cvpr cvpr2013 cvpr2013-318 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Sitapa Rujikietgumjorn, Robert T. Collins
Abstract: We present a quadratic unconstrained binary optimization (QUBO) framework for reasoning about multiple object detections with spatial overlaps. The method maximizes an objective function composed of unary detection confidence scores andpairwise overlap constraints to determine which overlapping detections should be suppressed, and which should be kept. The framework is flexible enough to handle the problem of detecting objects as a shape covering of a foreground mask, and to handle the problem of filtering confidence weighted detections produced by a traditional sliding window object detector. In our experiments, we show that our method outperforms two existing state-ofthe-art pedestrian detectors.
Reference: text
sentIndex sentText sentNum sentScore
1 edu Abstract We present a quadratic unconstrained binary optimization (QUBO) framework for reasoning about multiple object detections with spatial overlaps. [sent-6, score-0.511]
2 The method maximizes an objective function composed of unary detection confidence scores andpairwise overlap constraints to determine which overlapping detections should be suppressed, and which should be kept. [sent-7, score-1.069]
3 The framework is flexible enough to handle the problem of detecting objects as a shape covering of a foreground mask, and to handle the problem of filtering confidence weighted detections produced by a traditional sliding window object detector. [sent-8, score-0.93]
4 In our experiments, we show that our method outperforms two existing state-ofthe-art pedestrian detectors. [sent-9, score-0.28]
5 Notwithstanding these difficulties, good progress has been made on the problem of detecting individual walking pedestrians through the use of statistical machine learning meth- ods for training pedestrian object detectors [4]. [sent-12, score-0.361]
6 As shown in Figure 1 using the PLS detector [20] with its default non maximum suppression method, correct candidate detections were present that were suppressed by stronger (a)(b) Figure 1. [sent-17, score-0.684]
7 (a) PLS detector using its default non maximum suppression method misses one person. [sent-18, score-0.357]
8 (b) Examining candidate ob- ject center locations from the PLS detector without non maximum suppression shows that candidate detections were generated for that person, but they were subsequently suppressed. [sent-19, score-0.788]
9 The aim of this paper is to show that quadratic optimization for reasoning about overlapping detections can improve the performance of a pedestrian detection system, especially when there are multiple overlapping people. [sent-21, score-0.946]
10 Loosely speaking, the unary scores reward candidates with high detector confidence, whereas the pairwise scores impose a penalty for excessive amounts of overlap between two candidates. [sent-23, score-0.909]
11 The problem is to find a binary vector that maximizes the quadratic objective function, which is a classic problem of quadratic unconstrained binary optimization (QUBO). [sent-24, score-0.782]
12 First, a large set of possible detection candidates (Figure 2(b) and 2(f)) is generated, based on shape covering of a foreground mask in the top row, or sampling from a confidence map produced by a standard pedestrian detec- tor (with non-maximum suppression disabled) in the bottom row. [sent-27, score-1.349]
13 In both cases, the object configuration that maximizes the quadratic objective function is found and shown in Figure 2(c) and 2(g). [sent-28, score-0.339]
14 The top row uses a foreground shape covering approach to produce a large set of candidate detections. [sent-31, score-0.483]
15 The bottom row samples from confidence maps produced by a sliding window human detector to generate candidate detections. [sent-32, score-0.668]
16 In both cases, we perform the same binary quadratic optimization procedure to choose the solution set of candidates that maximize a quadratic objective function. [sent-33, score-0.792]
17 (e) sliding window detector confidence map (only one scale level shown). [sent-37, score-0.522]
18 candidate detections to optimize the tradeoff between unary confidence scores and pairwise overlap penalties. [sent-40, score-0.955]
19 Of the several approaches that have been proposed for detecting pedestrians, one common method uses a pre-trained classifier within a sliding window to scan the whole image looking for people at all locations and scales. [sent-43, score-0.254]
20 Since sliding window methods usually generate multiple overlapping detections on a person, the common final step is to apply non-maximum suppression as an attempt to remove false positive detections [9, 11]. [sent-49, score-0.687]
21 One line of work proposes to segment foreground blobs into human shapes using an MCMC-based optimization ap- proach to determine the number and configuration of overlapping shapes [23, 24, 10]. [sent-51, score-0.55]
