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# 4. This problem investigates nearest neighbor and bilinear interpolation. For simplicity, we will focus on estimating the image intensity at a single location. Interpolation

## 4. This problem investigates nearest neighbor and bilinear interpolation. For simplicity, we will focus on estimating the image intensity at a single location. Interpolation is used when transforming an image through resizing, rotating, etc., in which case, the image intensity will need to be estimated at a number of locations. Consider the diagram below of four pixels 1 3 X 2 4 X Y where the dots represent the locations where we know the image intensity and the represents the location where we would like to estimate the image intensity. By convention, the vertical axis is the x-axis and the horizontal axis is the y-axis. Suppose the four pixels are at the following locations (indicated by (x,y)) and have the following intensity values (indicated by p) (x, y) = (4,10) (x2, y) = (4,11) (X3, y3) = (5,10) (x4, y4) = (5,11) and that we would like to estimate the image intensity at a fifth location (x5, y5) = (4.2,10.2) P = 40 P = 45 P3 = 100 = 150 P4 = That is, we want to estimate p5. a) Provide an estimate for p5 using nearest neighbor interpolation. b) Provide an estimate for p using bilinear interpolation. Round your value to the nearest integer. You can use either of the two methods discussed in lecture. (You might want to use both methods to check your answer.) 4. This problem investigates nearest neighbor and bilinear interpolation. For simplicity, we will focus on estimating the image intensity at a single location. Interpolation is used when transforming an image through resizing, rotating, etc., in which case, the image intensity will need to be estimated at a number of locations. Consider the diagram below of four pixels 1 3 X 2 4 X Y where the dots represent the locations where we know the image intensity and the represents the location where we would like to estimate the image intensity. By convention, the vertical axis is the x-axis and the horizontal axis is the y-axis. Suppose the four pixels are at the following locations (indicated by (x,y)) and have the following intensity values (indicated by p) (x, y) = (4,10) (x2, y) = (4,11) (X3, y3) = (5,10) (x4, y4) = (5,11) and that we would like to estimate the image intensity at a fifth location (x5, y5) = (4.2,10.2) P = 40 P = 45 P3 = 100 = 150 P4 = That is, we want to estimate p5. a) Provide an estimate for p5 using nearest neighbor interpolation. b) Provide an estimate for p using bilinear interpolation. Round your value to the nearest integer. You can use either of the two methods discussed in lecture. (You might want to use both methods to check your answer.)

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