## Discrete Driver Assistance

Citations: | 1 - 1 self |

### BibTeX

@MISC{Klette_discretedriver,

author = {Reinhard Klette and Ruyi Jiang and Ino Morales and Tobi Vaudrey},

title = {Discrete Driver Assistance},

year = {}

}

### OpenURL

### Abstract

Abstract. Applying computer technology, such as computer vision in driver assistance, implies that processes and data are modeled as being discretized rather than being continuous. The area of stereo vision provides various examples how concepts known in discrete mathematics (e.g., pixel adjacency graphs, belief propagation, dynamic programming, max-flow/min-cut, or digital straight lines) are applied when aiming for efficient and accurate pixel correspondence solutions. The paper reviews such developments for a reader in discrete mathematics who is interested in applied research (in particular, in vision-based driver assistance). As a second subject, the paper also discusses lane detection and tracking, which is a particular task in driver assistance; recently the Euclidean distance transform proved to be a very appropriate tool for obtaining a fairly robust solution.

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Citation Context ...Ω. See Figure 1; the third view has been used in [17] for prediction error analysis. Thus, stereo pixel correspondence is basically a 1D search problem, compared to motion pixel correspondence (e.g., =-=[10]-=-) which is a continuous 2D search problem. Two corresponding pixels pL = (x, y) and pR(x − ∆(x, y), y) identify a disparity ∆(x, y) which defines the depth bf/∆(x, y), where b is the base distance bet... |

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Citation Context ...abel ∆p or assigns the new label α; this defines a partition of the graph into set S (old label) and S (new label). Equation (9) defines the energy for this partitioning (labeling). See, for example, =-=[1]-=- for more details. 3 Improving Stereo Results by Preprocessing Obviously, the illustrated resulting depth maps are not satisfactory for DAS. Errors are often due to varying illumination conditions or ... |

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Citation Context ... energy function for reducing this streak effect. A further option is to combine forward DP also with the following backward DP strategy: E m ⎛ M∑ (∆) = ⎝Dx(∆x) + ∑ ⎞ C(∆x, ∆ˆx) ⎠ with E(∆) = E 1 (∆) =-=(4)-=- x=m ˆx∈A(x) where ∆m is selected as that l ∈ L which minimizes Dm(l) + C(l, ∆m−1) + Em−1(∆) + C(l, ∆m+1) + E m+1 (∆) (5) (Em−1(∆) and E m+1 (∆) can be ignored again.) Obviously, this requires to proc... |

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Citation Context ...Sandino Morales, and Tobi Vaudrey 2 Stereo Algorithms Stereo algorithms are designed for calculating pairs of corresponding pixels in concurrently recorded images. After calibration and rectification =-=[6]-=-, images L (left) and R (right) are in standard stereo geometry (i.e., parallel optical axes, coplanar image planes, aligned image rows), defined on pixels of an M × N grid Ω. See Figure 1; the third ... |

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Citation Context ...b-Optimal Solutions Basically, current stereo algorithms follow one of the following three paradigms: scanline optimization often implemented by (DP) dynamic programming [18], (BP) belief propagation =-=[3]-=-, or (GC) graph-cut [15]. These paradigms aim at finding a sub-optimal solution to the stereo matching problem. SGM using Scanline Optimization. Semi-global matching (SGM) is commonly identified with ... |

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Citation Context ... a higher weight. Finding a global minimum ∆, which minimizes the energy in Equation (1), assuming a continuity function which is not enforcing some kind of over-smoothing, is an NP-hard problem; see =-=[15]-=-. Purely local matching strategies (e.g., hierarchical correlation based methods) failed to provide reasonable approximate solutions. Strategies favored recently follow some semi-global optimization s... |

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Citation Context ... (i.e., neighboring pixels represent surface points which are at about the same distance to the cameras). A convex function C supports efficient global optimization, but leads to oversmoothed results =-=[11]-=-. Common choices for a unary continuity function are either a simple step function (Pott’s model), a linear function, or a quadratic function, where the latter two need to be truncated for avoiding ov... |

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Citation Context ..., [14], for distance transforms in general. Experiments have been performed with various kinds of distance transforms, and preference was given to the Euclidean distance transform (EDT). For example, =-=[2]-=- proved that a 2D EDT can efficiently calculated by two subsequent 1D EDT. (The developed procedure for calculating lower envelops is also applicable for calculating lower envelops in a BP algorithm w... |

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Citation Context ...GM using Scanline Optimization. Semi-global matching (SGM) is commonly identified with applying scanline optimization along several digital rays, all incident with the start pixel p in the base image =-=[9]-=-. Original dynamic programming stereo [18] was defined for energy minimization along a single scan line. Assume that row y remains constant; matching aims at minimizing ⎛ m∑ Em(∆) = ⎝Dx(∆x) + ∑ ⎞ C(∆x... |

