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作成日: 2025年10月24日

使用モデル O3 by Chat01

質問

IMG_20251024_133027.jpgIMG_20251024_133027.jpg
IMG_20251024_133046.jpgIMG_20251024_133046.jpg

Реши

Python

python
from PIL import Image
import matplotlib.pyplot as plt

img1 = Image.open('/mnt/data/IMG_20251024_133027.jpg')
plt.imshow(img1)
plt.axis('off')

(-0.5, 4623.5, 3471.5, -0.5)

Python

python
img2 = Image.open('/mnt/data/IMG_20251024_133046.jpg')
plt.imshow(img2)
plt.axis('off')

(-0.5, 4623.5, 3471.5, -0.5)

Python

python
import numpy as np
# Crop approximate central region
w, h = img2.size
crop = img2.crop((int(w*0.3), int(h*0.3), int(w*0.85), int(h*0.8)))
plt.imshow(crop)
plt.axis('off')

(-0.5, 2542.5, 1735.5, -0.5)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(crop.crop((0,0,350,350)))
plt.axis('off')

(-0.5, 349.5, 349.5, -0.5)

Python

python
plt.figure(figsize=(5,5))
# Crop rectangle around points
# Use crop region manual: maybe 350 to 1000 on x, 50 to 700 on y
# But easier: show central horizontally.
plt.imshow(crop)
plt.axis('off')

(-0.5, 2542.5, 1735.5, -0.5)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(crop.crop((0,80,400,600)))
plt.axis('off')

(-0.5, 399.5, 519.5, -0.5)

Python

python
plt.figure(figsize=(6,6))
plt.imshow(crop)
plt.xlim(0, crop.shape[1])
plt.ylim(crop.shape[0], 0)
plt.show()

思考

plt.figure(figsize=(6,6)) plt.imshow(crop) plt.xlim(0, crop.shape[1]) plt.ylim(crop.shape[0], 0) plt.show()

Thought for 1m 7s

Python

python
import numpy as np
arr = np.array(crop)
plt.figure(figsize=(6,6))
plt.imshow(arr)
plt.xlim(0, arr.shape[1])
plt.ylim(arr.shape[0], 0)
plt.show()

Python

python
# crop right region around red circles
plt.figure(figsize=(4,4))
plt.imshow(crop.crop((1500,100,2400,900)))
plt.axis('off')

(-0.5, 899.5, 799.5, -0.5)

Python

python
# annotate image coordinates with grid lines maybe; show with some transparency?
plt.figure(figsize=(6,6))
plt.imshow(arr)
plt.show()

Python

python
# crop around area of red cluster
plt.figure(figsize=(4,4))
plt.imshow(crop.crop((1600,200,2100,900)))
plt.axis('off')

(-0.5, 499.5, 699.5, -0.5)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(crop.crop((1850,350,2500,950)))
plt.axis('off')

(-0.5, 649.5, 599.5, -0.5)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(crop.crop((1600,0,2300,350)))
plt.axis('off')

(-0.5, 699.5, 349.5, -0.5)

Python

python
# crop region with green
plt.figure(figsize=(4,4))
plt.imshow(crop.crop((1100,800,1800,1400)))
plt.axis('off')

(-0.5, 699.5, 599.5, -0.5)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(crop.crop((1200,1000,1900,1600)))
plt.axis('off')

(-0.5, 699.5, 599.5, -0.5)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(crop.crop((1100,1200,1900,1800)))
plt.axis('off')

(-0.5, 799.5, 599.5, -0.5)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(crop.crop((1400,1000,2300,1450)))
plt.axis('off')

(-0.5, 899.5, 449.5, -0.5)

Python

python
# let's detect luminance to approximate grey dots positions 
import cv2
gray = cv2.cvtColor(arr, cv2.COLOR_BGR2GRAY)
# threshold to find small darkish points
th = cv2.threshold(gray, 180, 255, cv2.THRESH_BINARY_INV)[1]  # invert to find dark pixels
# let's dilate small to get bigger
kernel = np.ones((3,3), np.uint8)
th2 = cv2.dilate(th, kernel, iterations=1)
# find contours
contours, _ = cv2.findContours(th2, cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)
# filter contours which are small (points) maybe grey dots
candidates = []
for cnt in contours:
    x,y,wc,hc = cv2.boundingRect(cnt)
    if wc<10 and hc<10:
        candidates.append((x,y))
# let's group by y approximate
ys = [y for x,y in candidates]
# cluster y by near equal spacing
ys_sorted = sorted(ys)
print(ys_sorted[:50])

