Antoine Tran
email: antoine.[tran@ensta-paristech.fr

Antoine Manzanera
email: manzanera]@ensta-paristech.fr

Mixing Hough and Color Histogram Models for Accurate Real-Time Object Tracking

This paper presents a new object tracking algorithm, which does not rely on offline supervised learning. We propose a very fast and accurate tracker, exclusively based on two complementary low-level features: gradient-based and color-based features. On the first hand, we compute a Generalized Hough Transform, indexed by gradient orientation. On the second hand, a RGB color histogram is used as a global rotation-invariant model. These two parts are processed independently, then merged to estimate the object position. Then, two confidence maps are generated and combined to estimate the object size. Experiments made on VOT2014 and VOT2015 datasets show that our tracker is competitive among all competitors (in accuracy and robustness, ranked in the top 10 and top 15 respectively), and is one of the few trackers running at more than 100 fps on a laptop machine, with one thread. Thanks to its low memory footprint, it can also run on embedded systems.

Introduction

Object tracking is a very popular task in computer vision. Basically, the goal is to accurately localize one defined object (the target) in a video. Among difficulties, we can cite object deformation, motion change, rotation, scaling or those linked to the context (illumination change, occlusion, camouflage, camera motion). Applications such as human-computer interaction or augmented reality require reactive algorithms, so the computational cost may be a critical issue.

For efficiency, our tracker is based on very light methods, and combines lowlevel shape and color features. It is a model-free tracker, meaning that the offline training is done only at the first frame of the sequence. The gradient orientation is computed and used as an index of a Generalized Hough Transform (GHT) [START_REF] Ballard | Generalizing the Hough transform to detect arbitrary shapes[END_REF]. A RGB histogram is used to represent the color aspect of the target object, and distinguish it from the background. These two parts are processed independently, and merged to finally estimate the object location. They are complementary: the original GHT is robust to illumination, but weak against scale and rotation, unlike the color histogram model. By testing and evaluating our tracker on VOT2014 and VOT2015 [START_REF] Kristan | The visual object tracking VOT2015 challenge results[END_REF][START_REF] Kristan | The visual object tracking vot2014 challenge results[END_REF], we show that this combination leads to high performance in terms of accuracy and robustness. Moreover, by associating low-level features and light algorithms, our tracker can run at more than 100 fps on a laptop machine, without explicit multithreading. It is one of the fastest among all competitors, while being ranked second among real-time trackers in terms of accuracy and robustness criteria from VOT2015. Its lightness also makes it suitable to embedded systems.

This paper is organized that way: after a short state-of-the-art of object tracking, we will explain our method. Finally, we will show some results obtained in the academic datasets.

Related Work

Given a sequence, object tracking consists in estimating the state of one target object at each frame. This state can be its center, its bounding box or its silhouette. Many works have addressed the tracking problem, and we refer to Yilmaz' survey for a coverage of the task [START_REF] Yilmaz | Object tracking: A survey[END_REF].

Structurally, our tracker belongs to the class of trackers combining different methods [START_REF] Babenko | Robust object tracking with online multiple instance learning[END_REF][START_REF] Bertinetto | Staple: Complementary learners for real-time tracking[END_REF][START_REF] Duffner | Pixeltrack: a fast adaptive algorithm for tracking non-rigid objects[END_REF][START_REF] Maresca | Clustering local motion estimates for robust and efficient object tracking[END_REF][START_REF] Yang | Robust visual tracking via multiple kernel boosting with affinity constraints[END_REF]. Among recent works, STAPLE [START_REF] Bertinetto | Staple: Complementary learners for real-time tracking[END_REF] is related to our technique: it combines correlation and color histogram model to provide an effective and fast tracker. As we are using the GHT in its original form, our templatepart tracker is simpler and lighter than Bertinetto's, as it only requires gradient computation (instead of HOG features [START_REF] Dalal | Histograms of oriented gradients for human detection[END_REF]). Duffner's PixelTrack [START_REF] Duffner | Pixeltrack: a fast adaptive algorithm for tracking non-rigid objects[END_REF] is also close to our tracker: it combines a GHT with a foreground/background color model into a very fast tracking algorithm (above 100 fps).

