Steerable kernel for image interpolation

An apparatus for providing a representation of image data, the apparatus comprising:

• accessing means for accessing a plurality of discrete sample values of said image data;
• angle orientation determining means for determining an angle of orientation of said sample values;
• calculating means for calculating kernel values for each of said discrete sample values, using one of a plurality of first kernels depending upon the angle of orientation of said discrete sample value, wherein said first kernels are constructed by rotating a second kernel from a first angle of orientation to a second angle of orientation;
• and
• convolving means for convolving said kernel values with said discrete sample values to provide a representation of said image data.

A computer readable medium for storing a program for an apparatus which processes data, said processing comprising a method of providing a representation of image data, said program comprising:

• code for accessing a plurality of discrete sample values of said image data;
• code for determining an angle of orientation of said sample values;
• code for calculating kernel values for each of said discrete sample values using one of a plurality of first kernels depending upon the angle of orientation of said discrete sample value, wherein said first kernels are constructed by rotating a second kernel from a first angle of orientation to a second angle of orientation;
• and
• code for convolving said kernel values with said discrete sample values to provide a representation of said image data.

A method of providing a representation of image data, the method comprising the following steps:

• (i) accessing a plurality of discrete sample values of said image data;
• (ii) determining an angle of orientation of each said sample values;
• (iii) calculating kernel values for each of said discrete sample values using one of a plurality of first kernels depending upon the angle of orientation of said discrete sample value, wherein said first kernels are constructed by rotating a second kernel from a first angle of orientation to a second angle of orientation;
• and
• (iv) convolving said kernel values with said discrete sample values to provide a representation of said image data, wherein said first kernels are of the form:
• h ⁡ ( s x , s y ) θ = 0 = 1 2 ⁢ { h ( ( s x ) c = 0.5 · h ⁡ ( s y ) c = 0 } ( 3 ) h ⁡ ( s x , s y ) θ = π / 2 = 1 2 ⁢ { h ⁡ ( s x ) c = 0 · h ⁡ ( s y ) c = 0.5 ( 4 ) h ⁡ ( s x , s y ) θ = π / 4 = 1 2 ⁢ { h ⁡ ( s x + s y 2 ) c = 0.5 · h ⁡ ( s x - s y 2 ) c = 0 } ( 5 ) h ⁡ ( s x , s y ) θ = 3 ⁢ ⁢ π / 4 = 1 2 ⁢ { h ⁡ ( s x + s y 2 ) c = 0 · h ⁡ ( s x - s y 2 ) c = 0.5 } ( 6 )
• and wherein s=t/Δt and θ is the angle of orientation of the sample.

An apparatus for providing a representation of image data, said apparatus comprising:

• accessing means for accessing a plurality of discrete sample values of said image data;
• angle of orientation determining means for determining an angle of orientation of each said sample values;
• calculating means for calculating kernel values for each of said discrete sample values using one of a plurality of first kernels depending upon the angle of orientation of said discrete sample value, wherein said first kernels are constructed by rotating a second kernel from a first angle of orientation to a second angle of orientation;
• and
• convolving means for convolving said kernel values with said discrete sample values to provide a representation of said image data, wherein said first kernels are of the form:
• h ⁡ ( s x , s y ) θ = 0 = 1 2 ⁢ { h ( ( s x ) c = 0.5 · h ⁡ ( s y ) c = 0 } ( 3 ) h ⁡ ( s x , s y ) θ = π / 2 = 1 2 ⁢ { h ⁡ ( s x ) c = 0 · h ⁡ ( s y ) c = 0.5 ( 4 ) h ⁡ ( s x , s y ) θ = π / 4 = 1 2 ⁢ { h ⁡ ( s x + s y 2 ) c = 0.5 · h ⁡ ( s x - s y 2 ) c = 0 } ( 5 ) h ⁡ ( s x , s y ) θ = 3 ⁢ ⁢ π / 4 = 1 2 ⁢ { h ⁡ ( s x + s y 2 ) c = 0 · h ⁡ ( s x - s y 2 ) c = 0.5 } ( 6 )
• and wherein s=t/Δt and θ is the angle of orientation of the sample.

