Digital image warping

Figure 1.5 shows the relationship between the various stages in a geometric

transformation. It is by no means a strict recipe for the order in which warping is

achieved. Instead, the purpose of this figure is to convey a conceptual layout, and to

serve as a roadmap for this book.

Scanline Algorithms (Chp. 7)

I Image Resamplin..g (Cap. 5)

Ima e Reconstructran

Scene '11 Acquisitinll ] [ ' I]

(Cap. 2) / /

Spatial FAit (Cap. 6)

Transformation

(Cap. 3) T

Output

Figure 1.5: Conceptual layout.

An image is first acud by a digital image acquisition system. It then passes

through the image resamplng gtage, consisting of a reconstruction substage to compute a

continuous image and a saling substage that samples it at any desired location. The

exact positions at which resampling oc0urs is defined by the spatial transformation. The

output image is obtained once image resampling is completed.

In order to avoid artifacts in the output, the msampling stage must abide by the prin-

ciples of digital filtering. Antialias filtering is introduc..xl for this purpose. It serves to

process the image so that artifacts due to undersampling are mitigated. The theory and

justification for this filtering is derived from sampling theory. In practice, image msam-

pling and digital filtering am collapsed into efficient algorithms which are tightly cou-

pled. As a result, the stages that contribute to image resampling are depicted as being

integrated into scanline algorithms.

2

PRELIMINARIES

In this chapter, we begin our study of digital image warping with a review of some

basic terminology and mathematical preliminaries. This shall help to lay our treatment

of image warping on firm ground. In particular, elements of this chapter comprise a for-

mulation that will be found to be recurring throughout this book. After the definitions

and notation have been clarified, we turn to a description of digital image acquisition.

This stage is responsible for converting a continuous image of a scene into a discrete

representation that is suitable for digital computers. Attention is given to the imaging

components in digital image acquisition systems. The operation of these devices is

explained and an overview of a general imaging system is given. Finally, we conclude

with a presentation of input images that will be used repeatedly throughout this book.

These images will later be subjected to geometric transformations to demonstrate various

warping and filtering algorithms.