Python

python
# show bottom left region
plt.figure(figsize=(4,4))
plt.imshow(arr[1200:1700, 0:400])
plt.axis('off')

(-0.5, 399.5, 499.5, -0.5)

Python

python
print(arr.shape)

Python

python
# locate left axis x coordinate roughly
# find columns with many dark pixels to find axis line
gray = cv2.cvtColor(arr, cv2.COLOR_BGR2GRAY)
# consider columns with many low intensity maybe
cols_dark = [ (x, np.sum(gray[:,x]<50)) for x in range(arr.shape[1])]
# Let's find peaks
xs = sorted(cols_dark, key=lambda t: t[1], reverse=True)[:10]
xs

[(1072, 64),
 (1070, 62),
 (1071, 62),
 (1069, 61),
 (1093, 59),
 (1094, 59),
 (1241, 58),
 (2080, 56),
 (634, 54),
 (480, 53)]

Python

python
plt.figure(figsize=(4,4))
plt.imshow(crop.crop((1700,800,2400,1450)))
plt.axis('off')

(-0.5, 699.5, 649.5, -0.5)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(crop.crop((1200,900,1900,1250)))
plt.axis('off')

(-0.5, 699.5, 349.5, -0.5)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(crop.crop((1200,1100,1900,1500)))
plt.axis('off')

(-0.5, 699.5, 399.5, -0.5)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(arr[1000:1400, 1000:2000])
plt.axis('off')

(-0.5, 999.5, 399.5, -0.5)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(arr[1000:1400, 800:1200])
plt.axis('off')

(-0.5, 399.5, 399.5, -0.5)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(arr[600:950, 350:1250])
plt.axis('off')

(-0.5, 899.5, 349.5, -0.5)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(arr[600:950, 200:450])
plt.axis('off')

(-0.5, 249.5, 349.5, -0.5)

Python

python
plt.figure(figsize=(6,4))
plt.imshow(arr[500:900, 0:600])
plt.axis('off')

(-0.5, 599.5, 399.5, -0.5)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(arr[1000:1300, 300:800])
plt.axis('off')

(-0.5, 499.5, 299.5, -0.5)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(arr[900:1200, 550:850])
plt.axis('off')

(-0.5, 299.5, 299.5, -0.5)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(arr[800:1100, 1350:1650])
plt.axis('off')

(-0.5, 299.5, 299.5, -0.5)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(arr[1100:1400, 1300:2000])
plt.axis('off')

(-0.5, 699.5, 299.5, -0.5)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(arr[1100:1400, 1000:1400])
plt.axis('off')

(-0.5, 399.5, 299.5, -0.5)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(arr[1200:1550, 800:1500])
plt.axis('off')

(-0.5, 699.5, 349.5, -0.5)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(arr[900:1150, 1000:1400])
plt.axis('off')

(-0.5, 399.5, 249.5, -0.5)

Python

python
plt.imshow(arr[1100:1350, 1850:2300])
plt.axis('off')

(-0.5, 449.5, 249.5, -0.5)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(arr[900:1150, 1600:2000])
plt.axis('off')

(-0.5, 399.5, 249.5, -0.5)

Python

python
# detect greenish pixels in arr (RGB)
mask_green = (arr[:,:,1] > 130) & (arr[:,:,0] < 150) & (arr[:,:,2] < 150)
# morphological close to fill triangle interior maybe expand
mask_green = cv2.dilate(mask_green.astype(np.uint8)*255, np.ones((5,5), np.uint8), iterations=3)
# find contours
contours, _ = cv2.findContours(mask_green, cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)
centers = []
for cnt in contours:
    x,y,w,h = cv2.boundingRect(cnt)
    if w>20 and h>20:
        cx, cy = x + w//2, y + h//2
        centers.append((cx,cy))
# print centers
print(len(centers))
print(sorted(centers, key=lambda p: p[0]))

