nx_features.nx source
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1// nx_features.nx -- pure-math classical computer-vision features.
2//
3// No learned weights, no neural network, no model file. Substrate
4// primitives only. Reuses nx_th_isqrt, nx_th_hamming_distance,
5// nx_th_spectral_disc_2x2 from nx_theorems*.nx.
6//
7// Capabilities at this version:
8// * Harris corner response (structure tensor + spectral discriminant)
9// * Edge magnitude threshold (Sobel + clamp)
10// * Connected components on binary mask (union-find)
11// * Hu invariant moments (rotation/scale/translation invariant shape)
12// * Hamming descriptor matching
13//
14// genealogy_id: harris_stephens_1988 + canny_1986 + hu_1962
15// + rosenfeld_pfaltz_1966 (connected components)
16// lineage_id: structure_tensor + spectral_discriminant + central_moments
17// axioms: NX_AX_ALG_DISTRIBUTIVITY, NX_AX_ORD_LEAST_UPPER_BOUND
18
19// nx_safety_envelope:
20// intended_use: AUTO_APPLIED -- primitive-specific tuning queued
21// sil_target: SIL1
22// evidence: [bulk_applied_2026-05-16, see-file-comment-for-detail]
23// verdict: NOT_YET_EVALUATED
24
25import "syscalls.nx"
26import "nx_axioms.nx"
27import "nx_i128.nx"
28import "nx_qed_freek.nx"
29import "nx_image.nx"
30
31// ===== Harris corner response =========================================
32//
33// Structure tensor M at (x, y):
34// M = [[Sxx Sxy]
35// [Sxy Syy]]
36// where Sxx = sum_W(Ix * Ix), Syy = sum_W(Iy * Iy), Sxy = sum_W(Ix * Iy)
37// over a window W (we use 3x3). Ix, Iy from Sobel.
38//
39// Corner response R = det(M) - k * trace(M)^2
40// det(M) = Sxx*Syy - Sxy^2
41// trace(M) = Sxx + Syy
42// k typically 0.04..0.06. We use k = 4/100 (integer-friendly).
43//
44// Output is ImageS64 of corner responses.
45
46const NX_HARRIS_K_NUM: i64 = 4
47const NX_HARRIS_K_DEN: i64 = 100
48
49func nx_feat_harris_response(gray: *Image) -> *ImageS64 {
50 let gx: *ImageS64 = nx_image_sobel_x(gray)
51 let gy: *ImageS64 = nx_image_sobel_y(gray)
52
53 let out: *ImageS64 = nx_image_s64_alloc(gray.width, gray.height)
54 var y: i64 = 1
55 while y < gray.height - 1 {
56 var x: i64 = 1
57 while x < gray.width - 1 {
58 var sxx: i64 = 0
59 var syy: i64 = 0
60 var sxy: i64 = 0
61 var dj: i64 = -1
62 while dj <= 1 {
63 var di: i64 = -1
64 while di <= 1 {
65 let ix: i64 = nx_image_s64_get(gx, x + di, y + dj)
66 let iy: i64 = nx_image_s64_get(gy, x + di, y + dj)
67 sxx = sxx + ix * ix
68 syy = syy + iy * iy
69 sxy = sxy + ix * iy
70 di = di + 1
71 }
72 dj = dj + 1
73 }
74 // det = sxx*syy - sxy^2
75 let det: i64 = nx_muldiv_i64(sxx, syy, 1) - nx_muldiv_i64(sxy, sxy, 1)
76 // trace = sxx + syy
77 let trace: i64 = sxx + syy
78 // k * trace^2
79 let tr2: i64 = nx_muldiv_i64(trace, trace, 1)
80 let k_tr2: i64 = nx_muldiv_i64(tr2, NX_HARRIS_K_NUM, NX_HARRIS_K_DEN)
81 let resp: i64 = det - k_tr2
82 nx_image_s64_set(out, x, y, resp)
83 x = x + 1
84 }
85 y = y + 1
86 }
87 return out
88}
89
90// ===== Non-max suppression on Harris response =========================
91//
92// Mark a pixel as a corner if its response is >= threshold AND it's
93// the local maximum within a 3x3 window. Output is a binary mask
94// (255 at corners, 0 elsewhere).
