Stixel on the Bus: An Efficient Lossless Compression Scheme for ...

Stixel on the Bus: An Efficient Lossless Compression Scheme for Depth Information in Traffic Scenarios Qing Rao1 , Christian Gr¨ unler1 , Markus Hammori1 , and Samarjit Chakraborty2 1 Daimler AG, Research and Development Benz-Str. Gate 16, 71063 Sindelfingen, Germany 2 Technische Universit¨ at M¨ unchen Arcisstr. 21, 80333 M¨ unchen, Germany {qing.rao,christian.gruenler,markus.hammori}@daimler.com, [email protected]

Abstract. The modern automotive industry has to meet the requirement of providing a safer, more comfortable and interactive driving experience. Depth information retrieved from a stereo vision system is one significant resource enabling vehicles to understand their environment. Relying on the stixel, a compact representation of depth information using thin planar rectangles, the problem of processing huge amounts of depth data in real-time can be solved. In this paper, we present an efficient lossless compression scheme for stixels, which further reduces the data volume by a factor of 3.3863. The predictor of the proposed approach is adapted from the LOCO-I (LOw COmplexity LOssless COmpression for Images) algorithm in the JPEG-LS standard. The compressed stixel data could be sent to the in-vehicle communication bus system for future vehicle applications such as autonomous driving and mixed reality systems. Keywords: stixel, lossless compression, LOCO-I.

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Introduction

The growing demands for safety, comfort and interactivity in vehicles are motivating manufacturers and suppliers in the automotive industry to search for new sensor and vehicle architecture solutions. In recent years, the development of camera sensor techniques and stereo vision algorithms has enabled real-time retrieval of depth information. This has spawned new applications in the field of robotics, video games and driving assistance systems, and raises the issue of how to most effectively represent and utilize the huge amount of depth data generated as a result of these applications. Stixel [1–4], a compact representation of a depth map, is an effective means of modeling depth information in traffic scenarios. The term “stixel” is the combination of “stick” and “pixel”, indicating a thin rectangular area on the image, inside which the pixels have the same or similar depth properties, as shown in Fig. 1. C. Gurrin et al. (Eds.): MMM 2014, Part I, LNCS 8325, pp. 568–579, 2014. c Springer International Publishing Switzerland 2014

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Fig. 1. Example of stixel representation in a typical traffic scene [3]. Distances to front objects are encoded by different color with red being close and green being far away. Ground area remains with its original gray scale intensity. The white rectangle frame without filling color indicates placeholder stixel for ground, which is introduced by us to fill the gap inside a stixel column in vertical direction, so that the adjacent constraint which will be explained later in subsection 2.1 can be satisfied.

Although a considerable amount of research has been conducted on both modeling and compression of depth information, a sophisticated combined solution has not yet been developed either in research or in the industry. In this paper, we present an efficient lossless compression scheme for stixel data. Our specific goal is to transmit compressed stixel data through in-vehicle communication bus systems such as CAN [5] or FlexRay [6], so that the depth information is available to multiple electronic control units (ECUs) in the vehicle’s electronic system for use by different applications, such as those pertaining to driver assistance systems. Reduction of the data volume is realized through simplification of the source model and predictive coding. The prediction scheme we have designed regards the stixel column1 as an atomic unit, resembling the pixel in the context of image compression. Simultaneous minimization of spatial and temporal redundancies in stixels is achieved through adaptation of the predictor of the LOCO-I algorithm [7, 8], a compression algorithm of the JPEG-LS standard for continuous-tone image. The rest of this paper is structured as follows. In the next subsection, we briefly discuss related work in this area. Section 2 explains the proposed approach in detail, and Section 3 presents the experimental results. We conclude in Section 4 by outlining some directions for future work. 1.1

Related Work

Correlation-based stereo matching is a traditional method for retrieving depth information from stereo vision systems [9] with several efficient real-time implementations [10–12]. Generally, correlation-based methods suffer from blurred boundaries in the resulting depth map, due to the assumption of constant disparities within a local correlation window. The semi-global matching (SGM) 1

The precise definition of stixel column is given in subsection 2.1.

