Paper Summaries Any takers? Character Animation Projects - PDF document

Paper Summaries • Any takers? Character Animation Projects Assignment #1 • Presentations • All grades – Schedule is now up on Web site – Comments / grades via e-mail – Please e-mail me with your preference of – Doing “real time” in realtime. presentation day/time • First come, first served – All slots now taken…thanks. Assignment 2/3 Plan for today • Assignment 2: On queue to be graded • Articulated Figure Motion – Reminder: grace period ends tonight – Intro / Forward Kinematics / Constraints – Inverse Kinematics – Walking • Assignment 3 – Advanced Algorithms – Due Feb 11 th – Today: Character Animation • Levels of control / Motion capture systems 1

Motivation Films Motivational Film • Animations by Chris Landreth • The End (1995) – Alias / Wavefront ( since 1994 ) – Nominated for 1996 Academy Award for best animated short. Motivational Film Plan For Today • Bingo (1998) • Topics – Test case for Maya – Motion Capture Data – Levels of Control Role of Animation Motion Capture • Degrees of freedom • The idea between motion capture – You want realistic human motion? – Number of parameters • Go to the source whose values must be • No, not Newton this time… defined in order to fully • Use an actual human position the articulated – Disney has used this approach as far back as Snow figure White � Purpose of animation • Using video as a guide • Rotoscoping – tracing recorded video frames as basis for � Provide values to each of the DOF animation for each time step. 2

Motion Capture Motion Capture • What motion capture gives us: – Sampled values for each DOF in time. • Since captured directly from human motion – Subtleties of motion come for free. – Difficult for an animator to keyframe these subtleties Watt/Policarpo Motion Capture Motion Capture • Types of motion capture systems • Types of motion capture systems – Optical – Prosthetic • Incorporate directionally-reflective balls referred to • set of armatures attached all over the performer’s as markers which attach to the performer. body • Three (at least) video cameras that track markers. • The armatures are connected to each other by using a series of rotational and linear encoders. • Accurate, though cumbersome for the performer • Provides most flexibility for performers. • Problem: Markers may be occluded from cameras views. Motion Capture Systems Motion Capture Systems • Types of motion capture systems • Types of motion capture systems – Acoustic – Magnetic • An array of audio transmitters are strapped to • Much like acoustic except magnetic various parts of the performers body. transmitters/receivers used instead of acoustic • Three receivers are triangulated to provide a point in 3D space. • No occlusion problem. • Cables are cumbersome to performers • No occlusion problem. • Metal / other magnetic fields may interfere. • Cables are cumbersome to performers • Ambient sound may interfere 3

Motion capture Systems Motion Capture Systems • Challenges: • Challenges: – Even if motion capture data was perfect, we still have – Signal is not perfect the following challenges: • Noisy • Re-use – use the motion for a slightly different purpose • missing data • Creating impossible motion – Motion capture won’t do it, but • not perfectly aligned with joints may be desired in animation • Change of intent – we can’t always predict what motion we – Retargeting will need • Data is only valid for virtual character who – Take Home Message: Motion Capture captures a possesses same scale as real character. particular, single motion. Motion Capture Systems Motion Capture Data • So what CAN we do with motion capture • Examples data? – From Eurographics Computer Animation – We can and Simulation EGCAS'96 • speed up • slow down • time warp • Motion warp – However, one must remember that Captured data is Sampled Data. Sampling Theory Sampling Theory • Signal - function that conveys information • Point Sampling – Audio signal (1D - function of time) – start with continuous signal – Image (2D - function of space) – calculate values of signal at discrete, evenly spaced points (sampling) • Continuous vs. Discrete – convert back to continuous signal for display or – Continuous - defined for all values in range output (reconstruction) – Discrete - defined for a set of discrete points in range. 4