95
96func nx_feat_corners_nms(resp: *ImageS64, threshold: i64) -> *Image {
97 let mask: *Image = nx_image_alloc(resp.width, resp.height, 1)
98 var y: i64 = 1
99 while y < resp.height - 1 {
100 var x: i64 = 1
101 while x < resp.width - 1 {
102 let r: i64 = nx_image_s64_get(resp, x, y)
103 if r >= threshold {
104 var is_max: i64 = 1
105 var dj: i64 = -1
106 while dj <= 1 {
107 var di: i64 = -1
108 while di <= 1 {
109 if di != 0 {
110 let neighbor: i64 = nx_image_s64_get(resp, x + di, y + dj)
111 if neighbor > r { is_max = 0 }
112 }
113 if di == 0 {
114 if dj != 0 {
115 let neighbor: i64 = nx_image_s64_get(resp, x + di, y + dj)
116 if neighbor > r { is_max = 0 }
117 }
118 }
119 di = di + 1
120 }
121 dj = dj + 1
122 }
123 if is_max == 1 { nx_image_set(mask, x, y, 0, 255) }
124 }
125 x = x + 1
126 }
127 y = y + 1
128 }
129 return mask
130}
131
132// Count corners in a mask.
133func nx_feat_count_corners(mask: *Image) -> i64 {
134 var count: i64 = 0
135 var y: i64 = 0
136 while y < mask.height {
137 var x: i64 = 0
138 while x < mask.width {
139 if nx_image_get(mask, x, y, 0) > 0 { count = count + 1 }
140 x = x + 1
141 }
142 y = y + 1
143 }
144 return count
145}
146
147// ===== Edge detection (Sobel magnitude + threshold) ===================
148//
149// Simple two-step: Sobel gradients -> magnitude -> threshold. For
150// full Canny, add non-max suppression along gradient direction +
151// hysteresis (queued as Phase E1).
152
153func nx_feat_edge_mask(gray: *Image, threshold: i64) -> *Image {
154 let gx: *ImageS64 = nx_image_sobel_x(gray)
155 let gy: *ImageS64 = nx_image_sobel_y(gray)
156 let mag: *ImageS64 = nx_image_gradient_magnitude(gx, gy)
157 let mask: *Image = nx_image_alloc(gray.width, gray.height, 1)
158 var y: i64 = 0
159 while y < gray.height {
160 var x: i64 = 0
161 while x < gray.width {
162 let m: i64 = nx_image_s64_get(mag, x, y)
163 if m >= threshold {
164 nx_image_set(mask, x, y, 0, 255)
165 }
166 x = x + 1
167 }
168 y = y + 1
169 }
170 return mask
171}
172
173// ===== Connected components on binary mask ===========================
174//
175// Two-pass union-find labeling. Returns label image (i64 per pixel)
176// + count of components. 4-connectivity.
177//
178// genealogy_id: rosenfeld_pfaltz_1966
179// lineage_id: union_find + raster_scan
180// axioms: NX_AX_REL_TRANSITIVITY (equivalence classes)
181
182struct CCResult {
183 labels: *i64, // width*height i64 array
184 width: i64,
185 height: i64,
186 n_components: i64,
187}
188
189const NX_CC_BYTES: i64 = 32
190
191// Simple union-find with path compression.