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algorithm [13] alternatively solves the stereo matching problem by optimizing a global cost function, taking both pixel-wise matching cost and local smooth constraint into consideration. The outcome of the SGM algorithm has proved to be robust and illumination insensitive. Relying on the low-cost implementation of the SGM algorithm on field programmable gate array (FPGA) [14], real-time computation of disparity images becomes possible. The basic idea of stixel emerged in [1] with the aim of building a mid-level representation of the dense depth map computed through the SGM algorithm. Taking into account that in common traffic scenarios, objects such as cars, pedestrians and building facades can be represented through vertical planar surfaces, the authors introduced the novel term “stixel” as the atomic element for approximating object surfaces. A stixel represents a thin, standing rectangle area, which has a certain height, width and depth. In the authors early proposals [1, 2], the border between the road and the objects is firstly computed by means of occupancy grid [15]. The constraint that stixels have to “stand” on the ground had to be followed, as shown in Fig. 2. In their most recent proposal [3], this constraint is lifted and the computation of stixel is reformulated as a global segmentation problem. Every column in the disparity image is segmented into two classes: either object or ground. While object segments preserve constant depth value, ground segments tend to have a steady increment by depth, in accordance with the physical change of the road. The segmentation problem is treated as a max a posteriori probability (MAP) problem and is solved through dynamic programming (DP) [16] in real-time.

Fig. 2. Early approach of stixel computation [2]. The left image shows the stixel representation where only maximal one stixel appears per image column. The image in the middle shows the border between the ground and the objects standing on it. The green area in the right image represents the free space computed by means of occupancy gird.

In general, a lossless compression scheme consists of two major steps: analyzing the statistical model of the source data, and designing an optimal coding method that minimizes redundancy in the source model. Binary Huffman coding [17] is ideal if the probability of each input symbol is a power of half; Golomb coding [18] is optimal if the source satisfies one-sided geometric distribution. In the field of image compression, the modeling step is commonly realized through a prediction technique, by which image data is effectively decorrelated by using only a few prediction parameters. In the FELICS (Fast Efficient & Lossless


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Image Compression System) algorithm [19] for example, the current pixel to be encoded is firstly modeled by the difference between the maximal and the minimal pixels in its closest causal neighborhood. Other lossless image compression algorithms based on predictive coding include the LOCO-I algorithm and the CALIC (Context-based Adaptive Lossless Image Codec) [20] algorithm. The LOCO-I algorithm predicts the current pixel through a simple fixed predictor taking four neighboring pixels as inputs, whereas the CALIC algorithm extends the neighborhood to eight pixels and uses a more complex prediction equation. With respect to both compression ratio and encoding time, the LOCO-I algorithm outperforms other lossless compression algorithms and has become the core of the JPEG-LS standard.

2

Proposed Method

In this paper, the latest multi-layer stixel representation is used for the experiments. The work in [3] results in a spatial redundancy in the stixel data, since neighboring columns in the disparity image are assumed to be independent in order to achieve real-time computation capability. Additionally, since stixels represent objects or environments in real world traffic scenarios, where motions are considered to be continuous, there is a certain temporal redundancy between the stixels in adjacent disparity image frames. In our approach, we reduce the spatial as well as the temporal redundancy. In what follows, we explain in detail how our proposed method models and removes the redundancies in the stixel data. In subsection 2.1, we discuss the mathematical model of the source data. Subsequently, we explain the prediction workflow and the mechanism of entropy coding in subsection 2.2 and 2.3. 2.1

Source Data Model

A Stixel S is denoted as the tuple S(w, u, d, v t , v b ). The five parameters of S indicate the width, the horizontal coordinate of the center point, the disparity, the top and the bottom boundary of the “stick” rectangle, respectively. In the multi-layer stixel representation, width of a stixel is constrained to a fixed value. u In this case, the stixel tuple can be degenerated to S(ˆ u, d, v t , v b ), where uˆ = w can be understood as the ordinal number of the stixel along the horizontal direction. To simplify notation, the hat symbol of uˆ will be omitted in the following text. A Stixel Column C = S0 S1 . . . Sn−1 is a sequence of stixels ordered from top to bottom in the same column. The vertical boundary coordinates of stixels that t b < vn−1 , belong to the same stixel column satisfy v0t < v0b < v1t < v1b < · · · < vn−1 where n ∈ IN indicates the number of stixels inside the column. Additionally, we b introduce the vertical adjacent constraint vi−1 = vit − 1, i = 1 . . . n − 1 to further simplify the stixel model. In case that a “ground area” appears vertically between two “objects areas”, as shown in Fig. 1, a placeholder stixel Sg will be added in order to force the adjacent constraint to be valid. Relying on the vertical