The VOT committee annually proposes a dataset to evaluate and rank trackers [START_REF] Kristan | The visual object tracking VOT2016 challenge results[END_REF][START_REF] Kristan | The visual object tracking VOT2015 challenge results[END_REF][START_REF] Kristan | The visual object tracking vot2014 challenge results[END_REF]. In this challenge, the most accurate trackers are based on Convolutional Neural Network [START_REF] Nam | Modeling and propagating cnns in a tree structure for visual tracking[END_REF][START_REF] Nam | Learning multi-domain convolutional neural networks for visual tracking[END_REF] and correlation filters [START_REF] Bertinetto | Staple: Complementary learners for real-time tracking[END_REF][START_REF] Danelljan | Beyond correlation filters: Learning continuous convolution operators for visual tracking[END_REF]. If we focus on the fastest algorithms of VOT15 challenge, Vojir's tracker [START_REF] Vojir | Robust scale-adaptive mean-shift for tracking[END_REF] based on the Meanshift [START_REF] Comaniciu | Real-time tracking of non-rigid objects using mean shift[END_REF] proposes decent accuracy, with a speed far beyond real-time. Maresca [START_REF] Maresca | Clustering local motion estimates for robust and efficient object tracking[END_REF] proposes a fast tracker based on estimation of object motion, obtained by the combination of several light trackers.

Our proposed tracker is based on very low-level features and lightweight operations: color histogram and GHT. Color histogram is popular in object tracking [START_REF] Comaniciu | Real-time tracking of non-rigid objects using mean shift[END_REF][START_REF] Possegger | In defense of color-based model-free tracking[END_REF][START_REF] Vojir | Robust scale-adaptive mean-shift for tracking[END_REF], since it is fast and robust to scale and in-plane rotation changes. The GHT is an extension of the Hough Transform [START_REF] Duda | Use of the Hough transformation to detect lines and curves in pictures[END_REF], used to detect arbitrary shapes. It consists in considering some elements of this shape (pixels, patches) and, according to their local appearances, make them vote for potential positions of the shape center. The estimated center is then determined by the location that has accumulated the highest number of votes. The GHT is robust to illumination changes and to camouflage issue, compensating some weaknesses of the color-based model. In tracking context, the main issue of the GHT is the robustness to scale and rotation changes. However, several authors proposed Hough-based trackers [START_REF] Duffner | Pixeltrack: a fast adaptive algorithm for tracking non-rigid objects[END_REF][START_REF] Gall | Hough forests for object detection, tracking, and action recognition[END_REF][START_REF] Godec | Hough-based tracking of non-rigid objects[END_REF][START_REF] Maresca | Matrioska: A multi-level approach to fast tracking by learning[END_REF] by modifying the original GHT, or using complementary methods. Amongst Hough-based trackers, only Hua [START_REF] Hua | Online object tracking with proposal selection[END_REF] outperforms our algorithm, but is 100 times slower. However, his algorithm essentially relies on a HOG-based detector, which estimates several candidates locations, and the Hough Transform is only used to discard wrong candidates. PixelTrack [START_REF] Duffner | Pixeltrack: a fast adaptive algorithm for tracking non-rigid objects[END_REF] is at a same order of magnitude in speed, but much less accurate and robust.

In the last VOT challenges [START_REF] Kristan | The visual object tracking VOT2016 challenge results[END_REF][START_REF] Kristan | The visual object tracking VOT2015 challenge results[END_REF], few trackers belong to the category of realtime trackers (21 competitors among 132), with diverse performances in accuracy and robustness. In this category, our method is one of the fastest (more than 100 fps), but also one of the most accurate and robust (only beaten by [START_REF] Vojir | Robust scale-adaptive mean-shift for tracking[END_REF]). Compared to slower tracker, ours is still competitive: ranked in the top 15 for both criteria in VOT2015 [START_REF] Kristan | The visual object tracking VOT2015 challenge results[END_REF] and ranked in the top 10 in VOT2014 [START_REF] Kristan | The visual object tracking vot2014 challenge results[END_REF].