A computer readable medium for storing a program for an apparatus which processes data, said processing comprising a method of providing a representation of image data, said program comprising:

• code for accessing a plurality of discrete sample values of said image data;
• code for determining an angle of orientation of each said sample values;
• code for calculating kernel values for each of said discrete sample values using one of a plurality of first kernels depending upon the angle of orientation of said discrete sample value, wherein said first kernels are constructed by rotating a second kernel from a first angle of orientation to a second angle of orientation;
• and
• code for convolving said kernel values with said discrete sample values to provide a representation of said image data, wherein said first kernels are of the form:
• h ⁡ ( s x , s y ) θ = 0 = 1 2 ⁢ { h ( ( s x ) c = 0.5 · h ⁡ ( s y ) c = 0 } ( 3 ) h ⁡ ( s x , s y ) θ = π / 2 = 1 2 ⁢ { h ⁡ ( s x ) c = 0 · h ⁡ ( s y ) c = 0.5 ( 4 ) h ⁡ ( s x , s y ) θ = π / 4 = 1 2 ⁢ { h ⁡ ( s x + s y 2 ) c = 0.5 · h ⁡ ( s x - s y 2 ) c = 0 } ( 5 ) h ⁡ ( s x , s y ) θ = 3 ⁢ ⁢ π / 4 = 1 2 ⁢ { h ⁡ ( s x + s y 2 ) c = 0 · h ⁡ ( s x - s y 2 ) c = 0.5 } ( 6 )
• and wherein s=t/Δt and θ is the angle of orientation of the sample.

A method of providing a representation of image data, the method comprising the following steps:

• (i) accessing a plurality of discrete sample values of said image data;
• (ii) determining an angle of orientation of each said sample values;
• (iii) calculating kernel values for each of said discrete sample values using one of a plurality of first kernels depending upon the angle of orientation of said discrete sample value, wherein said first kernels are constructed by rotating a second kernel from a first angle of orientation to a second angle of orientation;
• and
• (iv) convolving said kernel values with said discrete sample values to provide a representation of said image data, wherein said first kernels are of the form:
• h ⁢ ( s x , s y ) 0 ≤ θ ≤ π / 2 = 1 2 ⁢ { h ⁡ ( ( 1 - 2 ⁢ ⁢ θ / π ) ⁢ s x + ( 2 ⁢ ⁢ θ / π ) ⁢ s y ) c = 0.5 · h ⁡ ( ( ( 2 ⁢ ⁢ θ / π ) ⁢ s x + ( 2 ⁢ ⁢ θ / π - 1 ) ⁢ s y ) ⁢ w ⁢ ⁢ ( θ ) ) c = 0 } h ⁢ ( s x , s y ) π / 2 < θ < π = 1 2 ⁢ { h ⁡ ( ( 2 ⁢ ⁢ θ / π - 1 ) ⁢ s x + ( 2 ⁢ ⁢ θ / π - 2 ) ⁢ s y ) c = 0.5 · h ⁡ ( ( ( 2 ⁢ ⁢ θ / π - 2 ) ⁢ s x + ( 1 - 2 ⁢ ⁢ θ / π ) ⁢ s y ) ⁢ w ⁢ ⁢ ( θ ) ) c = 0 } ,
• and wherein s=t/Δt and θ is the angle of orientation of the sample.

An apparatus for providing a representation of image data, said apparatus comprising:

• accessing means for accessing a plurality of discrete sample values of said image data;
• angle of orientation determining means for determining an angle of orientation of each said sample values;
• calculating means for calculating kernel values for each of said discrete sample values using one of a plurality of first kernels depending upon the angle of orientation of said discrete sample value, wherein said first kernels are constructed by rotating a second kernel from a first angle of orientation to a second angle of orientation;
• and
• convolving means for convolving said kernel values with said discrete sample values to provide a representation of said image data, wherein said first kernels are of the form:
• h ⁢ ( s x , s y ) 0 ≤ θ ≤ π / 2 = 1 2 ⁢ { h ⁡ ( ( 1 - 2 ⁢ ⁢ θ / π ) ⁢ s x + ( 2 ⁢ ⁢ θ / π ) ⁢ s y ) c = 0.5 · h ⁡ ( ( ( 2 ⁢ ⁢ θ / π ) ⁢ s x + ( 2 ⁢ ⁢ θ / π - 1 ) ⁢ s y ) ⁢ w ⁢ ⁢ ( θ ) ) c = 0 } h ⁢ ( s x , s y ) π / 2 < θ < π = 1 2 ⁢ { h ⁡ ( ( 2 ⁢ ⁢ θ / π - 1 ) ⁢ s x + ( 2 ⁢ ⁢ θ / π - 2 ) ⁢ s y ) c = 0.5 · h ⁡ ( ( ( 2 ⁢ ⁢ θ / π - 2 ) ⁢ s x + ( 1 - 2 ⁢ ⁢ θ / π ) ⁢ s y ) ⁢ w ⁢ ⁢ ( θ ) ) c = 0 } ,
• and wherein s=t /Δt and θ is the angle of orientation of the sample.