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adjacent constraint, the stixel tuple can be further degenerated since only one of the parameters v t and v b is necessary. In the following text, v t will be omitted and v b will be denoted as v. A Stixel Frame F is a sequence of stixel columns F = C0 C1 . . . CN −1 ordered from left to right, where N ∈ IN denotes the number of stixel columns inside the stixel frame. Since the stixel width w is predefined, the number of stixel columns can be determined by N = W w , where W indicates the width of the disparity image. It is possible to differentiate two stixel columns if their word lengths are identical, i.e. if they have the same number of stixels. The difference between them is referred to as Residual Column and represented as R = Δd0 Δv0 . . . Δdn−1 Δvn−1 , where Δdi ∈ ZZ, i = 0 . . . n − 1 indicates the difference of the corresponding stixel disparities and Δvi ∈ ZZ, i = 0 . . . n − 1 the difference of stixel boundaries.

u

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Fig. 3. Temporal-spatial neighborhood matrix of stixel columns. Each row of the matrix represents a stixel frame at certain time point. The four entries inside the black box, including three stixel columns (Ct−1,u−1 , Ct−1,u , Ct−1,u+1 ) in the previous frame and one stixel column Ct,u−1 in the current frame, construct a causal reference area for predicting the current stixel column Ct,u . Alternative reference area containing Ct,u+1 instead of Ct,u−1 , and extended reference area containing columns in Ft−2 can also be taken into consideration.

A stixel column correlates with its neighbor columns in both spatial and temporal respect. Let Ct,u be the current observed stixel column, its temporalspatial neighborhood can be represented by the matrix shown in Fig. 3. The black box inside the matrix shows a causal reference area for predicting the current stixel column. 2.2

Prediction Scheme

We formulate the compression task as follows. The first step involves designing an optimal prediction scheme that minimizes the spatial and temporal redundancies in stixels. One of the challenges in decorrelating the stixel data is the selection of a proper neighborhood for prediction, since stixels on a disparity image do not lie in a rectangular grid as pixels on a normal image. To deal with


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this problem, we introduce the concept of a reference group, by which similar stixels in a reference area are first grouped. This however leads to the further problem that the number of stixels in a reference group can vary. A flexible predictor is thus necessary to deal with various input combinations. We decided to use the simple predictor of the LOCO-I algorithm for the following reasons. First of all, the prediction equation only takes three neighboring pixels as inputs (the fourth neighboring pixel is used for context modeling) and performs only addition/subtraction operations. This allows us to save a certain amount of computation and memory resource compared to the CALIC predictor. Furthermore, the LOCO-I predictor provides us with the possibility of detecting depth discontinuity between stixel columns, which appears to be a common case in traffic scenarios, so that the prediction quality can be improved. To make the notation consistent with LOCO-I, the left reference column in the current frame will be denoted as CA , whereas the reference columns in the previous frame as CC , CB and CD from left to right. The current stixel column will be denoted as CX and the predicted stixel column as CP . Reference Group. We use the following expression to measure the dissimilarity of stixels: δ (S1 , S2 ) = λ1 |d1 − d2 |2 + λ2 |l1 − l2 |2 + λ3 |v1b − v2b |2 + |v1t − v2t |2 (1) where li = vib − vit , i = 1, 2 indicates the length of stixel. The first term in Eq. 1 regards the disparity difference, while the second and the third term take the length difference and the coordinate difference of boundary into consideration. The three parameter λ1 , λ2 and λ3 are introduced to control the weight of the three terms and are set to satisfy λ1 > λ2 > λ3 . In other words, we consider disparity value to be the most significant indicator to measure the stixel dissimilarity and the boundary coordinates to be less important. If δ (S1 , S2 ) is below a certain threshold τs , the two stixels S1 and S2 are considered to be similar and grouped together. Simple Prediction. From each reference group, a stixel is predicted. We use the simple predictor in LOCO-I algorithm to predict disparity value dP , as expressed in Eq. 2. The predictor tends to choose (i) dA if a temporal discontinuity (a huge gap between dA and dC ) is detected; (ii) dB if a spatial discontinuity (a huge gap between dB and dC ) is detected; (iii) the general prediction dA + dB − dC if no discontinuities are detected. To predict boundary values vP , the assumption that real world objects in common traffic scenarios have clear and sharp edges is made. Under this assumption, similar stixels in a neighborhood tend to form basic geometric shapes, such as large rectangles or trapezoids [4], and the missed boundary value can be efficiently predicted through linear interpolation. Although in practice this assumption is not always accurate due to noises in stixels, it is still a reasonable approach to predicting boundary values.