Our state representation is based on a bounding box. Given a frame t, the aim is to estimate the bounding box B t = (c t , w t , h t ) of an object O, where each parameter is respectively: bounding box's center, width and height.

Our contribution

First, we explain how to initialize our tracker. Second, we deal with state estimation. As position is estimated before scale, we will explain these two steps in different sections. Third, we explain the model updating process.

Initialization

Our tracker is initialized at the first frame I 0 , with a manually set bounding box B 0 . Let I(B) be the restriction of an image I to any subset of pixels B.

First, the target RGB histogram H 0 of I 0 (B 0 ), with n c × n c × n c bins, is generated (n c = 12). H t will denote the target RGB histogram at the frame t.

Second, for the geometrical model, let M 0 and Φ 0 be the gradient magnitude and orientation of I 0 (B 0 ). The goal is to initialize the R-Table R (which will be updated over the time), indexed by n o = 16 orientations. It consists in considering all pixels p ∈ I 0 (B 0 ), for which M 0 (p) > M ( M = 70.0) and whose quantified gradient orientation is θ p , then to store in R(θ p ) the couple ( -→ u = -→ pc 0 , ω-→ u ), which is the displacement from p to the bounding box center c 0 , and ω-→ u = 1.0 a default weight value.

Estimation of position

Given an image I t from a sequence, our tracker first estimates the object center, then its scale. We will explain these two steps independently.

On the one hand, we perform a basic GHT. As during initialization, it requires to evaluate gradient image from I t , keep pixels p whose gradient magnitude is above M , and quantify its orientation as θ p . Then, for each couple ( -→ u , ω-→ u ) ∈ R(θ p ), p votes for all displacements p + -→ u with the weight ω-→ u . More formally: with δ the Kronecker function. Finally, when all pixels have voted, the created map (the Hough Transform) HT t emphasizes the most probable locations of the object center, with respect to the geometrical model. The GHT is performed under its simplest form, unlike [START_REF] Duffner | Pixeltrack: a fast adaptive algorithm for tracking non-rigid objects[END_REF] who indexes their R-Table using gradient and color features and [START_REF] Godec | Hough-based tracking of non-rigid objects[END_REF][START_REF] Maresca | Matrioska: A multi-level approach to fast tracking by learning[END_REF] who use machine learning classifiers.

HT t (p) = q ( - → u ,ω)∈R(θq) ω • δ(p, q + - → u ) (1)
We then blur HT t (3 × 3 discrete Gaussian filter), in order to add robustness to deformation. The GHT is intrinsically robust to illumination change (conservation of the orientation), but not to scaling (pixels votes spread away from the center) nor to rotation (pixels vote according to the wrong list in the R-Table ).

On the other hand, to exploit the color model, we define foreground and background areas. We use the color model histogram H t-1 , and build a background histogram H bck t . These features have the advantage to compensate for the GHT weaknesses, and vice-versa. Given the last estimated bounding box B t-1 , let S t be the background area, defined by all pixels inside the bounding box of center c t-1 , and dimension (α • w t-1 , α • h t-1 ) (α = 2.0), excluding B t-1 . From S t , we build H bck t . Then, for every pixel p ∈ (B t-1 ∪ S t ), let q p t be its quantified color in I t . As proposed in [START_REF] Possegger | In defense of color-based model-free tracking[END_REF], we define the foregroundness with respect to the object O, knowing the object color histogram H t-1 and the background color model:

F (Ht-1,H bck t ) O (p) = Ht-1(q p t ) Ht-1(q p t )+H bck t (q p t ) if p ∈ (B t-1 ∪ S t ) 0 otherwise (2)
F (Ht-1,H bck t ) O
(p) indicates how probably p belongs to the target. Unlike [START_REF] Possegger | In defense of color-based model-free tracking[END_REF], we do not combine Eq. 2 with a distractor-aware model, as we aim to remain as simple as possible. Compared to PixelTrack [START_REF] Duffner | Pixeltrack: a fast adaptive algorithm for tracking non-rigid objects[END_REF], this method only needs a model histogram and no prior information about background. Then, given a bounding box B of size (w t-1 , h t-1 ) inside (B t-1 ∪ S t ), let S c,t (B) be the normalized score evaluating whether the target is inside B:

