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Comment: Migrated to Confluence 4.0

(This is a work in progress; currently quite rough)

Overview

[Stub] 

Key Points:

  1. Problem statement
  2. Integrating top-down and bottom-up processes
  3.  

Bottom-Up Progress - Stem detection and reconstruction

We're continuing to develop an approach for reconstructing 3D stems directly from 2D image features.  This will provide a rich set of stem hypothesis to be refined and expanded during top-down inference.

The approach can be summarized in two steps:

  1. Detection of high-quality stem fragments in 2D and
  2. Reconstruction of 3D stem curves from 2D curve fragments in several views

Stem Detection

Goal: Detect stem regions in images

Typical stem features:

  1. Strong, parallel edge pairs at borders
  2. textureless interior

These characteristics are shared by images of text (letters, numbers, etc.)

Idea: use state-of-the-art text-detection as first-step in algorithm to detect stems.

Step 1: Stroke-width transform
Algorithm extracts "strokes" in an image, i.e. regions between two parallel edges with relatively constant width.  Pixels with with similar stroke-widths are grouped into several disjoint regions.  Designed for text detection, but works equally well for plant stems.

Step 2: Extract medial axis from stroke regions
:
    * Convert stroke regions to points on stroke's medial axis
    * Infer linear ordering on points and prune outliers using euclidean graph analysis
    * Use cubic interpolating spline to smooth-out quantization error and detector noise

Result: High quality stem-fragments

<Image here: 1. original image, 2. detected edges, 3. stroke regions, 4. medial axis curves>

Some fragments can be merged using heuristics, others will be joined using top-down inference.

Top-Down Progress - Edge Distance

General idea - compare edges in two images. 
    why? - need to evalaute hypothesized structure.  color/patch based methods fail at surface boundaries.  Our boundary-to-surface ratio is too high.
    how? - 
    criteria - fast/parallel; encourages good fit;  close fits aren't ruled out

Edge Distance #1: Chamfer distance

For each point, find nearest neighbor.  Sum of squared distances

Additional terms to penalize missed correspondences.

Pros:

  • Fast: Implemented in CUDA; simple operations

Cons

  • Asymmetric:  d(a,b) != d(b,a)
  • Fails in "Double-edge" scenario.
  • Discontinuities when correspondence switches
  • Requires several approximations to achieve parallelism
  • Difficult to represent as a probability distribution -> unintuitive parameters require hand-tuning

Edge Distance #2: Gaussian Mixture distance

Each point in B is "generated" by a point in A plus some gaussian noise.  Model includes some uniform noise, too.

Correspondences are unknown (average over all possible correspondences).

Pros:

  • Fast: Implemented in CUDA
  • Elegant probabilistic model
  • Function is smooth - no correspondence switches

Cons

  • Asymetric
  • Slower than Chamfer distance due to blurring operation.
  • Fails to enforce one-to-one correspondence
  • Precise correspondences are unknown.
  • Fails to penalize "missing data"

Edge Distance #3: Blurred-Difference distance

Pros

  • Fast: Implemented in CUDA
  • Penalizes noise and missing data.
  • Symmetric
  • Semi-learned from data.

Cons

  • Blurring radius feels arbitrary
  • Implausible generative model
  • Faulty assumption of conditional independence of pixels
  • can't adjust noise penalty vs. missing penalty
  •  
  •  
  • Troubles with old Edge-based likelihood
  • New Edge-based likelihood
  • Stroke-width transform for stem-detection
  • 3D reconstruction of curves from stem fragments
  • ?