Sampling Theory Sampling Theory • Sampling can be described as creating a set of values representing a function evaluated at evenly spaced samples = ∆ = K f n f ( i ) i 0 , 1 , 2 , , n ∆ = interval between samples = range / n. … Foley/VanDam 0 1 2 n Sampling Theory Sampling Theory • Sampling Rate = number of samples per unit • Example -- CD Audio – sampling rate of 44,100 samples/sec – ∆ = 1 sample every 2.26x10 -5 seconds = 1 f ∆ Sampling Theory Sampling Theory • Rich mathematical foundation for sampling • Spatial vs frequency domains theory – Most well behaved functions can be described • Hope to give an “intuitive” notion of these as a sum of sin waves (possibly offset) at various frequencies mathematical concepts – Describing a function by the contribution (and offset) at each frequency is describing the function in the frequency domain – Higher frequencies equate to greater detail 5

Sampling Theory Sampling Theory • Nyquist Theorum – A signal can be properly reconstructed if the signal is sampled at a frequency (rate) that is greater than twice the highest frequency component of the signal. Foley/VanDam Sampling Theory Sampling Theory • Nyquist Theory • Example -- CD Audio – Said another way, if you have a signal with – sampling rate of 44,100 samples/sec – ∆ = 1 sample every 2.26x10 -5 seconds highest frequency component at f h , you need at lease 2f h samples to represent this signal accurately. Sampling Theory Sampling Theory • Nyquist Theory -- examples • Aliasing – CDs can accurately reproduce sounds with – Failure to follow the Nyquist Theorum results frequencies as high as 22,050 Hz. in aliasing . – Aliasing is when high frequency components of a signal appear as low frequency due to inadequate sampling. 6

Sampling Theory Sampling Theory • Aliasing - example • applet Foley/VanDam Sampling Theory Sampling Theory • Anti-Aliasing • Fourier analysis – What to do in an aliasing situation – Given f(x) we can generate a function F(u) which indicates how much contribution each • Increase your sampling rate (supersampling) frequency u has on the function f. • Decrease the frequency range of your signal (Filtering) – F(u) is the Fourier Transform – Fourier Transform has an inverse – How do we determine the contribution of each frequency on our signal? Sampling Theory Sampling Theory • Fourier Transforms • How do we calculate the Fourier Transform? f(x) – Use Mathematics Inverse – For discrete functions, use the Fast Fourier Fourier Fourier F(u) Transform Transform algorithm (FFT) Transform f(x) 7

Sampling Theory Sampling Theory • Filtering -- Frequency domain • Anti-Aliasing – Place function into frequency domain F(u) – What to do in an aliasing situation – simple multiplication with box filter S(u) • Increase your sampling rate (supersampling) • Decrease the frequency range of your signal − ≤ ≤ ⎧ (Filtering) 1 , when k u k = ⎨ S ( u ) – Since we already have the data sampled, we ⎩ 0 , elsewhere can’t supersample motion capture data – Thus, we need to filter Sampling Theory Sampling Theory • Filtering - frequency domain • Filtering -- Spatial Domain – Convolution ∞ ∫ = ∗ = τ − τ τ h ( x ) f ( x ) g ( x ) f ( ) g ( x ) d − ∞ Taking a weighted average of the neighborhood around each point of f, weighted by g centered at that point. Foley/VanDam Sampling Theory Sampling Theory • Convolution Applet • Convolution and Filtering – Convolution in the spatial domain is equivalent to multiplication in the frequency domain – Use Fourier Transform to convert filter from spatial to frequency & visa versa 8

Sampling Theory Sampling Theory • Convolving with a sinc function in the spatial • Anti-aliasing -- Filtering domain is the same as using a box filter in the – Removes high component frequencies from a frequency domain signal. – Removing high frequencies results in removing detail from the signal. – Can be done in the frequency or spatial domain Foley/VanDam Sampling Theory Motion capture data • So what does all this mean w.r.t. motion capture • Filtering - Convolution data? – To avoid aliasing must filter before modifying data in time • Motion capture sampling rates can be as high as 144 samples / sec – Filtering can also remove “noisy” data by removing high frequency components. • Questions? • Break! Foley/VanDam Putting it all together Role of Animation • We spent the last several weeks looking at • Degrees of freedom various aspects of articulated figure motion – Number of parameters • The 2 nd half of this lecture is an attempt to whose values must be defined in order to fully summarize into a single framework position the articulated – Added bonus: Intro to facial animation figure � Purpose of animation � Provide values to each of the DOF for each time step. 9