S c,t (B) = p∈B F (Ht-1,H bck t ) O (p) w t-1 • h t-1 (3)
This formulation is simpler than Possegger's [START_REF] Possegger | In defense of color-based model-free tracking[END_REF], who proposed a method to discard distractors. We also use a prediction map, that indicates the likelihood to find c t at x, given B t-1 :

Π Bt-1 t (x) = exp( -(x -c t-1 ) 2 2 • min(w t-1 , h t-1 ) 2 ) (4)
Finally, for all pixels x, we define M t such as

M t (x) = HT t (x) • S c,t (B x ) • Π Bt-1 t
(x) with B x the rectangle centered in x of size (w t-1 , h t-1 ). From M t , we finally estimate the object position c t as follows:

c t =    argmax x (M t (x)) if max x (M t (x)) = 0 c t-1 + -----→ c t-2 c t-1 otherwise (5)
The second case of Eq. 5 assumes that, when the support of HT t and S c,t are disjoint, the target is translating with a vector -----→ c t-2 c t-1 . We choose a pixel-wise multiplication to merge our two trackers, unlike STAPLE [START_REF] Bertinetto | Staple: Complementary learners for real-time tracking[END_REF] who used a weighted average. In that way, we do not have to deal with the difference of magnitude of HT t and S c,t , and to adjust a weight. We also differ from PixelTrack [START_REF] Duffner | Pixeltrack: a fast adaptive algorithm for tracking non-rigid objects[END_REF], where the final position is obtained by linear combination of the centers estimated by the GHT on one hand and the color segmentation map on the other hand. Fig. 1 describes all steps for our position estimation.

Estimation of scale

The second step consists in estimating object scale.

On the one hand, from the GHT, let us define the backprojection map BP t , for all pixels p fulfilling conditions to be stored in the R-Table:

BP t (p) = ( - → u ,ω)∈R(θp) M t (p + - → u ) |R(θ p )| (6)
with |R(θ p )| the cardinality of R(θ p ). The approach is similar to Duffner's one [START_REF] Duffner | Pixeltrack: a fast adaptive algorithm for tracking non-rigid objects[END_REF]. However, Duffner only backprojects the peak of the GHT, while we consider the sum of the voted positions for all pixels. In both cases, the made assumption is that the higher the backprojection is, the more likely it belongs to the target. On the other hand, we consider

F (Ht-1,Ht bck ) O
, defined Eq. 2, as a color confidence map. Then, let BF t be the final confidence map:

BF t = 0.5 • (BP t + F (Ht-1,Ht bck ) O ) (7)
Fig. 2 illustrates these maps. Then, inspired by Posseger [START_REF] Possegger | In defense of color-based model-free tracking[END_REF], we consider the set of object pixels OP t = {p|BF t (p) > 0.5} ∪ R t , with R t a safe foreground area defined as the rectangle centered on c t , of size (β

• w t-1 , β • h t-1 ) (β = 0.20).
From OP t , we only retain the connected component that contains c t , to discard isolated pixels that could generate scale overestimation. Finally, we estimate a potential bounding box by computing the bounding box Bt of this connected component. Then, we reject bounding box sizes whose relative area variation with respect to B t-1 is above 5%. Otherwise, we update object's size using the same aspect ratio, as follows:

(a) It (b) BPt (c) F (H t-1 ,H bck t ) O (d) BFt
X t = λ t • X t-1 (8)
with X ∈ {w, h} and λ t = min(1.05, max(0.95, A( Bt) A(Bt-1) )) (A being the area operator). Fig. 3 summarizes scale estimation operations. Finally, to prepare the updating process, let SG t be the shape and color-based confidence map such that SG t (p) = BF t (p) if p ∈ B t , and 0 otherwise.