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Citation Context ...uch as numerical algorithms [13], or concepts in discrete mathematics such as adjacency sets A(p) of pixels p, digital straight lines, or distance transforms, which are examples from digital geometry =-=[14]-=-. Typically, continuous models are used in motion analysis up to the moment when mapping those concepts into algorithms, but matching techniques for multi-ocular vision typically already start with a ... |

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Citation Context ...e goals (i-iii). After specifying a processing model, possibly in continuous space, any specification for its algorithmic use will depend on discrete mathematical models, such as numerical algorithms =-=[13]-=-, or concepts in discrete mathematics such as adjacency sets A(p) of pixels p, digital straight lines, or distance transforms, which are examples from digital geometry [14]. Typically, continuous mode... |

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Citation Context ...2 Semi-Global Paradigms for Sub-Optimal Solutions Basically, current stereo algorithms follow one of the following three paradigms: scanline optimization often implemented by (DP) dynamic programming =-=[18]-=-, (BP) belief propagation [3], or (GC) graph-cut [15]. These paradigms aim at finding a sub-optimal solution to the stereo matching problem. SGM using Scanline Optimization. Semi-global matching (SGM)... |

10 | R.: Belief propagation for stereo analysis of night-vision sequences
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Citation Context ...label l. At the end of an iteration t, that disparity with minimum cost is selected as being the result for pixel p ∈ Ω. BP fails in cases of photometric inconsistencies between left and right image; =-=[5]-=- showed that some edge preprocessing of both images is of benefit, and [19] performed a systematic study which shows the residual images (rather than original input images) carry the important informa... |

7 |
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(Show Context)
Citation Context ... selected as being the result for pixel p ∈ Ω. BP fails in cases of photometric inconsistencies between left and right image; [5] showed that some edge preprocessing of both images is of benefit, and =-=[19]-=- performed a systematic study which shows the residual images (rather than original input images) carry the important information for correspondence analysis.sDiscrete Driver Assistance 7 The calculat... |

6 | Lane detection and tracking using a new lane model and distance transform
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(Show Context)
Citation Context ...imized parameters on preprocessed input data, and GC also improves on preprocessed input data. 4 Lane Detection and Tracking Lane detection and tracking has been a successful research subject in DAS. =-=[12]-=- reviews briefly related work in vision-based DAS and discusses a new lane model, also providing two algorithms for either time-efficient or robust lane tracking (to be chosen in dependency of current... |

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(Show Context)
Citation Context ...ons. As a general conclusion, single-line DP is quite robust and provides a fast and approximate depth map (“a good draft”, and some kind of temporal or spatial propagation of results might be useful =-=[16]-=-), SGM-BT fails absolutely on original data but seems to perform better than SGM-MI on preprocessed images, BP is highly sensitive to illumination changes, and improves very nicely when using optimize... |

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(Show Context)
Citation Context ... subsequent 1D EDT. (The developed procedure for calculating lower envelops is also applicable for calculating lower envelops in a BP algorithm while using a truncated quadratic continuity function.) =-=[20]-=- suggested the orientation distance transform (ODT) which separates EDT values into a row and a column component, represents as complex numbers. We use the real (i.e., row) part of the ODT. See Figure... |

4 |
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(Show Context)
Citation Context ... given by Dx(l) = |L(x, y) − R(x − l, y)| b , for a fixed row y, 1 ≤ x ≤ M, and b either 1 or 2, assuming that image pairs are photo-consistent (i.e., corresponding pixels have about the same value). =-=[7]-=- compares various data terms within a the-winner-takes-all strategy: for each pixel p = (x, y) in the left image, a selected data term is applied for all potential matches q = (x − l, y) in the right ... |

4 |
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Citation Context ..., all those Ena−1(∆) can be deleted for minimization, and algorithmic time optimization (say, scanline optimization along all lines at first, and then combining results) leads to a feasible solution. =-=[8]-=- also includes a second-order prior into the used energy function. Belief Propagation. Belief propagation is a very general way to perform probabilistic inference; the BP stereo matching algorithm in ... |

2 | Prediction Error Evaluation of Various Stereo Matching Algorithms on Long Stereo Sequences
- Klette, Morales
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(Show Context)
Citation Context ...R (right) are in standard stereo geometry (i.e., parallel optical axes, coplanar image planes, aligned image rows), defined on pixels of an M × N grid Ω. See Figure 1; the third view has been used in =-=[17]-=- for prediction error analysis. Thus, stereo pixel correspondence is basically a 1D search problem, compared to motion pixel correspondence (e.g., [10]) which is a continuous 2D search problem. Two co... |