Python

python
import math, itertools, collections

# define training data
training = [
    ((8,3),0),
    ((9,2),0),
    ((2,3),1),
    ((4,3),1),
    ((5,3),1),
    ((6,0),2),
    ((7,0),2),
    ((7,-1),2),
    ((8,-1),2),
    ((1,2),3),
    ((2,1),3),
    ((2,0),3),
    ((4,2),3),
    ((4,1),3),
    ((6,1),3)
]
tests = [
    ((3,4),1),
    ((8,2),0),
    ((5,0),2)
]

def classify(point,k):
    x,y = point
    dists = []
    for (px,py),cl in training:
        dist = math.hypot(px-x, py-y)
        dists.append((dist, cl, (px,py)))
    # sort by dist then class number
    dists.sort(key=lambda t: (t[0], t[1]))
    neighbors = dists[:k]
    counts=collections.Counter([cl for _,cl,_ in neighbors])
    maxfreq = max(counts.values())
    tied_classes = [cl for cl,cnt in counts.items() if cnt==maxfreq]
    if len(tied_classes)==1:
        return tied_classes[0]
    # tie: choose class with smaller sum distances
    sums = {cl: sum(dist for dist,cl2,_ in neighbors if cl2==cl) for cl in tied_classes}
    minsum = min(sums.values())
    mins = [cl for cl,s in sums.items() if s==minsum]
    if len(mins)==1:
        return mins[0]
    # still tie: choose smaller class number
    return min(mins)

valid_k=[]
for k in range(1,16):
    ok=True
    for (pt,truth) in tests:
        pred=classify(pt,k)
        if pred!=truth:
            ok=False
            break
    if ok:
        valid_k.append(k)
valid_k

[1, 2, 5]

Python

python
for k in range(1,16):
    preds=[classify(pt,k) for pt,_ in tests]
    print(k,preds)

思考

for k in range(1,16): preds=[classify(pt,k) for pt,_ in tests] print(k,preds)

Thought for 7m 8s

回答

Решение

В таблицах ниже указаны 15 обучающих точек (три контрольные - (8, 2), (3, 4), (5, 0) – заранее убраны)
и рассчитаны расстояния от каждой из них до этих трёх контрольных точек.

№Коорд-тыКласс
1(8, 3)0
2(9, 2)0
3(2, 3)1
4(4, 3)1
5(5, 3)1
6(6, 0)2
7(7, 0)2
8(7, -1)2
9(8, -1)2
10(1, 2)3
11(2, 1)3
12(2, 0)3
13(4, 2)3
14(4, 1)3
15(6, 1)3

1. Точка (3, 4) — истинный класс 1

Ближайшие точки по возрастанию расстояния

rкоординатыкласс
√2(2, 3)1
√2(4, 3)1
√5(5, 3)1
………

Большинство среди первых k соседей будет класс 1 при любом k ≤ 5
(дальние объекты не успевают набрать голосов).
Начиная с k ≥ 6 голосов у классов 1 и 3 становится поровну;
правило «меньшая сумма расстояний» оставляет 1 только до k = 6,
а при k ≥ 7 побеждает 3.

2. Точка (8, 2) — истинный класс 0

rкоординатыкласс
1(8, 3)0
1(9, 2)0
√2(8, 1) — отсутствует
………

Первые два ближайших объекта уже дают большинство классу 0;
ни при каком k класс 0 больше не уступает, пока k ≤ 5.
При k = 6 и 7 появляются четыре зелёных треугольника ⇒
частота классов 0 и 2 равна 2×2,
но сумма расстояний у красных меньше ⇒ выбирается 0.
Начиная с k = 8 красных уже недостаточно и метод выдаёт 2, затем 3.

3. Точка (5, 0) — истинный класс 2

rкоординатыкласс
1(6, 0)2
√2(4, 1)3
√2(6, 1)3
2(7, 0)2
√5(7, -1)2
………
  • k = 1 → 2
  • k = 2: частоты 2 : 3 = 1 : 1,
    но сумма расстояний у класса 2 (1) меньше, выбираем 2.
  • k = 3, 4 дают 2 голоса классу 3 → ошибка.
  • k = 5: 3 голоса у 2, 2 у 3 → верно.
    При k ≥ 6 класс 3 получает большинство.

Итог

Метод k-ближайших соседей правильно определяет все три контрольные точки только при

k=1,  2,  5.\boxed{k = 1,\;2,\;5}.

Для остальных значений k хотя бы одна из трёх точек классифицируется неверно.

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