Model update

The last step consists in updating the model, knowing the estimated bounding box B t . To update the color model, let H o t be the color histogram of I t (B t ) and µ c = 0.05 the color updating rate:

H t = (1 -µ c ) • H t-1 + µ c • H o t . (9)
To update the R-Table R, we start by reducing all displacement weights:

∀θ, ∀( - → u , ω-→ u ) ∈ R(θ), ω-→ u ← (1 -µ g ) • ω-→ u (10)
Then, considering the confidence map SG t , and the object center c t , for all pixels p ∈ B t with gradient orientation θ p , we consider the displacement -→ v = -→ pc t , with a weight equal to µ g • SG t (p). Then, we consider two cases:

-if - → v is in R(θ p )
, we increment its weight by µ g • SG t (p) (µ g = 0.05), in order to reinforce the most relevant elements of the R-Table otherwise we add an entry into R(θ p ) with the weight µ g • SG t (p) Finally, for each index of the R-Table , we keep only the N R = 200 displacements with the strongest weights, to limit computational and memory cost.

Experiments

Before dealing with experiments on academic datasets, we will detail our implementation setup.

Implementations details

Our algorithm is developed using C++ and the OpenCV 2.4.9 library, and tested on a laptop at 2.4 GHz, without explicit multithreading. In terms of implementation, iterative pixel access is done using image pointers, and image histogram computation is done using Look Up Table . At frame t, our tracker only processes area centered in c t-1 , and of size two times the last bounding box area. To evaluate the map S c,t , we use integral images. Otherwise, no major algorithmic optimization has been done.

In terms of memory footprint, target's informations, composed of the color histogram (n c 3 = 12 3 floating point numbers), the R-Table (n 0 • N R • 2 • 4 integers for displacements and n 0 • N R • 2 floats for weights) and the two last states (4 integers for coordinates and scales), resulting, with our set of parameters, in a memory footprint of about 45 ko. This quantity is independent of target' size. It is however negligible compared to the number of temporary images: 2 8-bit images (gradient orientation and magnitude maps), 1 RGB image (the sub-image in which we are tracking the target) and 5 32-bit images (float) (HT t , BP t ,

S c,t , F (Ht-1,H bck t ) O
and BF t ), which depends on object's size (and its associated search window): for a 100 × 100 object's size, the footprint will reach 2 Mo. Considering the speed obtained experimentally, we are convinced that our method is suitable embedded systems. The code of our implementation will be made available soon. All parameters have been tuned for the best trade-off between performance and speed on VOT2015 [START_REF] Kristan | The visual object tracking VOT2015 challenge results[END_REF]. For experiments case, we will denote as CHT the position tracker only, and CHTs our complete tracker.

Results on VOT 2014 and VOT 2015

Each year, the VOT committee proposes a dataset to test and evaluate trackers. Each frame from each sequence is labeled according to its difficulty (occlusion, camera motion, size, motion or illumination change). Evaluation criteria are:

-Accuracy: based on overlap measure O(GT t , B t ) = GTt∩Bt GTt∪Bt , with GT t the ground truth at the frame t -Robustness: given by the number of failures (frames where O(GT t , B t ) = 0) -Speed: based on a normalized speed (EFO units, see [START_REF] Kristan | The visual object tracking VOT2015 challenge results[END_REF])

The VOT committee provides results of all competitors, and a toolkit to evaluate and rank trackers. For all experiments, we use the function report challenge to get weighted mean rank (based on ranks for all difficulties), pooled rank (based on all sequences), expected overlap, and speed. We also compute ranking with the whole set of results, but only display those of relevant trackers. Results for VOT2014 and VOT2015 are summarized Tab. 1.

