hinton.ps

手写识别是模式识别中研究得一个热点

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612 792 0 FMBEGINPAGE
108 54 540 54 2 L
0.25 H
2 Z
0 X
0 K
N
0 8 Q
(Elastic Matching II) 108 42.62 T
(November 30, 1993) 292.13 42.62 T
(2) 536 42.62 T
1 14 Q
(3.1  Generation) 108 710.67 T
0 12 Q
(If one wanted to do the opposite procedure - generate rather than recognize we could use) 108 684 T
(our spline models. Along the curve of the spline, with some arbitrary orientation and) 108 670 T
(deformation, \322Gaussian ink generators\323 are uniformly distributed. Then, according to) 108 656 T
(these \322Gaussian beads\323 we can place a number of ink pixels according to the distribution) 108 642 T
(of the beads, along with some random noise. Each digit) 108 628 T
2 F
(possible) 377.16 628 T
0 F
( has some probability) 416.47 628 T
(associated with it.) 108 614 T
1 14 Q
(3.2  Recognition) 108 580.67 T
0 12 Q
(When recognizing isolated digits, we want to \336nd the model that was most likely to have) 108 554 T
-0.27 ( generated the it. The deformation ener) 108 528 P
-0.27 (gy is given by) 293.04 528 P
-0.27 ( where) 478.88 528 P
2 F
-0.27 (P) 513.65 528 P
2 10 Q
-0.22 (ij) 520.98 525 P
0 12 Q
-0.27 ( is) 526.53 528 P
(the control point) 108 514 T
2 F
(i) 190.29 514 T
0 F
( on the spline vertex) 193.62 514 T
2 F
(j) 293.89 514 T
0 F
(.) 297.22 514 T
(The ener) 108 488 T
(gy for the model is the dif) 150.07 488 T
(ference between) 274.45 488 T
2 F
(E) 355.69 488 T
2 10 Q
(deform) 363.02 485 T
0 12 Q
( and the sum of the log proba-) 391.33 488 T
(bilities of each pixel given the best model instance.) 108 474 T
(The search procedure involves conver) 108 448 T
(ging the beads of the model to the image.) 290.29 448 T
(For all Gaussian beads, compute the \322responsibility\323 each bead has for a pixel. Next, bal-) 108 422 T
(ance the control points between the pixels and their home locations. In other words the) 108 408 T
(\322forces\323 acting on the pixel depend on the Gaussian distribution of the beads and the) 108 394 T
-0.36 (Gaussian distribution of the 8 control points. W) 108 380 P
-0.36 (e now have a modi\336ed set of control points) 333.05 380 P
(from our prototype model. Now we choose an af) 108 366 T
(\336ne transformation that minimizes the) 341.27 366 T
(distances between object-based frame to the image frame. This allows costless rotation,) 108 352 T
-0.26 (scaling, etc. After choosing the best transformation, any dif) 108 338 P
-0.26 (ferences left over are the defor-) 390.47 338 P
(mation ener) 108 324 T
(gy) 164.74 324 T
(.) 175.96 324 T
1 14 Q
(3.3  Learning) 108 290.67 T
0 12 Q
(Learning is accomplished by moving the variances and home control points in prototype) 108 264 T
(models.) 108 250 T
1 16 Q
(4.0  Conclusion) 108 209.33 T
0 12 Q
(The spline representation has a much smaller space than some other representations such) 108 182 T
(as neural nets. This should allow for faster learning. Splines models are probably a closer) 108 168 T
(representation of handwriting with regard to its physical characteristics.) 108 154 T
(This method, because af) 108 128 T
(\336ne transformations are costless, should be much more \337exible) 224.36 128 T
(than many other methods which usually depend, at least, on orientation.) 108 114 T
(The disadvantage is speed. The authors admit that this method is extremely slow) 108 88 T
(.) 493.97 88 T
362.6 513.63 478.88 545.74 C
2 9 Q
0 X
0 K
(E) 363.6 528 T
2 7 Q
(d) 369.44 524.87 T
(e) 373.47 524.87 T
(f) 377.11 524.87 T
(o) 379.6 524.87 T
(r) 383.63 524.87 T
(m) 386.88 524.87 T
2 9 Q
(P) 458.9 528 T
2 7 Q
(i) 464.73 524.87 T
(j) 467.21 524.87 T
3 9 Q
(\050) 455.01 528 T
(\051) 469.55 528 T
0 7 Q
(2) 474.39 530.8 T
2 F
(i) 438.57 516.15 T
0 F
(1) 449.02 516.15 T
3 F
