage of pixels that differ. This metric lacks any spatial considerations on how the pixels that differ are distributed in the image and result in a poor visual ....

....to interpret and lacks any Invited entry for the Encyclopedia of Statistical Sciences, update volume. Address: Department of Mathematical Sciences, The Norwegian University of Science and Technology, N 7034 Trondheim, Norway. E mail: havard.rue imf.unit.no theoretical justification [1, 2]. The delta metric proposed by Baddeley [1, 2] has reasonable visual performance, good theoretical properties and an intuitive interpretation. The Delta Metric A pixel lated image x can be thought of as a matrix where the matrix element k; l corresponds to the pixel value at position (k; l) in ....

[Article contains additional citation context not shown here]

A. J. Baddeley. An error metric for binary images. In W. Forstner and S. Ruwiedel, editors, Robust Computer Vision: Quality of Vision Algorithms, pages 59--78. Wichmann Verlag, 1992.

....the desiderata of [56, p. 72 ff. it is defined as an L p mean of pixel contributions so that it has an average risk interpretation and is reasonably stable to noise. The underlying theory [3] is also applicable to grey level images, but here we discuss only the binary case; see also [4]. Related work is in [2, 65, 72] Section 1 lists notation and assumptions. Section 2 introduces the desired topology, the myopic topology, and the associated Hausdorff metric. In section 3 we study error measures that are in current use, giving some examples of undesirable properties in practice, ....

A. J. Baddeley. An error metric for binary images. In W. Forstner and S. Ruwiedel, editors, Robust Computer Vision, pages 59--78, Karlsruhe, 1992. Wichmann.

.... of two techniques stemming from the study of edge detection algorithms: counting the number of incorrect pixels in the reconstruction (how many false positives in response to an edge, and how many missed edges) and measuring the localisation of these errors (how close the response to an edge is) [2, 8]. Much discussion of the latter has been made with regard to edge detection [1, 2, 3, 23, 28] Although these methods are reasonable measures of error, the rates of error computed using either type of binary error measure are not entirely satisfactory, and their pitfalls have been noted [2, 3, ....

.... the number of incorrect pixels in the reconstruction (how many false positives in response to an edge, and how many missed edges) and measuring the localisation of these errors (how close the response to an edge is) 2, 8] Much discussion of the latter has been made with regard to edge detection [1, 2, 3, 23, 28]. Although these methods are reasonable measures of error, the rates of error computed using either type of binary error measure are not entirely satisfactory, and their pitfalls have been noted [2, 3, 22] The situation is complicated further with the addition of more possible grey levels, as in ....

[Article contains additional citation context not shown here]

A. J. Baddeley. An error metric for binary images. In W. Forstner and S. Ruwiedel, editors, Robust Computer Vision, pages 59--78, Karlsruhe, 1992. Wichmann.

No context found.

A.J. Baddeley, An error metric for binary images, in: W. Forstner, S. Ruwiedel (Eds.), Proceedings of Robust Computer Vision, 1992, pp. 59 -- 78.

No context found.

A. J. Baddeley. An error metric for binary images. In W. Forstner and S. Ruwiedel, editors, Robust Computer Vision, pages 59--78, Karlsruhe, 1992. Wichmann.

No context found.

Baddeley, A. J. (1992a). An error metric for binary images, in W. Forstner and S. Ruwiedel (eds), Robust Computer Vision: Quality of Vision Algorithms, Wichmann Verlag, pp. 59--78.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC