Motion Detection andEstimation

INTRODUCTION

• Motion detection - image points be identified as moving or stationary (surveillance)

• Motion detection – measure of how they move

• Motion segmentation - identification of groups of image points moving similarly

motion detection

• motion detection is formulated as hypothesis testing, maximuma posteriori probability (MAP) estimation, and variational problem

• motion estimation is described in two parts. – models, estimation criteria, and search strategies – motion estimation algorithms

MOTION DETECTION• PRELIMINARIES & NOTATION• Let I :T →R be the intensity of image

sequence defined over spatial domain temporal domain T .

• Let x (x1,x2)T and t T denote spatial ∈ ∈and temporal positions of a point in this sequence

• Let I (x, t ) denote a continuous-coordinate representation of intensity at (x, t ), and let It denote a complete image at time t .

NOTATIONS Cont…• spatial pixel position x is approximated by n = (n1,n2)T , whereas temporal position t is approximated by

tk or k.

• I [n,k] denotes a discrete-coordinate representation of I (x, t )• Motion in continuous images can be described by velocity

vector (1,2)T • (x) is a velocity at spatial position x, • t will denote a velocity field or motion field, that is, the set

of all velocity vectors within the image, at time t .

MOTION DETECION Binary Hypothesis Testing

• Let y be an observation and let Y be the associated random variable. Suppose that there are two hypotheses H0 andH1 with corresponding probability distributions P(Y= y|H0) and P(Y = y|H1)

• The goal is to decide from which of the two distributions a given y is more likely to have been drawn.

• four possibilities exist (true hypothesis/decision): H0/H0, H0/H1, H1/H0, and H1/H1.

• Although H0/H0 and H1/H1 correspond to correct choices, H0 /H1 and H1/ H0 are erroneous.

Binary Hypothesis Testing

• Under the Bayes criterion, two a priori probabilities are assigned to the two

hypotheses H0 and H1, respectively• cost is assigned to each of the four scenarios listed

previously.• design a decision rule so that on average the

cost associated with making a decision based on y is minimal.

Binary Hypothesis Testing

• Assuming costs associated with erroneous decisions are higher than those associated with the corresponding correct decisions, optimal decision can be made according to the following rule

• (3.1)• The quantity on the left is called the likelihood ratio

and is a constant dependent on the costs of the four scenarios.

• If 0 and 1 are predetermined as well, the above hypothesis test compares the likelihood ratio with a fixed threshold.

MOTION DETECTION

• to identify which image points, or, which regions of the image moved.

• motion of image points is not perceived directly but through intensity changes.

• intensity changes over time may be also induced by camera noise or illumination variations.

Hypothesis Testing with Fixed Threshold

be an observation, upon which we intend to select one of the two hypotheses.

Hypothesis Testing with Fixed Threshold

• taking the natural logarithm of both sides of (3.1) the hypothesis test can be written as follows:

• The above pixel-based hypothesis test is not robust to noise in the image; for small ’ “noisy” detection masks result (many isolated small regions), whereas for large ’s only object boundaries and its most textured parts are detected.

• To attenuate the impact of noise, the method can be extended by averaging the observations over an N-point spatial window Wn centered at n:

• Motion detection based on frame differences, as described above, does not perform well for large, untextured objects

• Only pixels n where |Ik [n]-Ik-1[n]| is sufficiently large can be reliably detected.

• Such pixels concentrate in narrow areas close to moving boundaries where object intensity is distinct from the background in the previous frame. This leads to excessive false negatives,

An intensity at location n in framek is deemed stationary only if it is likely to have been drawn from PS. This improves robustness of the detection to small parasitic movements that are accounted for in PS.

since the PS model is based on K recent frames, it adapts to slow background changes such as illumination variations.

in order to avoid model contamination intensities frommoving areas in previous frames need to be excluded fromthe summation in (3.8),

Hypothesis Testing with Adaptive Threshold