VOT2014 [START_REF] Kristan | The visual object tracking vot2014 challenge results[END_REF] is a dataset composed of 25 sequences, and results for 40 trackers are available. We choose to show our results compared to DSST [START_REF] Danelljan | Accurate scale estimation for robust visual tracking[END_REF] (VOT2014 winner), Hough-based trackers [START_REF] Duffner | Pixeltrack: a fast adaptive algorithm for tracking non-rigid objects[END_REF][START_REF] Maresca | Matrioska: A multi-level approach to fast tracking by learning[END_REF][START_REF] Maresca | Clustering local motion estimates for robust and efficient object tracking[END_REF] and real-time trackers [START_REF] Duffner | Pixeltrack: a fast adaptive algorithm for tracking non-rigid objects[END_REF][START_REF] Henriques | High-speed tracking with kernelized correlation filters[END_REF][START_REF] Maresca | Clustering local motion estimates for robust and efficient object tracking[END_REF][START_REF] Vojíř | The enhanced flock of trackers[END_REF]. Amongst Hough-based trackers, our method is as well ranked as Matflow, combining Matrioska [START_REF] Maresca | Matrioska: A multi-level approach to fast tracking by learning[END_REF] and bdf [START_REF] Maresca | Clustering local motion estimates for robust and efficient object tracking[END_REF], but is 6 times faster (in EFO units). In the real-time trackers category, ours is the second fastest one, beaten by FoT [START_REF] Vojíř | The enhanced flock of trackers[END_REF] but our method is much more robust. KCF [START_REF] Henriques | High-speed tracking with kernelized correlation filters[END_REF] is more accurate and robust than our method, but is slower. Globally, our tracker is well ranked (top 10 among 40 competitors) but is one of the tracker proposing the best trade-off between effectiveness and speed. Surprisingly, our position-only tracker (CHT) and our complete one have similar performance in terms of accuracy and robustness, but the complete one is faster (probably due to object size reduction). VOT2015 challenge is composed of 60 sequences and results for 62 competitors are available. Compared to MDNET [START_REF] Nam | Learning multi-domain convolutional neural networks for visual tracking[END_REF], VOT2015 winner based on CNNs, and STAPLE [START_REF] Bertinetto | Staple: Complementary learners for real-time tracking[END_REF] (results from author's website, without speed results) our tracker is less effective, but faster (being lighter, and knowing that the author mentioned 80 fps on a 4.0GHz CPU, we expect our method to be faster than STAPLE). Compared to STAPLE, our shape-based tracker relies on the GHT, with gradient computation only, while STAPLE requires a more complex algorithm (correlation-based tracker using HOG features). Amongst real-time trackers [START_REF] Maresca | Clustering local motion estimates for robust and efficient object tracking[END_REF][START_REF] Vojíř | The enhanced flock of trackers[END_REF][START_REF] Vojir | Robust scale-adaptive mean-shift for tracking[END_REF], our tracker is one of the few above 100 EFO, and is only beaten by Vojir's extension of Meanshift [START_REF] Vojir | Robust scale-adaptive mean-shift for tracking[END_REF] in rankings and speed, but with slightly higher expected overlap. Otherwise, we are better ranked than other real-time trackers. We perform better than other Hough-based trackers [START_REF] Godec | Hough-based tracking of non-rigid objects[END_REF][START_REF] Maresca | Matrioska: A multi-level approach to fast tracking by learning[END_REF], including Matflow, which was on par with our tracker in VOT2014, but excluding sPST [START_REF] Hua | Online object tracking with proposal selection[END_REF], which is 100 times slower and relies on an object detector. Compared to Possegger [START_REF] Possegger | In defense of color-based model-free tracking[END_REF], from which our color part tracker is inspired, we demonstrate the usefulness of the Hough part, since, in weighted mean ranking, our method is slightly more robust. Some results are shown We also used VOT2015 to see performances of each part of the tracker (Hough and color ones). In both cases, the loss of performance is dramatic, as we can see on Fig. 6, where we show the results of different versions in terms of expected overlap (the higher, the better) and failures (the lower, the better) for several difficulties, both obtained on the set of frames concerned by the difficulties.

