Introduction to Digital Image Processing

MONOCHROME IMAGE RECONSTRUCTION SYSTEMS 107

for (4.3-2a)

for (4.3-2b)

provides the first-order linear sample interpolation with triangular interpolation

waveforms. Figure 4.3-3 illustrates one-dimensional interpolation using sinc, square

and triangle functions.

The triangle function may be considered to be the result of convolving a square

function with itself. Convolution of the triangle function with the square function

yields a bell-shaped interpolation waveform (in Figure 4.3-2d). It is defined as

for (4.3-3a)

for (4.3-3b)

for . (4.3-3c)

FIGURE 4.3-3. One-dimensional interpolation.

R

1

x() x 1+=

1– x 0≤≤

R

1

x() 1 x–=

0 x 1≤<

R

2

x()

1

2

---

x

3

2

---

+()

2

3

4

---

x()

2

–