22 We propose to use Quadratic Unconstrained Binary Optimization (QUBO) for pedestrian detection in order to reason more directly/thoroughly about overlapping detection candidates and their associated confidence scores and overlap penalties. [sent-53, score-1.119]
23 A quadratic cost function is used to represent criteria relating object confidence, overlapping hypotheses, and spatial interactions between pairs of objects from different classes. [sent-56, score-0.332]
24 Proposed Optimized Detection Framework Figure 3 presents a “big picture” overview of how our approach would be incorporated into a typical pedestrian detection pipeline. [sent-63, score-0.358]
25 First, an existing pedestrian detector is applied to produce a detection confidence score map, or if that is not available as output, a set of unfiltered bounding boxes with associated confidence scores. [sent-65, score-1.142]
26 A unary confidence score is computed for each candidate, to represent the quality of that proposed detection. [sent-67, score-0.512]
27 Furthermore, for candidates that overlap, a pairwise score is computed to specify a penalty that will be incurred if both candidates are kept in the final solution. [sent-68, score-0.535]
28 The purpose of this penalty is to prohibit excessive amounts of overlap while still allowing some amount of reasonable overlap to occur. [sent-69, score-0.298]
29 In the second step, unary and pairwise scores are grouped into a cost matrix to form the objective function for a quadratic unconstrained binary optimization (QUBO) problem. [sent-70, score-0.788]
30 In this QUBO problem, the unknown binary variables to solve for represent whether to keep or discard each pedestrian candidate from the final solution set of detections. [sent-71, score-0.549]
31 An optimization algorithm is then applied to search for an assignment of 0’s and 1’s to candidates yielding a high, ideally the maximum, objective function value. [sent-72, score-0.352]
32 1 discusses generation of candidates and objective function scores for two very different types of detection approach. [sent-74, score-0.43]
33 The first is a shape covering approach, based on finding size and placement of a set of pedestrian shapes in order to cover the pixels of a foreground mask computed by, e. [sent-75, score-0.814]
34 Overview of the Proposed Optimized Detection Framework proach uses a multi-scale confidence map produced by an existing, publicly available appearance-based detector. [sent-79, score-0.343]
35 2 discusses the second step of transforming into a binary quadratic objective function and efficient methods for generating high-quality approximate solutions to the resulting QUBO problem. [sent-81, score-0.457]
36 1 Detection Candidates by Shape Covering Previous works have considered the problem of detecting people as a “shape covering” of foreground mask data [10, 23]. [sent-86, score-0.289]
37 That is, given a foreground mask computed by background subtraction or motion analysis, a solution is sought as to the number, location, size and possibly articulation of a set of shapes to cover as many foreground pixels as possible while leaving as many background pixels as possible uncovered. [sent-87, score-0.528]
38 To avoid unnecessary proliferation of overlapping shapes, these methods augment the covering quality term of the objective function with either prior terms on the number of objects present, or with data terms that penalize object overlap. [sent-88, score-0.336]
39 To use this shape covering approach in practice, we first generate a lookup table relating location (x,y) in the image to expected height and width of a pedestrian centered at that location. [sent-91, score-0.673]
40 Given an automatically computed foreground mask, a candidate set of shapes is generated by methodically sampling midpoint locations every 10 pixels in x and y, looking up the expected width and height at each location, and computing a unary score ci for each candidate xi. [sent-95, score-0.98]
41 We use three common pedestrian poses shown in Figure 4 as the three shapes that can be proposed for shape covering. [sent-96, score-0.426]
42 For each candidate xi, three unary confidence scores are computing using each of these three pedestrian shapes, scaled to the size of the detection candidate bounding box. [sent-97, score-1.216]
43 2 Detection Candidates by Bounding Box Filtering Many object detection approaches use a sliding window based detector to generate a confidence score map, and then generate a set of final detections through a process of non maximum suppression. [sent-106, score-0.89]
44 For our approach, we modify an existing Histogram of Oriented Gradients (HOG) based pedestrian detector [1], available in OpenCV, and apply it at multiple scales without non maximum suppression to generate a multi-scale detection confidence map. [sent-107, score-0.934]
45 In the experiment, a set of 500 detection candidates is then randomly sampled from each detection scale, with the likelihood of a candidate being sampled at location (x,y) being proportional to the detector confidence at that location and scale. [sent-108, score-0.876]
