nips nips2002 nips2002-132 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: David R. Martin, Charless C. Fowlkes, Jitendra Malik
Abstract: The goal of this work is to accurately detect and localize boundaries in natural scenes using local image measurements. We formulate features that respond to characteristic changes in brightness and texture associated with natural boundaries. In order to combine the information from these features in an optimal way, a classifier is trained using human labeled images as ground truth. We present precision-recall curves showing that the resulting detector outperforms existing approaches.
Reference: text
sentIndex sentText sentNum sentScore
1 edu ¡ Abstract The goal of this work is to accurately detect and localize boundaries in natural scenes using local image measurements. [sent-7, score-0.532]
2 We formulate features that respond to characteristic changes in brightness and texture associated with natural boundaries. [sent-8, score-0.689]
3 In order to combine the information from these features in an optimal way, a classifier is trained using human labeled images as ground truth. [sent-9, score-0.391]
4 We present precision-recall curves showing that the resulting detector outperforms existing approaches. [sent-10, score-0.301]
5 1 Introduction Consider the image patches in Figure 1. [sent-11, score-0.185]
6 The goal of this paper is to use features extracted from the image patch to estimate the posterior probability of a boundary passing through the center point. [sent-13, score-0.497]
7 Such a local boundary model is integral to higher-level segmentation algorithms, whether based on grouping pixels into regions [21, 8] or grouping edge fragments into contours [22, 16]. [sent-14, score-0.569]
8 The traditional approach to this problem is to look for discontinuities in image brightness. [sent-15, score-0.185]
9 For example, the widely employed Canny detector [2] models boundaries as brightness step edges. [sent-16, score-0.45]
10 The image patches show that this is an inadequate model for boundaries in natural images, due to the ubiquitous phenomenon of texture. [sent-17, score-0.339]
11 The Canny detector will fire wildly inside textured regions where high-contrast contours are present but no boundary exists. [sent-18, score-0.586]
12 In addition, it is unable to detect the boundary between textured regions when there is only a subtle change in average image brightness. [sent-19, score-0.553]
13 These significant problems have lead researchers to develop boundary detectors that explicitly model texture. [sent-20, score-0.249]
14 Texture descriptors over local windows that straddle a boundary have different statistics from windows contained in either of the neighboring regions. [sent-22, score-0.305]
15 Clearly, boundaries in natural images are marked by changes in both texture and brightness. [sent-24, score-0.693]
16 Evidence from psychophysics [18] suggests that humans make combined use of these two cues to improve detection and localization of boundaries. [sent-25, score-0.226]
17 There has been limited work in computational vision on addressing the difficult problem of cue combination. [sent-26, score-0.196]
18 For example, the authors of [8] associate a measure of texturedness with each point in an image in order to suppress contour processing in textured regions and vice versa. [sent-27, score-0.349]
19 A large dataset of natural images that have been manually segmented by multiple human subjects [10] provides the ground truth label for each pixel as being on- or off-boundary. [sent-30, score-0.55]
20 The task is then to model the probability of a pixel being on-boundary conditioned on some set of locally measured image features. [sent-31, score-0.238]
21 This sort of quantitative approach to learning and evaluating boundary detectors is similar to the work of Konishi et al. [sent-32, score-0.296]
22 Our work is distinguished by an explicit treatment of texture and brightness, enabling superior performance on a more diverse collection of natural images. [sent-34, score-0.511]
23 In Section 2 we describe the oriented energy and texture gradient features used as input to our algorithm. [sent-36, score-0.743]
24 Section 4 presents our evaluation methodology along with a quantitative comparison of our method to existing boundary detection methods. [sent-38, score-0.411]
25 1 Oriented Energy In natural images, brightness edges are more than simple steps. [sent-41, score-0.215]
26 The oriented energy (OE) approach [12] can be used to detect and localize these composite edges [14]. [sent-43, score-0.395]
27 We compute OE at 3 half-octave scales starting at the image diagonal. [sent-49, score-0.185]
28 The filters are elongated by a ratio of 3:1 along the putative boundary direction. [sent-50, score-0.249]
29 2 Texture Gradient We would like a directional operator that measures the degree to which texture varies at a location in direction . [sent-52, score-0.518]
30 A natural way to operationalize this is to consider a disk of radius centered on , and divided in two along a diameter at orientation . [sent-53, score-0.143]
31 We can then compare the texture in the two half discs with some texture dissimilarity measure. [sent-54, score-0.863]