Conclusion

In this paper, we proposed a tracker working without offline training and tracking arbitrary objects. Unlike most state-of-the-art trackers, our method is based on a very low level representation. First, our geometrical model is only based on gradient, through a GHT. Then, an object color histogram is used to generate a map indicating the likeliness of the pixel to belong to the object. These two operations, done independently, are combined to estimate object center. Second, from the two features, we generate two confidence maps, and merge them in order to estimate the object size. The final confidence map is built from the fusion of these two maps and used to update the object geometrical and color models. Our whole tracker relies on computationally efficient operations, and performs tracking task beyond real-time (about 100 fps) with a low memory footprint. Experiments were done on recent academic dataset [START_REF] Kristan | The visual object tracking VOT2015 challenge results[END_REF][START_REF] Kristan | The visual object tracking vot2014 challenge results[END_REF], for which our tracker is ranked in the first third for accuracy and robustness. It is also one of the fastest from VOT2014 and VOT2015 challenges. Thanks to its speed and low memory footprint, our algorithm can be implemented on embedded systems, combined with other trackers to improve accuracy and robustness or with object detection or background subtraction to automatically initialize tracked regions.

Fig. 1 :

 1 Fig. 1: Position tracking diagram.

Fig. 2 :

 2 Fig. 2: Cropped frame from car1 from VOT2015, with the ground truth in blue. Backprojection map BP t and pixel color likelihood map F (Ht-1,H bck t ) O are complementary: while the first one indicates which border pixels are more likely to belong to the target, the second one gives high results for pixels of car's back.

Fig. 3 :

 3 Fig. 3: Scale estimation diagram.

Fig. 4 :

 4 Fig.4: The first line illustrates failures due to the transparency of the glove (ground truth in blue, tracker output in red), making its color similar to the chair. The GHT still performs correctly (sharp peak on the second image). On the second line the GHT fails due to the rotation of the book: the peak disappears from HT 1 to HT 2 .

Fig. 5 :

 5 Fig. 5: Results from VOT2014 and 2015. White bounding boxes are ground truth, red ones are obtained with our tracker. The two first images are cropped from sphere and torus sequences from VOT2014 (PixelTrack in blue, and MatFlow in green). The two last are cropped from birds2 and motocross sequences from VOT2015 (DAT in blue, and STAPLE in green).

Fig 4 and

 4 Fig 5.

Fig. 6 :

 6 Fig. 6: Expected overlap and number of failures for our complete tracker, and for partial versions (position tracking only, Hough only and Color only)

Table 1 :

 1 Results in VOT2014 and VOT2015 for different trackers. Real-time trackers appear in bold.

			VOT2014
	Tracker	Weighted mean rank	Pooled rank	Expected	Speed
		Accuracy Robustness Accuracy Robustness overlap (EFO) (fps)
	CHTs	8.83	4.33	6	9	0.2960 129.77 159.21
	CHT	8.42	4.08	6	9	0.2916 109.75 134.65
	DSST [6]	1.83	4.33	1	3	0.3693	5.80 13.07
	Matrioska [17]	9.83	12	6	9	0.2671 10.20 21.88
	bdf [18]	10.67	7.50	10	9	0.3097 46.82 100.45
	Matflow [17, 18]	8.67	3.17	6	4	0.3120 19.08 40.94
	FoT [22]	7	18.17	6	22	0.2859 114.64 306.52
	PTp [9]	25.33	11.17	30	9	0.2519 49.89 127.87
	KCF [12]	2	4.67	1	5	0.3641 24.23 63.42
			VOT2015
	CHTs	12.67	13.67	13	17	0.2606 103.89 111.22
	CHT	13.83	15.67	13	20	0.2615 101.91 109.10
	Staple [3]	1	4.33	1	5	0.345
	ASMS [23]	7.50	11	2	13	0.2353 115.09 142.26
	bdf [18]	29.33	32	27	43	0.2054 200.24 78.43
	FoT [22]	19.50	42.50	16	53	0.1934 143.62 177.53
	DSST [6]	4.0	23.67	1	38	0.2707	3.29 4.47
	DAT [21]	13.73	17.33	6	20	0.2428	9.82 14.87
	HT [11]	20	28.50	13	43	0.2045	0.91 0.56
	Matflow [17, 18] 22.17	27.33	23	43	0.2098 81.34 31.86
	MDNET [20]	1	1.33	1	1	0.3789	0.87 0.97
	sPST [13]	1.67	4.50	1	5	0.3134	1.03 1.16

Acknowledgments

We gratefully acknowledge financial support from the French Government Defense procurement and technology agency (DGA/MRIS).