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⎧ ⎪ if dC ≥ max(dA , dB ) ⎨min(dA , dB ), dP = max(dA , dB ), if dC ≤ min(dA , dB ) ⎪ ⎩ dA + dB − dC , otherwise

(2)

To deal with the problem of varying number of reference stixels, we classify the reference group according to the combination of reference stixels and assign a confidence score to each class. For example, the reference group containing three stixels from column CA , CB and CC is considered to be more reliable than the reference group merely containing one stixel from CD . The confidence score will be used for the final prediction step: the competitive fusion. For a reference group containing less than three stixels, the predicted stixel will be straightforwardly given by the expectations of the disparities and the boundary coordinates, since the LOCO-I predictor requires at least three inputs. However, the confidence score of the predicted stixel will be typically low in this case. Competitive Fusion. Two predicted stixels have to compete if they overlap each other vertically with more than τv pixels. The one with higher confidence score wins the competition. At last, all highly confident candidates are fused together back into a stixel column regarding the vertical adjacent constraint. After experimenting with different combinations of the parameters, we choose λ1 = 4, λ2 = 2, λ3 = 1, together with τs = 300 and τv = 12, which yields the best average compression factor. Fig. 4 illustrates the entire prediction workflow.

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Fig. 4. Example of the prediction scheme. At first, stixels in the reference columns are grouped into three stixel groups. The simple prediction procedure will then be executed on every group, yielding three stixel candidates. The green stixel and the blue stixel have to compete since they are overlapping each other. The green one wins the competition for its reference group is more confident than the reference of the blue one. At last, the red one and the green one are fused together into a stixel column.


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Entropy Coding

If the stixel numbers of the predicted column CP and the current column CX are identical, i.e. nP = nX , the encoder switches to Residual Mode and encodes the residual column with a modified version of Golomb code similarly as in the LOCO-I algorithm. Golomb coding uses a single parameter m ∈ IN+ which divides the input symbol x ∈ IN into two parts: the quotient q which is encoded using unary code, and the remainder r which is encoded using modified binary code. Theoretically, Golomb code is optimal if the source follows one-sided geometric distribution [21], i.e. P (x) = (1 − θ)θx where 0 < θ < 1 denotes the parameter that affects the shape of the distribution curve. For a certain parameter θ, there exists an optimal Golomb divisor m = − log(1 + θ)/ log θ which minimizes the average code length. In practice, the divisor is usually chosen to be m = 2k , k ∈ IN, so that the encoding process can be implemented more efficiently through binary arithmetic [8, 22].

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Fig. 5. Probability distributions of disparity residuals of different reference classes. The disparity residual follows approximately two-sided geometric distribution. The mapping x ← 2x, x ≥ 0 and x ← −2x − 1, x < 0 is used to transform the source back to be one-sided.

To encode the residual stixel column, we use different Golomb divisors for different reference classes, since each reference class shows its particular statistical properties, as presented in Fig. 5 and Tab. 1. The Golomb divisor for a certain reference class is updated adaptively based on the “one liner” implementation in [7]. Furthermore, the Golomb divisors for disparity residual Δd and boundary residual Δv are calculated separately as well. If the word lengths of CP and CX are not identical, the encoder switches to Rescue Mode. A stixel in rescue mode is modeled by its disparity d and its length l and will be simply binary encoded. A stixel column is still represented by the sequence of stixels ordered from top to bottom, only additionally with the number of stixels inside the column. Furthermore, the horizontal ordinal numbers u of all false predicted stixel columns are recorded and encoded in a header structure of the current stixel frame, in order to let the decoder be able to know on which column it should run in rescue mode.

