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AV (Behavior Recognition with HMM (algorithm (forward algorithm…

- - - - state
      - state transition
      - observation
    - - gather sample sequences
      - calculate transition and observation probabilities from sample sequences
      - Baum-Welch algorithm
  - - - 得到 suitable HMM(i)
      - forward algorithm (based on observation)
        
        得每一步的state probability
      - 计算每一种Model的probability
    - - based on HMM(i) and observation
      - prediction and innovation
        
        也需要上一步的state probability 所以也要用forward algorithm
  - - - 计算每一步的state probability
        
        model comparison
        
        state estimation
- - - - comparison
  - - - Gaussian
        
        smoothing
      - Sobel
        
        partial derivatives
      - Hessian & Laplace
        
        2nd order derivative
      - LoG
        
        Laplace after Gauss
    - - intrinsic parameters
        
        convert camera co. into image co.
        
        describe imaging process of the camera
      - extrinsic parameters
        
        convert world co. to camera co.
        
        describe the pose of the camera relative to the vehicle co.
      - in. and ex. --> camera calibration
    - - idea 1
        
        canny
        
        Sobel
        
        detection of local maxima in gray-scale gradients
        
        threshold
      - idea 2
        
        LoG + threshold
- - - - filter with derivative filter (Sobel)
      - g(u,v,t+1)-g(u,v,t)
    - - idea : local environment
      - minimize the quadratic error
      - iterated lucas-kanade method
        
        linear approximation is insufficient for larger shifts
      - problem
        
        1 equation, 2 unkown variables
    - - 核心：G invertible
        
        Eigenvalues of G are roughly equal and >0
      - 分类讨论
        
        homogenous area
        
        corners
    - - too small
        
        aperture problem
      - too large
        
        mixing motion of different objects
      - adaptive
        
        large --> homogenous regions
        
        small --> corners
  - - - assumptions of similarity in space
- - - - distance
      - angle
      - orthogonal distance
    - - combination with tracking method
      - prediction s(t+1)=f[s(t)]
      - innovation z(t)=h[s(t)]
        
        measurement z(t) from one-shot localization
      - state = (x,y) 就是position
      - tracking fails P32
    - - known landmark position
      - estimate robot position
    - - known
      - task
        
        R and t
      - optimization problem
        
        minimize the difference
        
        SVD
      - problem: have same landmarks brute force/ ICP
    - - step1:找Q(observation)对应的最近的P(world co.)
      - step2:计算出R,t 使distance[Q,P]min
      - step3:move with R,t
      - iterative
  - - - estimate landmark position
      - known robot position
  - - - both unknown
- - - - paper 第2节
  - - - geometric model参数
      - position
    - - regrssion
      - incremental 'localization' [Kalman filter]
- - - - E --> camera co.
        
        epipoles
        
        epipolar line
      - F --> fundamental matrix
  - - - absolute
      - squared error
      - correlation
- - - - LoG --> L(u,v,σ)
      - maxima in scale space
      - larger than threshold (reduce noise)
      - Eigenvalues of H roughly the same
    - - rotational invariance
        
        calculate preferential direction
      - calculate direction histograms
      - build a feature vector from the direction histogram
    - - scaling
      - rotation
      - brightness
      - find point correspondences in any image pair without epipolar geometry
- - - - derivatives : regression
  - - - HMM
        
        特性
        
        depend on present state and not on previous states or observations
        
        流程
        
        prediction
        
        P(st+1) P26下面
        
        need P(state transition)
        
        innovation
        
        P(st) P26上面
        
        need P(observation)
    - - linear gaussian model
        
        Kalman Filter
        
        modeling
        
        dependency between state and measurement
        
        good example (P46)
        
        state transition
        
        流程
        
        predicting
        
        P37公式
        
        innovation
        
        P37公式
      - nonlinear but linearizable + Gaussian
        
        EKF
        
        UKF
      - represent the distribution with 1. mean 2. variance
    - - particle filter
        
        step1 : prediction
        
        step2 : weighted sample
        
        step3 : random sample
      - represent the distribution with weighted or random sample
    - - system state
      - observer