Passive ranging using image intensity and contrast measurements

Zarko P. Barbaric, Boban P. Bondzulic, Srdjan T. Mitrovic

This is a postprint of an article which appeared as:

Zarko P. Barbaric, Boban P. Bondzulic & Srdjan T. Mitrovic: Passive Ranging Using Image Intensity and Contrast Measurements, Electronics Letters 48 (18), pp. 1122-1123, 2012, DOI: 10.1049/el.2012.0632

Abstract

Proposed are two passive ranging approaches using a single camera, based on intensity and contrast measurements. According to the Beer-Lambert law and known atmosphere extinction coefficient and initial range, the range to a moving object is estimated. Using these approaches in a real infrared surveillance sequence, better results are obtained than with methods which use image size measurements. The relative error of 3.2% for contrast and 2.3% for intensity features are obtained. Results indicate that range estimation is possible to a fidelity required for object tracking.

1 Introduction

Passive ranging is of special interest for wide range of applications, such as video surveillance and security, air traffic control, speed control, obstacle detection, homing missile guidance, weapon fire control, etc. The most common techniques used to passively estimate range to an object employ optical flow or/and triangulation [1]. The methods given in [2, 3], exploit size changes of an object in the video sequence, as inferred by processing video frames, to compute distance. As we know, thermal image size measurement is difficult, since the edge of object is not clear [4]. The measurement of object size depends on image processing for object extraction. Furthermore, systems relying on triangulation require two or more sensors [1].

Two passive ranging methods using intensity and contrast measurements from one sensor are suggested in this paper. No prior knowledge about the sensor or about the size, shape or any other features of the object is assumed. Suggested methods allow accurate distance estimation even where multiple sensor views or active measurements are not possible.

2 Theory

The intensity or grey level

I

in the image is a function of scene radiance attenuated by transmission through the atmosphere, and characteristics of the image sensor. In its simplest form this relationship becomes:

I = G L τ = G L exp (- σ D)

(1)

where

G

is the sensor transfer function,

L

is the scene radiance,

σ

is the atmosphere extinction coefficient,

D

is optical path length through the atmosphere (distance), and transmittance of the atmosphere

τ

is described by Beer-Lambert low.
The image contrast is given by:

C = \frac{I^{T} - I^{B}}{I^{B}}

(2)

where

I^{T}

is the average grey level value of object (target), and

I^{B}

is the average grey level value of background. As we know, image contrast is scene contrast reduced by the transmittance of atmosphere:

C = {K C}^{S C} exp (- σ D)

(3)

where

K

is the sensor contribution, and

C^{S C}

is scene contrast, given by:

C^{S C} = \frac{L^{T} - L^{B}}{L^{B}}

(4)

where

L^{T}

is the radiance of target, and

L^{B}

is the radiance of its background.

D_{1}^{I} = D_{0}^{I} + \frac{1}{σ} \ln \frac{I_{0}}{I_{1}}

(5)

where

D_{0}^{I}

and

D_{1}^{I}

are object to sensor distances, or ranges, and

I_{0}

and

I_{1}

are average grey levels of the object in two successive frames. Also, we can derive the range from (3), where we suppose constant contrast in the scene:

D_{1}^{C} = D_{0}^{C} + \frac{1}{σ} \ln \frac{C_{0}}{C_{1}}

(6)

where

D_{0}^{C}

and

D_{1}^{C}

are object to sensor distances and

C_{0}

and

C_{1}

are the target contrast in two successive frames.
Passive range estimations from (4) and (5) are based on measurements of intensity and contrast. To resolve them we need reliable estimates of extinction coefficient

σ

and initial range

D_{0}

. Extinction coefficient

C_{0}

may be estimated on the base of optical visibility at 0.55μm by programs such as LOWTRAN, MODTRAN, or using known algorithms [5]. Initial range to the object

D_{0}

can be measured by a laser rangefinder and/or by other passive ranging methods.

3 Experiment

Theoretical passive ranging methods are tested on infrared image sequence for an airborne object. The sequence is generated by SkyTrack system, which is used for a tracking of air targets. This system uses two cameras for distance measurement. In this paper we use infrared image sequence from one of the cameras with distance given by the system for each frame. Figure 1. shows the first and the last frames of the sequence, with bounding boxes around the aircraft.

frame in real sequence — **Fig. 1.** The first (left) and the last (right) frames in real sequence.

The proposed passive ranging processing flow is depicted in Fig. 2. It consists of the following steps: detection - finding the object in the current frame, segmentation - extracting it from the background, feature extraction - obtaining object and/or background description, and finally combining the features with a known atmosphere extinction coefficient and initial range into the target distance estimate.

Detection and segmentation from Fig. 2. are done by Tsai's method [6] providing object region

A_{n}

. Mean value of object grey level

I_{n}

and object contrast

C_{n}

on Fig. 2. are calculated from the object in

A_{n}

. Range estimation given in Fig. 2,

D_{n}

, is calculated using three different approaches: proposed intensity (4) and contrast (5) methods and using image size as in [3]:

D_{n} = D_{0} \sqrt{\frac{A_{0}}{A_{n}}}

(7)

where

I_{0}

is the mean value of grey level and

D_{0}

is the distance in the initial frame. Final value of

σ

is median value of

σ_{n}

values for the entire test sequence

n = 1,2,...,16,

where

N = 16

is the test sequence length. On the Fig. 2 feedback means that we use object template in correlation algorithm for tracking [7]. In the initialization frame a moving object is manually detected and localized.

4 Analysis of results

Fig. 3 shows estimated target distances obtained using the proposed contrast and intensity methods as well as the area based method. Estimates provided by the proposed methods quickly stabilise close to the ground truth provided by the SkyTrack system for the first 300 frames. In the last 50 frames however sensor intensity saturation as the object moves closer to it causes divergence of the estimates and the true distance. Additionally, significant background changes during these frames influence the contrast measure.

**Fig. 3.** True and estimated distances.

From Fig. 3 it is obvious that distance estimation by image size significantly differs from true distance, over almost the whole sequence. At the end of the sequence its difference from the true distance has decreased to less than that of the proposed methods.
Using the proposed methods we obtain the relative error of 2.3% for intensity and 3.2% for contrast approaches, for the relevant (i.e. non-saturated) 300 frames.

5 Conclusion

We propose intensity and contrast methods for passive ranging using a single camera. Results indicate that proposed approaches are suitable for object tracking, because they provide relative ranging error of less than 3.5%, for large distances. Results obtained and analysed in this paper suggest the use of a hybrid approach with image size, intensity and contrast features all taken into account. Future work will include more complex object motion profiles and incorporating a Kalman tracker.

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