This week, we're going to discuss spatial temporal methods off filtering the observation background as we input to the protest in algorithms. Various a sequence off images S from t. Where s I G from T is the signal in pixel with coordinates. I n g off the image D and X is the number off columns and an Igric is the number of rows over 40 detector masic, and the signal in pixel includes a useful signal, a background signal and intrigue. Sick noise over censor in pixel over frame. Let's end the some designators that will be used further F is a set off numbers off a 40 detector Masic and Marx is a number off the brightest pixels. This number is selected by the user. F marks is a set off the brightest pixels. Numbers, if mean, is a difference between the full set and F marks. Let's have a look at the slide to repeat veggies igniters one more time F f marks f mean we're following. Parameters are commonly used to describe the statistical properties off signals in the frame. The first one is maximum value off a signal across the frame. Esmark's is equal to marks from S I G i G from F minimum value off a signal across the frame iss mean equal toe mean from S I g the i g from if the average value over signals in the frame but and marks off the brightest pixels in the frame are not taken into account. S average is equal to some. Bye i g from f mean from S I g divided by an ex multiplied by an Igric minus and marks with standard deviation obviously no value in the frame. The brightest pixels are also not taken into account. Sigma is equal to some i g from f mean from S I g squared, divided boy and eggs multiplied by an Igric minus and marks minus some bye I g from f mean from S I G Divided boy and ex and Igric minus and marks squared the large of a value off standard deviation. The more difficult for background noises becomes as far as the problem off object detection is considered, we suppose with sensors interested noises in pixels at us are not correlated for any sets off I, g and T and have a constant armas value we can find ourselves toe considering the class off filtering processes over falling form. Where s W from? T is the frame filter and result off a signal s from T and is equal to the difference between the signal and the background value forecast in pixel i n g over current frame before cast off, a background value is carried out based on the previous friends over slightly memory window over filtering algorithm. The filtering procedure is considered ideal if a background component B i g from T is completely suppressed and the useful signal s i G is not distorted. Bus ideal background filtering leads to the classical problem off extracting a useful signal from an edited mixture with uncorrelated noises. Wherefore we will call the frame right. Let's consider be from X Igric as the background signal in pixel centered at the point X Igric off the measurement system. If we choose the beginning over system and in the center over northwest corner, pixel off some reference frame over sequence when the signal is as follows. They're Delta X and Delta Igric, characterized by image frame resolution and dealt the eggs from T and dealt the Igric from tee off a frame shifts along the correspondent access off a measuring coordinate system relative to the reference frame. We assume that during the time interval refrigeration tee off periods off frame update It is possible to ignore changes in the function for physical reasons went lights, the conditions, temperature and concentration off cases and IRA souls in the atmosphere, conviction and hours in practice, we're fulfillment off such a condition requires, with selection off an appropriate frame refresh period. Under these assumptions, changes in the background signal in each pixel overtime caused only by sensor Russell ations. As a rule, in real cases with statistical properties off, a background and a solutions are unknown. We're synthesis off filter and algorithms will be carried out precisely under this assumption, which ensures were a business off algorithms with respect to changes in the white range, off statistical characteristics, off real backgrounds and isolations off optical access shifts off the frame along the axis off a measuring coordinate system are considered its arbitrary unknowns. Limited an absolute value by the maximum range off sensor isolations, and the background signal is an arbitrary unknown. No negative function bounded above by the maximum brightness off a background. We were special frequency region, strictly limited by the land size and smooth, no less than the function. Describing the signal from a point source, let's consider the option estimate off a signal that is calculated based on the frame. According toe. It's ideal filtering when the white and signal is represented, as it is shown on the slide, where X e G from T is a residual knows after filtering for real filtering processes of optimum estimate may differ from the actual signal value, even with no sense of noise. Duty of a distortion off a useful signal by residuals off, not completely suppressed background observation. In addition with statistical characteristics off residual noise, see, do not considered with with or four original noise we're preferred. Filtering algorithms are those for which were signal company is reproduced with a minimum difference in signal values and where optimal estimates the background is suppressed. The law was possible level limited by the presence off intrinsic noise, and the shift over frame is estimated with minimal error