32 Oriented texture processing along these lines has been pursued by [19]. [sent-55, score-0.448]
33 & & @8 6 A97 @8 6 C9B ' What texture dissimilarity measure should one use? [sent-56, score-0.448]
34 There is an emerging consensus that for texture analysis, an image should first be convolved with a bank of filters tuned to various orientations and spatial frequencies [4, 9]. [sent-57, score-0.688]
35 After filtering, a texture descriptor is then constructed using the empirical distribution of filter responses in the neighborhood of a pixel. [sent-58, score-0.415]
36 This approach has been shown to be very powerful both for texture synthesis [5] as well as texture discrimination [15]. [sent-59, score-0.83]
37 [15] evaluate a wide range of texture descriptors in this framework. [sent-61, score-0.457]
38 I E HG E FD ¡ ¢ ¡ ¢ Boundaries Non-Boundaries ¢ £¡ Intensity ¢ £¡ Image Figure 1: Local image features. [sent-67, score-0.185]
39 In each row, the first panel shows the image patch. [sent-68, score-0.249]
40 The features are raw image intensity, raw oriented energy , localized oriented energy , raw texture gradient , and localized texture gradient . [sent-70, score-2.132]
41 The challenge is to combine these features in order to detect and localize boundaries. [sent-72, score-0.275]
42 © ¨ ¥§ ¦¤ ¥ ¦¤ @8 6 C9B EHG E $ 5D G D " " E G E D ¨ 8 " ©§ ¨ We define the texture gradient (TG) to be the distance between these two histograms: The texture gradient is computed at each pixel of the image diagonal. [sent-73, score-1.178]
43 3 Localization The underlying function we are trying to learn is tightly peaked around the location of image boundaries marked by humans. [sent-75, score-0.422]
44 The texture gradient is particularly prone to this effect, since the texture in a window straddling the boundary is distinctly different than the textures on either side of the boundary. [sent-78, score-1.178]
45 This often results in a wide plateau or even double peaks in the texture gradient. [sent-79, score-0.488]
46 Since each pixel is classified independently, these spatially extended features are particularly problematic as both on-boundary pixels and nearby off-boundary pixels will have large OE and TG. [sent-80, score-0.358]
47 In order to make this spatial structure available to the classifier we transform the raw OE and TG signals in order to emphasize local maxima. [sent-81, score-0.152]
48 Given a feature 6 7 6 defined over spatial coordinate orthogonal to the edge orientation, consider the derived , where is the first-order approximation feature of the distance to the nearest maximum of . [sent-82, score-0.156]
49 By incorporating the localization term, will have narrower peaks than the raw . [sent-84, score-0.297]
50 1 This transformation is applied to the oriented energy and texture gradient signals at each orientation and scale separately. [sent-87, score-0.709]
51 This yields a 6-element consists of these localized signals feature vector at 12 orientations at each pixel. [sent-92, score-0.232]
52 0 1) ' (& 3 Cue Combination Using Classifiers We would like to combine the cues given by the local feature vector in order to estimate the posterior probability of a boundary at each image location . [sent-93, score-0.63]
53 Previous work on learning boundary models includes [11, 7]. [sent-94, score-0.216]
54 For example, one may wish to ignore brightness edges inside high-contrast textures where OE is high and TG is low. [sent-98, score-0.206]
55 75 1 Recall Figure 2: Performance of raw (left) and localized features (right). [sent-152, score-0.322]
56 The precision and recall axes are described in Section 4. [sent-153, score-0.182]
57 The left plot shows the performance of the raw OE and TG features using the logistic regression classifier. [sent-157, score-0.437]
58 The right plot shows the performance of the features after applying the localization process of Equation 1. [sent-158, score-0.263]
59 It is clear that the localization function greatly improves the quality of the individual features, especially the texture gradient. [sent-159, score-0.534]
60 The top curve in each graph shows the performance of the features in combination. [sent-160, score-0.183]
61 ¢ ¡ The ground truth boundary data is based on the dataset of [10] which provides 5-6 human segmentations for each of 1000 natural images from the Corel image database. [sent-168, score-0.902]
62 The authors of [10] show that the segmentations of a single image by the different subjects are highly consistent, so we consider all humanmarked boundaries valid. [sent-171, score-0.415]
63 We declare an image location to be on-boundary if it is within =2 pixels and =30 degrees of any human-marked boundary. [sent-172, score-0.313]
64 Note that a high degree of class overlap in any local feature space is inevitable because the human subjects make use of both global constraints and high-level information to resolve locally ambiguous boundaries. [sent-177, score-0.267]
65 4 Results The output of each classifier is a set of oriented images, which provide the probability of a boundary at each image location based on local information. [sent-178, score-0.616]
