Apparatus and method for locating camera towers and scheduling surveillance

A computer-implemented method for directing surveillance cameras to surveil POIs comprising the following:

• providing surveillance-requirements input to a processor, where the surveillance-requirements input defines a portion of a total time period during which each individual camera comprising a plurality of cameras aligns toward each POI comprising a plurality of POIs;
• utilizing the processor to direct each specific camera comprising the plurality of cameras, where the processor is programmed to perform steps comprising the following:
• receiving the surveillance-requirements input and defining surveillance requirements ƒ, where the surveillance requirements ƒ comprises elements ƒci, where each element ƒci is associated with a specific camera comprising the plurality of cameras and a specific POI comprising the plurality of POIs, and where the each element ƒci defines a portion of the total time period during which the specific camera aligns toward the specific POI;
• establishing a set of configuration vectors where each configuration vector gk comprises elements gkci, where each element gkci is associated with a single element ƒci, and where the each element gkci is equal to a first value or equal to a second value, and where the each element gkci is equal to the first value if the specific camera associated with the single element ƒci is aligned toward the specific POI associated with the single element ƒci and is equal to the second value if the specific camera associated with the single element ƒci is not aligned toward the specific POI associated with the single element ƒci, by performing steps comprising;
• generating a first configuration vector gk and including that vector in the set of configuration vectors, where the number of current configuration vectors is K=1;
• establishing a frequency-of-utilization vector α=(α1, α2, . . . , αK) and establishing a vector s which comprises elements sci corresponding to the each camera c and each POI i;
• quantifying the frequency-of-utilization vector α and quantifying the vector s by minimizing a primal objective function, where the primal objective function comprises a summation of the elements of the vector s, and where the minimization of the primal objective function is subject to a set of primal constraints;
• summing the elements of the vector s;
• and
• developing a subsequent configuration vector gk, where the subsequent configuration vector gk comprises elements gkci, where each element gkci is associated with a certain element ƒci, and where the each element gkci is equal to a first value or is equal to a second value, and where the each element gkci is equal to the first value if the specific camera associated with the certain element ƒci is aligned toward and focused on the specific POI associated with the certain element ƒci and is equal to the second value if the specific camera associated with the certain element ƒci is not aligned toward the specific POI associated with the certain element ƒci, by performing steps that comprise:
• valuing a dual vector μ using a dual of the primal objective function and the set of primary constraints, where the dual vector μ comprises elements μci where each element μci is associated with a single element sci comprising the vector s, thereby generating a valued dual vector μ;
• generating the subsequent configuration vector gk, by optimizing an assignment objective function, where the assignment objective function comprises the valued dual vector μ and the subsequent configuration vector gk thereby generating the subsequent configuration vector gk;
• including the subsequent configuration vector gk in the set of configuration vectors;
• and
• repeating the step that establishes the frequency-of-utilization vector α, quantifying the frequency-of-utilization vector α and quantifying the vector s by optimizing the primal objective function subject to the set of primal constraints;
• the summing the elements of the vector s step;
• the step that develops the subsequent configuration vector gk;
• the step that establishes the dual vector μ using the dual of the primal objective function and the set of primary constraints;
• the step that generates the subsequent configuration vector ĝ;
• and, the step that includes the subsequent configuration vector gk in the set of configuration vectors until the summation of the elements of the vector s is less than or equal to a pre-determined value approximating 0, thereby establishing the set of configuration vectors;
• and
• retrieving a final utilization vector α, where the final utilization vector α is the quantified frequency-of-utilization vector α when the optimized summation of the elements of the vector s called zSKED** is equal to zero;
• selecting an individual configuration vector gk using a probability distribution function (PDF) where the PDF returns a single configuration vector gk comprising the set of configuration vectors for a specific percentage of selections over a plurality of selections;
• and
• directing each single camera in the plurality of cameras to align toward a single POI comprising the plurality of POIs based on the individual configuration vector gk, thereby directing surveillance cameras to surveil POIs.

An apparatus for surveilling points-of-interest (POIs) for a specified period of time T comprising:

