Arithmetic unit, correlation arithmetic unit and dynamic image compression apparatus

A correlation arithmetic unit in which when two integers satisfying 1≦i≦j are denoted by i and j;

• j variables are given in the form of x1, x2 . . . , xj;
• and two functions are expressed by a (x1, x2 . . . , xj) and b (x1, x2 . . . , xj), an operation set forth below is applied to the two functions a (x1, x2 . . . , xj) and b (x1, x2 . . . , xj), c ⁡ ( Δ ⁢ ⁢ x 1 , Δ ⁢ ⁢ x 2 , … , Δ ⁢ ⁢ x i , x i + 1 , … , x j ) = ∑ x1 ⁢ ∑ x2 ⁢ … ⁢ ∑ xi ⁢ a ⁡ ( x 1 , x 2 , … , x j ) * b ( ⁢ x 1 + Δ ⁢ ⁢ x 1 , x 2 + Δ ⁢ ⁢ x 2 , … , x i + Δ ⁢ ⁢ x i , x i + 1 , … , x j ) ( 3 )
• where an operation g*h between optional two numbers g and h stands for an operation of f (g+h)−f (g−h) in which an even function involving a monotone variation when a variable x is in a predetermined positive area, where f (x)≠r·x2+s;
• r and s are constant, is denoted by f (x),
• wherein said correlation arithmetic unit has an arithmetic unit comprising:
• an adder unit for receiving input signals representing two functions a and b, and for outputting an addition signal representing a sum a+b of the two functions a and b;
• a first function generation unit for receiving the addition signal, and for applying to the addition signal an even function f (x) involving a monotone variation when a variable x is in a predetermined positive area, where f (x)≠r·x2+s;
• r and s are constant, thereby generating a first function signal representing f (a+b);
• a first subtracter unit for receiving input signals representing the two functions a and b, and for outputting a subtraction signal representing a difference a−b between the two functions a and b;
• a second function generation unit for receiving the subtraction signal, and for applying the even function f (x) to the subtraction signal, thereby generating a second function signal representing f (a−b);
• and
• a second subtracter unit for receiving the first function signal and the second function signal, and for outputting a signal representing a difference f(a+b)−f(a−b) between f (a+b) and f (a−b).

A correlation arithmetic unit in which when two integers satisfying 1≦i≦j are denoted by i and j;

• j variables are given in the form of x1, x2 . . . , xj;
• and two functions are expressed by a (x1, x2 . . . , xj) and b (x1, x2 . . . , xj), an operation set forth below is applied to the two functions a (x1, x2 . . . , xj) and b (x1, x2 . . . , xj), c ⁡ ( Δ ⁢ ⁢ x 1 , Δ ⁢ ⁢ x 2 , … , Δ ⁢ ⁢ x i , x i + 1 , … , x j ) = ∑ x1 ⁢ ∑ x2 ⁢ … ⁢ ∑ xi ⁢ a ⁡ ( x 1 , x 2 , … , x j ) * b ( ⁢ x 1 + Δ ⁢ ⁢ x 1 , x 2 + Δ ⁢ ⁢ x 2 , … , x i + Δ ⁢ ⁢ x i , x i + 1 , … , x j )
• where an operation g*h between optional two numbers g and h stands for an operation of f (g+h)−f (g−h) in which an even function involving a monotone variation when a variable x is in a predetermined positive area, where f (x)≠r·x2+s;
• r and s are constant, is denoted by f (x),
• wherein said correlation arithmetic unit has an arithmetic unit, and upon receipt of two functions a and b, said arithmetic unit applies a predetermined function g to the two functions a and b, and performs an operation of g (|a+b|)−g (|a−b|) by outputting:
• a signal representing g (a+b) and g (a−b), when a≦−b and a≦b
• a signal representing g (a+b) and g (b−a), when a≦−b and a≧b;
• a signal representing g (−a−b) and g (a−b), when a≧−b and a≦b;
• and
• a signal representing g (−a−b) and g (b−a), when a≧−b and a≧b.

A correlation arithmetic unit in which when two integers satisfying 1≦i≦j are denoted by i and j;