46 Figure2(f) shows candidate samples generated from the confidence score map in Figure2(e) (only one scale level of the map is shown). [sent-109, score-0.504]
47 For example, images taken by a camera near eye level will have a large allowable range of scales, whereas an elevated camera much farther away may not see any difference in pedestrian size across the image. [sent-113, score-0.346]
48 Expected pedestrian bounding box size learned as a regression function between y location in the image and height of a detected pedestrian at that location. [sent-116, score-0.746]
49 Some previous works have used apriori pedestrian height distribu- tions to estimate camera calibration information from noisy pedestrian detections [13, 18]. [sent-119, score-0.847]
50 In our work, we employ a simple online learning approach that learns a regression function on expected bounding box height versus location in the image from a set of detections of pedestrians at different locations in images taken from a stationary camera view. [sent-120, score-0.479]
51 The light blue line is a quadratic regression function learned for one frame only, while the dark blue line is the height approximation found using data acquired over several frames. [sent-123, score-0.284]
52 However, rather than apply a hard threshold to filter improperly sized detections, we reduce unary confidence scores according to the dissimilarity between a candidate bounding box scale and the expected detection height at that location. [sent-125, score-0.943]
53 The detection confidence score will be greatly reduced when the detected box is much larger or smaller than the learned size estimate, reducing the chances that the candidate will be kept in the solution vector returned by QUBO. [sent-126, score-0.62]
54 In this work, we use the quadratic objective function = ? [sent-134, score-0.284]
55 , n are the binary variables to be solved f∈or, { ci are n unary . [sent-150, score-0.32]
56 1 Objective Function The quadratic objective function in Eq. [sent-157, score-0.284]
57 2 is computed by combining unary and pairwise terms. [sent-158, score-0.261]
58 Each unary score ci is a measure of confidence that candidate xi represents a person, while the pairwise scores ci,j penalize excessive overlap between pairs of candidates. [sent-159, score-1.033]
59 The three elliptically shaped candidates from left to right have unary values 3425, 4412 and 3658 computed from Eq. [sent-164, score-0.371]
60 For each pair of distinct overlapping candidates xi and xj, the overlap penalty ci,j (xi, xj) is -4594 for shapes x1 and x2, -1998 for shapes x1 and x3, and -3432 for shapes x2 and x3. [sent-166, score-0.746]
61 We find that the optimal solution [1, 0, 1] specifies that candidates x1 and x3 should be kept, while candidate x2 should be discarded. [sent-170, score-0.339]
62 Note that if we applied a traditional, greedy non maximum suppression approach where the candidate with highest confidence score is chosen and overlapping candidates of lesser score are suppressed, we would have chosen to keep only the middle candidate x2, while suppressing the other two. [sent-171, score-1.27]
63 3 can be formed as Q = w1 U − w2 P (4) where U is a diagonal unary score matrix, P is the pair- wise score matrix (overlap ratios), and , w1 w2 are relative 333666999311 Figure 6. [sent-173, score-0.35]
64 Using quadratic binary optimization to find the best set of detection candidates. [sent-174, score-0.39]
65 2 by adding a second unary term that represents the score from a second detector or other additional information. [sent-178, score-0.371]
66 For example, in our experiments we have explored combining unary scores computed from foreground shapes with scores computed from a detector confidence map. [sent-179, score-0.95]
67 Weight Parameter Estimation (5) Even though the unary and pairwise scores are both normalized values between 0 and 1, they represent very different types of information, one being an appearance-based detection confidence and the other being an area ratio. [sent-183, score-0.665]
68 Furthermore, the amount of “acceptable” bounding box overlap for a given situation may depend on the expected density of people in the scene as well as on the camera viewpoint. [sent-184, score-0.281]
69 For this reason, it is better to weight the relative contributions of the unary and pairwise terms with weighting parameters learned from representative training data. [sent-185, score-0.261]
70 The single candidate that gives the highest unary score is first selected. [sent-197, score-0.407]
71 Then, given a set of previously selected candidates, each remaining candidate is tentatively added to the set, and the set yielding the highest new objective function value becomes the new current solution set. [sent-198, score-0.249]
72 The process stops when adding any single candidate to the solution set will reduce the objective function value. [sent-199, score-0.249]