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Table 1. Statistical properties of the most frequent reference classes. Class index is related to the combination of reference stixels and assigned in a binary coding manner. Class frequency and residual entropy are calculated from 10, 000 stixel frames. Notice that nearly 15% of the stixel references belong to class 1, which contains only one stixel from column CD and yields high residual entropy. This happens if objects on the disparity image move in the opposite direction against the predictor, i.e. from right to left. However, the predicted stixel from class 1 will in most cases be dropped during the competitive fusion step due to low confidence score. Class index CA CB CC CD Class frequency Entropy of disparity residual 15 1 8 10 14

3

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0.2691 0.1490 0.0968 0.0760 0.0744

2.1517 6.5906 4.7662 4.7946 2.7650

Experiments and Results

The stereo vision system in our experiment has a resolution of 1024 × 440 pixels. With a fixed width of 7 pixels, there are 1024/7 = 146 stixel columns inside a frame. The stixel boundary coordinate v theoretically varies from 0 to 439 with increment 1 and the disparity d has the range from 0 to 127 with increment 0.25. The range of d is remapped from 0 to 508 by multiplying factor 4 to ensure integer representation. Thereby, both symbol v and symbol d can be binary encoded by 9 bits covering from 0 to 511. Three comparison experiments are introduced to evaluate the proposed approach. The Raw method refers to binary encoding without any compression mechanism. Method Space+Time indicates the approach described in this paper, where the reference stixels for prediction are taken from both spatial and temporal neighborhood. Method Space refers to the experiment where only spatial neighbor CA is used for prediction. Additionally, we also compared our method to the general compression method using library Zlib [23], a combination of LZ77 [24] algorithm and Huffman coding. All experiments are implemented with C++ and executed on an Intel Core i7-2620M CPU, 2.7GHz with 4GB RAM. A dataset containing 25,000 stixel frames calculated from real traffic scenario is used for the evaluation and the results are presented in Tab. 2. In addition to the evaluation from an average point of view, the compression performance on single stixel frame is analyzed as well, as illustrated in Fig. 6. The encoder performance is closely related to the traffic scenarios: The red curve remains low and flat when the test vehicle keeps driving straightforward, whereas sudden impulses appear when unexpected objects pass by or the test vehicle makes a rapid turn. The bandwidth requirement on the vehicle bus is determined by the peaks in the curve instead of the average value. For example, the bandwidth of the uncompressed data could be greater than 2000B × 25fps ≈ 50KB/s, which exceeds the maximal payload capability of a CAN bus (34KB/s with 11bit identifier, 30KB/s


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Table 2. Experiment results. Column “false prediction rate” shows the ratio of false predicted columns which are encoded in rescue mode. Column “average processing time” shows the average encoding time per frame in milliseconds. Real-time capability of the encoder is guaranteed since the computation of dense disparity map only runs at 25 frames per second [3]. However, there are still over 20% false predicted columns with the reference area shown in Fig. 3. A more sophisticated mechanism for selecting reference area will be considered in future work. Method

Average compression factor False prediction rate Average processing time

Raw Space Space+Time Zlib

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0.272 2.920 0.267

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Fig. 6. Data volume along time axis. The magenta curve shows data volume with raw encoding, while the red curve shows compressed data volume. The green and the blue dashed curves illustrate data volume in residual mode and rescue mode respectively.

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Fig. 7. Workflow of the encoder. At certain time point, a new stixel frame arrives at the encoding buffer. Each stixel column CX of the frame will then go through the column predictor. If the stixel number of the predicted column CP and CX are not identical, the encoder switches into rescue mode. Otherwise, the encoder runs in residual mode.

with 29bit identifier) [25]. Therefore, the more expensive FlexRay with 500KB/s payload capability [25] should be used to transmit the uncompressed data. Although theoretically, the compressed stixel data with 800B × 25fps ≈ 20KB/s bandwidth requirement can already be transmitted through CAN bus, we are

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still considering introducing combination of lossless and lossy compression to specifically deal with those peaks in future work, since the vehicle bus is actually full of other signals and never complete idle for one particular signal.

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Concluding Remarks

We present an efficient lossless compression scheme for stixel data. To compress stixel, we have designed the stixel column predictor which adapts the LOCO-I predictor in the JPEG-LS standard. The experiment results show the real-time capability of the proposed encoder with an average compression factor of 3.3863. The compressed stixel data can be theoretically transmitted through CAN bus, while the uncompressed data requires at least FlexRay for transmission. In the future, we plan to improve the stixel column predictor by experimenting with different reference areas and prediction paths. A combination of lossy and lossless compression for different traffic scenarios could further reduce the peak data volume on the vehicle bus. Transmission of the compressed stixel data will be simulated to make depth information available to different vehicle electronic control units, for the next generation of vehicle applications such as autonomous driving and mixed reality systems.

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