• j variables are given in the form of x1, x2 . . . , xj and two functions are expressed by a (x1, x2 . . . , xj) and b (x1, x2 . . . , xj), an operation set forth below is applied to the two functions a (x1, x2 . . . , xj) and b (x1, x2 . . . , xj), c ⁡ ( Δ ⁢ ⁢ x 1 , Δ ⁢ ⁢ x 2 , … , Δ ⁢ ⁢ x i , x i + 1 , … , x j ) = ∑ x1 ⁢ ∑ x2 ⁢ … ⁢ ∑ xi ⁢ a ⁡ ( x 1 , x 2 , … , x j ) * b ( ⁢ x 1 + Δ ⁢ ⁢ x 1 , x 2 + Δ ⁢ ⁢ x 2 , … , x i + Δ ⁢ ⁢ x i , x i + 1 , … , x j ) ( 3 )
• where an operation g*h between optional two numbers g and h stands for an operation of f (g+h)−f (g−h) in which an even function involving a monotone variation when a variable x is in a predetermined positive area, where f (x)≠r·x2+s;
• r and s are constant, is denoted by f (x),
• wherein said correlation arithmetic unit comprises an absolute value operation unit and a sign operation unit, and said absolute value operation unit comprises:
• an adder unit for receiving input signals representing absolute values |a| and |b| of the two numerical values a and b, and for outputting an absolute value addition signal representing a sum |a|+|b| of the two absolute values |a| and |b|;
• a first function generation unit for receiving the absolute value addition signal, and for applying to the absolute value addition signal an even function f (x) involving a monotone variation when a variable x is in a predetermined positive area, where f (x)≠r·x2+s;
• r and s are constant, thereby generating a first function signal representing f (|a|+|b|);
• a first subtracter unit for receiving input signals representing absolute values |a| and |b| of the two numerical values a and b, and for outputting an absolute value subtraction signal representing a difference |a|−|b| between the two absolute values |a| and |b|;
• a second function generation unit for receiving the absolute value subtraction signal, and for applying the even function f (x) to the absolute value subtraction signal, thereby generating a second function signal representing f (|a|−|b|);
• and
• a second subtracter unit for receiving the first function signal and the second function signal, and for outputting a signal representing a difference f (|a|+|b|)−f (|a|−|b|) between f (|a|+|b|) and f (|a|−|b|), and
• wherein said sign operation unit outputs signals representing a plus and a minus in compliance with either one of a match and a mismatch of polarities “sign (a) and sign (b)” of the two functions a and b and the other, respectively.

A correlation arithmetic unit in which when two integers satisfying 1≦i≦j are denoted by i and j;

• j variables are given in the form of x1, x2 . . . , xj;
• and two functions are expressed by a (x1, x2 . . . , xj) and b (x1, x2 . . . , xj), an operation set forth below is applied to the two functions a (x1, x2 . . . , xj) and b (x1, x2 . . . , xj), c ⁡ ( Δ ⁢ ⁢ x 1 , Δ ⁢ ⁢ x 2 , … , Δ ⁢ ⁢ x i , x i + 1 , … , x j ) = ∑ x1 ⁢ ∑ x2 ⁢ … ⁢ ∑ xi ⁢ a ⁡ ( x 1 , x 2 , … , x j ) * b ( ⁢ x 1 + Δ ⁢ ⁢ x 1 , x 2 + Δ ⁢ ⁢ x 2 , … , x i + Δ ⁢ ⁢ x i , x i + 1 , … , x j ) ( 3 )
• where an operation g*h between optional two numbers g and h stands for an operation of f (g+h)−f (g−h) in which an even function involving a monotone variation when a variable x is in a predetermined positive area, where f (x)≠r·x2+s;
• r and s are constant, is denoted by f (x),
• wherein said correlation arithmetic unit comprises an absolute value operation unit and a sign operation unit,
• wherein said absolute value operation unit receives signals representing absolute values |a| and |b| of the two functions a and b, and applies a function g defined by g(|x|)=F (x) to the absolute values |a| and |b|, thereby outputting signals representing g (|a|+|b|)−g (|a| |b|) when |a|≧|b|, and g (|a|+|b|)−g (|b|−|a|) when |a|≦|b|, respectively, and
• wherein said sign operation unit outputs signals representing a plus and a minus in compliance with either one of a match and a mismatch of signs “sign (a) and sign (b)” of the two functions a and b and the other, respectively.

A correlation arithmetic unit comprising:

• Hough transform means for applying a Hough transform to two functions A (x, y) and B (x, y), x and y being variables, to derive two functions a (ρ, θ) and b (ρ, θ), ρ and θ being variables, where ρ is a variable representing a minimum distance between a straight line and an origin on a two-dimensional plane consisting of an x-axis and a y-axis, and θ is a variable representing a slant;
• correlation arithmetic means for applying to the two functions a (ρ, θ) and b (ρ, θ) an operation set forth below c ⁡ ( Δ , θ ) = ∑ ρ ⁢ a ⁡ ( ρ , θ ) * b ⁡ ( ρ + Δ , θ ) ( 4 )
• where an operation g*h between optional two numbers g and h stands for an operation for |g+h|−|g−h|;
• and
• inverse Hough transform means for applying an inverse Hough transform to an operation result c(Δ, θ) in said correlation arithmetic means to derive a function D(Δx, Δy), Δx, Δy being variables, where Δx is a variable representing a positional difference in an x-axis direction, and Δy is a variable representing a positional difference in a y-axis direction.