73 As a third approach, we relax the binary variable constraints into 0 ≤ xi ≤ 1to transform QUBO into a continuous quadratic programming problem. [sent-200, score-0.394]
74 Experimental Results In this section we evaluate our proposed quadratic binary optimization framework to detect overlapping pedes- trians. [sent-204, score-0.416]
75 We also evaluate three methods for solving the constructed QUBO optimization problem: Tabu search, greedy algorithm, and relaxation into a continuous quadratic program. [sent-206, score-0.327]
76 We use Matlab’s trust-region method to solve the relaxed quadratic programming problem. [sent-209, score-0.27]
77 Dataset We perform quantitative evaluation of our approach using a pedestrian dataset from EPFL called the Terrace sequences2 and on the PETS 2009 dataset. [sent-210, score-0.28]
78 These two datasets were chosen because of the large number of occlusions, a challenging issue in pedestrian detection. [sent-211, score-0.28]
79 (a) Comparison between Tabu search, Greedy, and Quadratic programming methods using foreground shape covering. [sent-216, score-0.254]
80 Figure 7(a) shows a quantitative comparison between Tabu Search, greedy algorithm, and quadratic programming results when candidates are generated based on foreground shape covering. [sent-219, score-0.717]
81 Both greedy algorithm and quadratic programming perform reasonably well. [sent-220, score-0.359]
82 Based on this result, we decided to use quadratic programming to evaluate our three options for generating candidates and unary confidence scores (foreground shape covering, detector confidence, confidence+foreground shape cover). [sent-225, score-1.194]
83 Two other approaches compared in those plots are OpenCV’s HOG-based human detector [1] and the PLS detector of [20], both using their default non-maximum suppression methods. [sent-230, score-0.354]
84 Approach 1 based on finding shape covering of a foreground mask works surprisingly well given the simplicity of the approach compared to the sophisticated appearancebased detectors it is being compared against. [sent-231, score-0.409]
85 Comparing approaches 1and 2, using detector confidence scores yields better results on the EPFL dataset, whereas foreground shape covering gives the better result on PETS. [sent-232, score-0.773]
86 In EPFL, people are large, with clearly visible edge appearance information, whereas the small / lowresolution crowds in PETS is a situation where fitting body shapes to cover foreground blobs yields better results. [sent-234, score-0.349]
87 In approach 3 we attempt to improve results using a hybrid of detector confidence combined with foreground covering as a second unary term, but with mixed results. [sent-235, score-0.878]
88 However, it demonstrates that the QUBO framework is flexible enough to be applied to a variety of detectors or combinations of unary and pairwise information. [sent-236, score-0.261]
89 Conclusion We have presented a framework for improving pedestrian detection performance in cases where there are mul- tiple, overlapping objects. [sent-243, score-0.462]
90 A QUBO framework is adopted where a quadratic objective function is formed from unary confidence scores and pairwise overlap penalties. [sent-244, score-0.977]
91 The unary terms are not limited to a specific type of detector and can be applied to various types of detection confidence scores with some adjustment. [sent-245, score-0.712]
92 Solving for the binary solution vector that maximizes this quadratic objective function automatically balances the trade off between encouraging multiple, high-quality detections, while discouraging excessive amounts of overlap. [sent-246, score-0.526]
93 Since finding exact solutions for largescale QUBO problems is not possible, we evaluate three approximate methods: heuristic Tabu search, greedy forward search, and relaxation to a continuous quadratic program. [sent-247, score-0.399]
94 Our results show that the use of binary quadratic optimization to explicitly reason about pedestrian candidate confidences and overlaps yields a performance improvement over existing detection methods that use nonmaximum suppression, in terms of lower miss rates and lower false positives. [sent-249, score-0.904]
95 sliding window detector that produces either a detection confidence map or a set of unfiltered, thresholded bounding boxes with associated confidence scores. [sent-254, score-0.926]
96 This covering approach can be generalized to use a library of realistic pedestrian shapes, such as those in [10, 23]. [sent-256, score-0.432]
97 Survey of pedestrian detection for advanced driver assistance systems. [sent-337, score-0.358]
98 Multistart tabu search strategies for the unconstrained binary quadratic optimization problem. [sent-373, score-0.807]
99 Hand tracking by binary quadratic programming and its application to retail activity recognition. [sent-405, score-0.344]
100 (c) Our approach 3: hybrid of confidence score and shape covering. [sent-417, score-0.389]
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