66 The left panel shows the performance of different combinations of the localized features using the logistic regression classifier: the 3 OE features (oe*), the 3 TG features (tg*), the best performing single OE and TG features (oe2+tg1), and all 6 features together. [sent-205, score-0.94]
67 Based on performance, simplicity, and low computation cost, we favor the logistic regression and its variants. [sent-210, score-0.188]
68 classifiers we consider, the image provides actual posterior probabilities, which is particularly appropriate for the local measurement model in higher-level vision applications. [sent-211, score-0.408]
69 ¥ ¤ ¥ ¦¤ In order to evaluate the boundary model against the human ground truth, we use the precision-recall framework, a standard evaluation technique in the information retrieval community [17]. [sent-213, score-0.439]
70 It is closely related to the ROC curves used for by [1] to evaluate boundary models. [sent-214, score-0.266]
71 The precision-recall curve captures the trade-off between accuracy and noise as the detector threshold is varied. [sent-215, score-0.253]
72 These are computed using a distance tolerance of 2 pixels to allow for small localization errors in both the machine and human boundary maps. [sent-217, score-0.607]
73 The precision-recall curve is particularly meaningful in the context of boundary detection when we consider applications that make use of boundary maps, such as stereo or object recognition. [sent-218, score-0.578]
74 The location of the maximum F-measure along the curve provides the optimal threshold given , which we set to 0. [sent-223, score-0.16]
75 ¤ ¢ ¢ $ ¤ £¤ ¨ ¡ Figure 2 shows the performance of the raw and localized features. [sent-225, score-0.274]
76 This provides a clear quantitative justification for the localization process described in Section 2. [sent-226, score-0.197]
77 Figure 3a shows the performance of various linear combinations of the localized features. [sent-228, score-0.208]
78 5 3 Tolerance (in pixels) Figure 4: The left panel shows precision-recall curves for a variety of boundary detection schemes, along with the precision and recall of the human segmentations when compared with each other. [sent-248, score-0.826]
79 The right panel shows the F-measure of each detector as the distance tolerance for measuring precision and recall varies. [sent-249, score-0.534]
80 We take the Canny detector as the baseline due to its widespread use. [sent-250, score-0.245]
81 Our detector outperforms the learning-based Nitzberg detector proposed by Konishi et al. [sent-251, score-0.465]
82 The results presented so far use the logistic regression classifier. [sent-253, score-0.188]
83 The plain logistic regression model performs extremely well, with the variants of logistic regression – quadratic, boosted, and HME – performing only slightly better. [sent-257, score-0.376]
84 3 2 Figure 4 shows the performance of our detector compared to two other approaches. [sent-261, score-0.262]
85 Because of its widespread use, MATLAB’s implementation of the classic Canny [2] detector forms the baseline. [sent-262, score-0.245]
86 We also consider the Nitzberg detector [13, 7], since it is based on a similar supervised learning approach, and Konishi et al. [sent-263, score-0.214]
87 The Nitzberg detector generates a feature vector containing eigenvalues of the 2nd moment matrix; we train a classifier on these 2 features using logistic regression. [sent-267, score-0.498]
88 Figure 4 also shows the performance of the human data as an upper-bound for the algorithms. [sent-268, score-0.175]
89 The human precision-recall points are computed for each segmentation by comparing it to the other segmentations of the same image. [sent-269, score-0.302]
90 The approach of this paper is a clear improvement over the state of the art in boundary detection, but it will take the addition of high-level and global information to close the gap between the machine and human performance. [sent-270, score-0.343]
91 C 3 C 3 5 Conclusion We have defined a novel set of brightness and texture cues appropriate for constructing a local boundary model. [sent-280, score-0.846]
92 By using a very large dataset of human-labeled boundaries in natural images, we have formulated the task of cue combination for local boundary detection as a supervised learning problem. [sent-281, score-0.606]
93 This approach models the true posterior probability of a boundary at every image location and orientation, which is particularly useful for higherlevel algorithms. [sent-282, score-0.496]
94 Based on a quantitative evaluation on 100 natural images, our detector outperforms existing methods. [sent-283, score-0.392]
95 Fundamental bounds on edge detection: an information theoretic evaluation of different edge cues. [sent-334, score-0.142]
96 A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. [sent-358, score-0.392]
97 Feature detection in human vision: a phase dependent energy model. [sent-373, score-0.262]
98 Detecting and localizing edges composed of steps, peaks and roofs. [sent-388, score-0.174]
99 Non-parametric similarity measures for unsupervised texture segmentation and image retrieval. [sent-397, score-0.69]
100 A probabilistic multi-scale model for contour completion based on image statistics. [sent-402, score-0.284]
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