A computer readable medium for storing a program for an apparatus which processes data, said processing comprising a method of providing a representation of image data, said program comprising:

• code for accessing a plurality of discrete sample values of said image data;
• code for determining an angle of orientation of each said sample values;
• code for calculating kernel values for each of said discrete sample values using one of a plurality of first kernels depending upon the angle of orientation of said discrete sample value, wherein said first kernels are constructed by rotating a second kernel from a first angle of orientation to a second angle of orientation;
• and
• code for convolving said kernel values with said discrete sample values to provide a representation of said image data, wherein said first kernels are of the form:
• h ⁢ ( s x , s y ) 0 ≤ θ ≤ π / 2 = 1 2 ⁢ { h ⁡ ( ( 1 - 2 ⁢ ⁢ θ / π ) ⁢ s x + ( 2 ⁢ ⁢ θ / π ) ⁢ s y ) c = 0.5 · h ⁡ ( ( ( 2 ⁢ ⁢ θ / π ) ⁢ s x + ( 2 ⁢ ⁢ θ / π - 1 ) ⁢ s y ) ⁢ w ⁢ ⁢ ( θ ) ) c = 0 } h ⁢ ( s x , s y ) π / 2 < θ < π = 1 2 ⁢ { h ⁡ ( ( 2 ⁢ ⁢ θ / π - 1 ) ⁢ s x + ( 2 ⁢ ⁢ θ / π - 2 ) ⁢ s y ) c = 0.5 · h ⁡ ( ( ( 2 ⁢ ⁢ θ / π - 2 ) ⁢ s x + ( 1 - 2 ⁢ ⁢ θ / π ) ⁢ s y ) ⁢ w ⁢ ⁢ ( θ ) ) c = 0 } ,
• and wherein s=t/Δt and θ is the angle of orientation of the sample.

A method of converting a first set of discrete data sample values of an image having a first sample rate to a second set of discrete data sample values of said image having a second sample rate, the method comprising the following steps:

• (i) accessing said first set of data sample values;
• and
• (ii) performing the following operations for each data value of said second set;
• (a) determining an angle of orientation for each of said discrete sample values of said first set;
• (b) calculating kernel values for each of said discrete sample values of said first set, according to one of a plurality of first kernels depending upon the angle of orientation of each of said discrete sample values, wherein said first kernels are constructed by rotating a second kernel from a first angle of orientation to a second angle of orientation;
• and
• (c) convolving said kernel values with said discrete sample values of said first data set to provide a current data value of said second set.

An apparatus for converting a first set of discrete data sample values of an image having a first sample rate to a second set of discrete data sample values of said image having a second sample rate, the method comprising the following steps:

• accessing means for accessing said first set of data sample values;
• and
• processing means for performing the following operations for each data value of said second set;
• (a) determining an angle of orientation for each of said discrete sample values of said first set;
• (b) calculating kernel values for each of said discrete sample values of said first set, according to one of a plurality of first kernels depending upon the angle of orientation of each of said discrete sample values, wherein said first kernels are constructed by rotating a second kernel from a first angle of orientation to a second angle of orientation;
• and
• (c) convolving said kernel values with said discrete sample values of said first data set to provide a current data value of said second set.

A computer readable medium for storing a program for an apparatus which processes data, said processing comprising a method of converting a first set of discrete data sample values of an image having a first sample rate to a second set of discrete data sample values of said image having a second sample rate, said program comprising:

• code for accessing said first set of data sample values;
• and
• code for performing the following operations for each data value of said second set;
• (a) determining an angle of orientation for each of said discrete sample values of said first set;
• (b) calculating kernel values for each of said discrete sample values of said first set, according to one of a plurality of first kernels depending upon the angle of orientation of each of said discrete sample values, wherein said first kernels are constructed by rotating a second kernel from a first angle of orientation to a second angle of orientation;
• and
• (c) convolving said kernel values with said discrete sample values of said first data set to provide a current data value of said second set.