02/14/02(c) University of Wisconsin 2002, CS 559 Last Time Filtering Image size reduction –Take the pixel you need in the output –Map it to the input –Place

02/14/02 (c) University of Wisconsin 2002, CS 559

Last Time

• Filtering

• Image size reduction– Take the pixel you need in the output

– Map it to the input

– Place a filter at that location, and do the weighted sum of neighboring pixels

– Place the filter value in the output image


Today

• Enlarging Images

• Morphing

• Compositing

• Project 1: Image Editing Software


Enlarging Images

• Warp function: f(x)=kx, k < 1• Problem: Have to create pixel data

– More pixels in output than in input

• Solution: Filter up to larger size– Apply the filter at intermediate pixel locations– eg: To get double image size, apply filter at every pixel and every

half pixel

• New pixels are interpolated from old ones– Filter encodes interpolation function– May want to edge-enhance images after enlarging


Enlargement


Ideal Enlargement

• Reconstruct original function

• Resample at higher frequency

• Original function was band-limited, so re-sampling does not add any extra frequency information


Image Morphing

• Process to turn one image into another– Also the basis for video effects like cross-dissolve

• Define path from each point in the original image to its destination in the output image– Color may change along path

– Many ways to define paths

• Animate points along paths– At each time increment, step pixels along their paths and interpolate

their colors

– Resample the result to get a regular image


Filtering and Color

• To filter a color image, simply filter each of R,G and B separately

• Re-scaling and truncating are more difficult to implement:– Adjusting each channel separately may change color significantly

– Adjusting intensity while keeping hue and saturation may be best, although some loss of saturation is probably OK


Compositing

• Compositing combines components from two or more images to make a new image

• The basis for film special effects (even before computers)– Create digital imagery and composite it into live action

• Important part of animation – even hand animation– Background change more slowly than foregrounds, so composite

foreground elements onto constant background


Very Simple Example

over =


Mattes

• A matte is an image that shows which parts of another image are foreground objects

• Term dates from film editing and cartoon production

• How would I use a matte to insert an object into a background?

• How are mattes usually generated for television?


Working with Mattes

• To insert an object into a background– Call the image of the object the source

– Put the background into the destination

– For all the source pixels, if the matte is white, copy the pixel, otherwise leave it unchanged

• To generate mattes:– Use smart selection tools in Photoshop or similar

• They outline the object and convert the outline to a matte

– Blue Screen: Photograph/film the object in front of a blue background, then consider all the blue pixels in the image to be the background


Alpha

• Basic idea: Encode opacity information in the image

• Add an extra channel, the alpha channel, to each image– For each pixel, store R, G, B and Alpha

– alpha = 1 implies full opacity at a pixel

– alpha = 0 implies completely clear pixels

• Images are now in RGBA format, and typically 32 bits per pixel (8 bits for alpha)


Smoothing Edges

• Reduce alpha gradually at edges to smooth them


Pre-Multiplied Alpha

• Instead of storing (R,G,B,), store (R,G,B,)

• The compositing operations in the next several slides are easier with pre-multiplied alpha

• To display and do color conversions, must extract RGB by dividing out =0 is always black

– Some loss of precision as gets small, but generally not a problem


Combining Images and Alpha

• If the image is of a translucent object, then represents the amount of the background that is blocked

• If combining two translucent objects:– (1-a)(1-b) of the background shows through both a(1-b) passes through B but is blocked by A b(1-a) passes through A but is blocked by B ab of the background is blocked by both

• Assume a pixel represents the color of a small area– Typically a square, but not necessarily

• Interpret to represent the fraction of the pixel area covered by an object– We’ll see ways of deciding how much background shows through when

images are combined


Compositing Assumptions

• We will combine two images, f and g, to get a third composite image– Not necessary that one be foreground and background

– Background can remain unspecified

• Both images are the same size and use the same color representation

• Multiple images can be combined in stages, operating on two at a time


Image Decomposition

• The composite image can be broken into regions– Parts covered by f only

– Parts covered by g only

– Parts covered by f and g

– Parts covered by neither f nor g

• Same goes for sub-pixels in places where 1


Basic Compositing Operation

• The different compositing operations define which image “wins” in each sub-region of the composite

• At each pixel, combine the pixel data from f and the pixel data from g with the equation:

• F and G describe how much of each input image survives, and cf and cg are pre-multiplied pixels, and all four channels are calculated

• To define a compositing operation, define F and G

gfo GcFcc


Sample Images

Image

Alpha


“Over” Operator


“Over” Operator

• Computes composite with the rule that f covers g

fG

F

1

1


“Inside” Operator


“Inside” Operator

• Computes composite with the rule that only parts of f that are inside g contribute

0

G

F g


“Outside” Operator


“Outside” Operator

• Computes composite with the rule that only parts of f that are outside g contribute

0

1

G

F g


“Atop” Operator


“Atop” Operator

• Computes composite with the over rule but restricted to places where there is some g

f

g

G

F

1


“Xor” Operator

• Computes composite with the rule that f contributes where there is no g, and g contributes where there is no f

f

g

G

F

1

1


“Xor” Operator


“Clear” Operator

• Computes a clear composite

• Note that (0,0,0,>0) is a partially opaque black pixel, whereas (0,0,0,0) is fully transparent, and hence has no color

0

0

G

F


“Set” Operator

• Computes composite by setting it to equal f

• Copies f into the composite

0

1

G

F


Unary Operators

• Darken: Makes an image darker (or lighter) without affecting its opacity

• Dissolve: Makes an image transparent without affecting its color

),,,(),( ffff bgrfdarken

),,,(),( ffff bgrfdissolve


“PLUS” Operator

• Computes composite by simply adding f and g, with no overlap rules

• Useful for defining cross-dissolve in terms of compositing:

gfo ccc

)1,( ),(),,( tgdissolveplustfdissolvetgfcross


Obtaining Values

• Hand generate (paint a grayscale image)• Automatically create by segmenting an image into

foreground background:– Blue-screening is the analog method

• Remarkably complex to get right

– “Lasso” is the Photoshop operation

• With synthetic imagery, use a special background color that does not occur in the foreground– Brightest blue is common– Why blue?


Compositing With Depth

• Can store pixel “depth” instead of alpha

• Then, compositing can truly take into account foreground and background

• Generally only possible with synthetic imagery– Image Based Rendering is an area of graphics that, in part, tries to

composite photographs taking into account depth

Documents

02/14/02(c) University of Wisconsin 2002, CS 559 Last Time Filtering Image size reduction –Take the pixel you need in the output –Map it to the input –Place