(=) 442.85 516.15 T
0 F
(4) 443.79 539.97 T
3 14 Q
(\345) 440.55 525.44 T
2 7 Q
(j) 423.63 516.15 T
0 F
(1) 434.08 516.15 T
3 F
(=) 427.91 516.15 T
0 F
(8) 428.85 539.97 T
3 14 Q
(\345) 425.61 525.44 T
0 9 Q
(l) 411.14 528 T
(o) 413.64 528 T
(g) 418.14 528 T
3 F
(-) 405.86 528 T
(=) 396.43 528 T
0 0 612 792 C
FMENDPAGE
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612 792 0 FMBEGINPAGE
108 54 540 54 2 L
0.25 H
2 Z
0 X
0 K
N
0 8 Q
(Elastic Matching II) 108 42.62 T
(November 30, 1993) 292.13 42.62 T
(1) 536 42.62 T
0 24 Q
(Elastic Matching II) 231.4 704 T
1 12 Q
(Paul Schermerhorn) 273.53 664 T
0 F
-0.52 (HINT) 108 636 P
-0.52 (ON, G.E., WILLIAMS, C.K.I. and REVOW) 136.42 636 P
-0.52 (, M.D. \0501991\051 \322Adaptive Elastic Models) 346.91 636 P
(for Hand-Printed Character Recognition\323) 108 622 T
1 16 Q
(1.0  Motivation) 108 581.33 T
0 12 Q
-0.04 (T) 108 554 P
-0.04 (appert modelled words with a series of points, and applied a brute-force method for \336nd-) 114.49 554 P
(ing the best match. Hinton and Revow have an interesting and signi\336cantly dif) 108 540 T
(ferent) 484.55 540 T
(approach using spline curves.) 108 526 T
1 16 Q
(2.0  Digr) 108 485.33 T
(ession: What is a spline?) 166.78 485.33 T
0 12 Q
(There are two basic branches of splines, ones which match data points exactly) 108 458 T
(, and those) 481.93 458 T
-0.26 (which do not. This distinction is denoted by) 108 444 P
2 F
-0.26 (\336tting) 319.47 444 P
0 F
-0.26 ( vs.) 347.46 444 P
2 F
-0.26 (faring.) 366.6 444 P
0 F
-0.26 (The latter seem to much less) 401.66 444 P
(useful except for) 108 430 T
(, perhaps, artistic purposes.) 188.12 430 T
(A cubic spline is a curve which is represented by an order) 108 404 T
(-3 polynomial. Normally this) 385.2 404 T
(can be speci\336ed by two points and two tangent vectors. The) 108 390 T
2 F
(basis spline) 397.8 390 T
0 F
( or B-spline is a) 454.11 390 T
(way of using multiple spline segments in a piecewise manner) 108 376 T
(, with the basis function) 401.66 376 T
-0.29 (specifying how the curve responds to the control points. The Bezier curve is a special case) 108 362 P
(of the B-spline.) 108 348 T
1 16 Q
(3.0  Method) 108 203.29 T
0 12 Q
(The characters are represented as cubic B-splines with 8 control points, with the \336rst and) 108 175.96 T
(last points doubled. The splines are deformable with the constraint that the control points) 108 161.96 T
(follow the Gaussian distribution from their \322home\323 locations. The model with the least) 108 147.96 T
(deformation ener) 108 133.96 T
(gy with respect to the prototype is the match.) 190.05 133.96 T
237.2 239.96 410.8 344 C
2 12 Q
0 X
0 K
(P) 261.65 290.5 T
(u) 276.79 290.5 T
3 F
(\050) 271.69 290.5 T
(\051) 283.39 290.5 T
2 F
(t) 312.47 286.67 T
0 9 Q
(3) 316.27 291.99 T
2 12 Q
(t) 324.76 286.67 T
0 9 Q
(2) 328.56 291.99 T
2 12 Q
(t) 337.05 286.67 T
0 F
(1) 344.39 286.67 T
2 F
(B) 354.59 290.5 T
(p) 367.12 316.71 T
2 9 Q
(i) 373.58 312.93 T
0 F
(1) 385.51 312.93 T
3 F
(-) 378.33 312.93 T
2 12 Q
(p) 374.08 298.77 T
2 9 Q
(i) 380.54 294.99 T
2 12 Q
(p) 367.12 280.94 T
2 9 Q
(i) 373.58 277.16 T
0 F
(1) 385.51 277.16 T
3 F
(+) 378.33 277.16 T
2 12 Q
(p) 367.12 263 T
2 9 Q
(i) 373.58 259.22 T
0 F
(2) 385.51 259.22 T
3 F
(+) 378.33 259.22 T
3 12 Q
(=) 295.39 290.5 T
313.97 284.07 309.97 284.07 2 L
0.33 H
0 Z
N
309.97 284.07 309.97 302.11 2 L
N
309.97 302.11 313.97 302.11 2 L
N
347.88 284.07 351.88 284.07 2 L
N
351.88 284.07 351.88 302.11 2 L
N
351.88 302.11 347.88 302.11 2 L
N
368.62 257.27 364.62 257.27 2 L
N
364.62 257.27 364.62 328.91 2 L
N
364.62 328.91 368.62 328.91 2 L
N
387.51 257.27 391.51 257.27 2 L
N
391.51 257.27 391.51 328.91 2 L
N
391.51 328.91 387.51 328.91 2 L
N
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