• a plurality of camera towers comprising a plurality of cameras where the plurality of cameras satisfies surveillance requirements ƒ over the total time period for a plurality of POIs, where each camera tower is located at a camera-tower location which is a location on a geographic area, and where an individual POI is located at a POI location on the geographic area, and where the plurality of cameras executes a joint camera schedule to satisfy the surveillance requirements ƒ, and where each camera comprising the plurality of cameras executes its part of the joint camera schedule;
• and
• a processor in data communication with the each camera comprising the plurality of cameras and the processor programmed to determine the joint camera schedule whose execution satisfies surveillance requirements ƒ by performing steps that comprise:
• I) receiving surveillance-requirements input and determining the surveillance requirements ƒ, where the surveillance requirements ƒ comprises elements ƒci, where each element ƒci defines the probability that camera c comprising the plurality of cameras aligns toward a specific POI i comprising the plurality of POIs, and where the surveillance requirements ƒ comprises a subset of elements ƒc corresponding to the specific camera, where the subset of elements ƒc comprises a single element ƒci corresponding to each POI comprising the plurality of POIs, such that the single element ƒci corresponds to the specific camera and the each POI;
• II) receiving a value zSKED** where the value zSKED** is greater than or equal to zero;
• III) establishing a set of configuration vectors where each configuration vector gk comprises elements gkci, where every element gkci is equal to a first value or is equal to a second value, and where the each configuration vector gk comprises a subset of elements gkc corresponding to the specific camera, where the subset of elements gkc comprises a single element gkci corresponding to the each POI, such that the single element gkci corresponds to the specific camera and the each POI, and where the single element gkci is equal to the first value if the specific camera is aligned toward the each point of interest and is equal to the second value if the specific camera is not aligned toward the each point of interest, by performing steps comprising;
• III)A) generating a first configuration vector g1 and including that vector in the set of configuration vectors, where the number of current configuration vectors is K=1;
• III)B) establishing a frequency-of-utilization vector α=(α1, α2, . . . , αK) and establishing a vector s which comprises elements sci corresponding to the each camera c and each POI i;
• III)C) quantifying the frequency-of-utilization vector α and quantifying the vector s by minimizing a primal objective function, where the primal objective function comprises a summation of the elements of the vector s, and where the minimization of the primal objective function is subject to a set of primal constraints comprising:
• III)C)1) a first constraint set wherein the single element sci corresponding to the specific camera and the each POI is equal to a difference between the single element ƒci corresponding to the specific camera and the each POI and a dot product of a first vector and a second vector, where the first vector comprises all single elements gkci comprising the set of configuration vectors and corresponding to the specific camera and the each POI, and where the second vector comprises all elements αk comprising the frequency-of-utilization vector α;
• III)C)2) a second constraint set wherein all elements αk comprising the frequency-of-utilization vector α are greater than or equal to zero;
• and
• III)C)3) a third constraint set wherein every element sci comprising the vector s is greater than or equal to zero, thereby quantifying the frequency-of-utilization vector α and quantifying the vector s;
• and
• III)D) summing the elements of the vector s;
• III)E) developing a subsequent configuration vector gk for k=K+1, if the summation of the elements of the vector s called zSKED** is greater than zero, where the subsequent configuration vector gk comprises elements gkci, where each such element is equal to the first value or is equal to the second value, and where the subsequent configuration vector gk comprises a subset of elements gkc corresponding to the specific camera, where the subset of elements gkc comprises a single element gkci corresponding to the each point-of-interest, such that the single element gkci corresponds to the specific camera and the each point-of-interest, and where the single element gkci is equal to the first value if the specific camera is aligned toward and focused on the point of interest i and is equal to the second value if the specific camera is not aligned toward and focused on the point of interest i, by performing steps that comprise:
• III)E)1) determining a set of optimal dual variables using the set of primal constraints;
• III)E)2) defining a dual objective function using the primal constraints;
• III)E)3) determining a dual vector μ, by maximizing the dual objective function subject to the set of dual constraints, where the dual vector μ comprises elements μci which correspond to the specific camera c and the specific point-of-interest i;
• III)E)4) generating the subsequent configuration vector gk for subsequent k=K+1, by minimizing an assignment objective function, where the assignment objective function comprises a dot product of a third vector comprising the valued dual vector μ and a fourth vector comprising the subsequent configuration vector gk, and where the minimization of the assignment objective function is subject to one constraint set wherein the specific camera comprising the plurality of cameras is aligned toward some point-of-interest in the plurality of POIs, and subject to an additional constraint set wherein only a single camera comprising the plurality of cameras is aligned toward specific point-of-interest comprising the plurality of POIs, thereby generating the subsequent configuration vector ĝ;
• and
• III)E)5) including the subsequent configuration vector g in the set of configuration vectors;
• updating the cardinality of the configuration set:
• K=K+1;
• and
• III)E)6) repeating step III)B), step III)C), step III)C)1), step III)C)2), step III)C)3), step III)D), step III)E), step III)E)1), step III)E)2), step III)E)3), step III)E)4), and step III)E)5) until the minimized summation of the elements of the vector s at step III)D) called zSKED** is equal to zero with a pre-specified accuracy;
• and
• IV) retrieving a final frequency-of-utilization vector α=(α1, α2, . . . , αK), which is a sufficiently accurate probability distribution function, meaning that all elements are non-negative, add up to exactly one, and zSKED** equals 0 with a pre-specified accuracy;
• V) selecting an individual configuration vector gk with probability αk;
• VI) directing each single camera in the plurality of cameras to align toward a single point-of-interest comprising the plurality of POIs based on the individual configuration vector gk for a period of time Δt if the system is operated with a constant time interval Δt, or for a period of time Δtk, if the system is operated with a randomly chosen time intervals Δtk;
• and
• VII) repeating step V) and step VI) until a period of time greater than the total time period has elapsed, thereby surveilling POIs over the total time period.