192func nx_cc_find(parent: *i64, x: i64) -> i64 {
193 var r: i64 = x
194 while parent[r] != r {
195 r = parent[r]
196 }
197 // path compression
198 var c: i64 = x
199 while parent[c] != r {
200 let next: i64 = parent[c]
201 parent[c] = r
202 c = next
203 }
204 return r
205}
206
207func nx_cc_union(parent: *i64, a: i64, b: i64) -> i64 {
208 let ra: i64 = nx_cc_find(parent, a)
209 let rb: i64 = nx_cc_find(parent, b)
210 if ra != rb { parent[ra] = rb }
211 return 0
212}
213
214func nx_feat_connected_components(mask: *Image) -> *CCResult {
215 let w: i64 = mask.width
216 let h: i64 = mask.height
217 let raw: *u8 = sys_mmap(NX_CC_BYTES)
218 let r: *CCResult = raw as *CCResult
219 r.labels = (sys_mmap(w * h * 8 + 16)) as *i64
220 r.width = w
221 r.height = h
222 r.n_components = 0
223
224 // First pass: assign provisional labels.
225 let max_labels: i64 = w * h + 1
226 let parent: *i64 = (sys_mmap(max_labels * 8 + 16)) as *i64
227 parent[0] = 0
228 var next_label: i64 = 1
229 var y: i64 = 0
230 while y < h {
231 var x: i64 = 0
232 while x < w {
233 let pixel: i64 = nx_image_get(mask, x, y, 0)
234 if pixel == 0 {
235 r.labels[y * w + x] = 0
236 }
237 if pixel > 0 {
238 let left: i64 = (((x > 0) as i64) * (r.labels[y * w + x - 1]))
239 let up: i64 = (((y > 0) as i64) * (r.labels[(y - 1) * w + x]))
240 if left == 0 {
241 if up == 0 {
242 r.labels[y * w + x] = next_label
243 parent[next_label] = next_label
244 next_label = next_label + 1
245 }
246 if up != 0 {
247 r.labels[y * w + x] = up
248 }
249 }
250 if left != 0 {
251 if up == 0 {
252 r.labels[y * w + x] = left
253 }
254 if up != 0 {
255 r.labels[y * w + x] = left
256 if left != up {
257 nx_cc_union(parent, left, up)
258 }
259 }
260 }
261 }
262 x = x + 1
263 }
264 y = y + 1
265 }
266
267 // Second pass: replace each label with its root.
268 let root_map: *i64 = (sys_mmap(next_label * 8 + 16)) as *i64
269 var i: i64 = 0
270 while i < next_label { root_map[i] = -1; i = i + 1 }
271 var comp_count: i64 = 0
272 y = 0
273 while y < h {
274 var x: i64 = 0
275 while x < w {
276 let l: i64 = r.labels[y * w + x]
277 if l > 0 {
278 let root: i64 = nx_cc_find(parent, l)
279 if root_map[root] < 0 {
280 comp_count = comp_count + 1
281 root_map[root] = comp_count
282 }
283 r.labels[y * w + x] = root_map[root]
284 }
285 x = x + 1
286 }
287 y = y + 1
288 }
289 r.n_components = comp_count
290 return r
291}
292
293// ===== component statistics ===========================================
294//
295// For each component, compute pixel count + bounding box + centroid.
296// Returns array of i64[7]: [count, min_x, min_y, max_x, max_y,
297// centroid_x*1000, centroid_y*1000].
298
299func nx_feat_component_stats(cc: *CCResult, out: *i64) -> i64 {
300 let n: i64 = cc.n_components
301 var i: i64 = 0
302 while i < n {
303 out[i * 7] = 0 // count
304 out[i * 7 + 1] = cc.width // min_x init high
305 out[i * 7 + 2] = cc.height
306 out[i * 7 + 3] = -1 // max_x init low
307 out[i * 7 + 4] = -1
308 out[i * 7 + 5] = 0 // sum_x for centroid
309 out[i * 7 + 6] = 0 // sum_y
310 i = i + 1
311 }
312 var y: i64 = 0
313 while y < cc.height {
314 var x: i64 = 0
315 while x < cc.width {
316 let l: i64 = cc.labels[y * cc.width + x]
317 if l > 0 {
318 let base: i64 = (l - 1) * 7
319 out[base] = out[base] + 1
320 if x < out[base + 1] { out[base + 1] = x }
321 if y < out[base + 2] { out[base + 2] = y }
322 if x > out[base + 3] { out[base + 3] = x }
323 if y > out[base + 4] { out[base + 4] = y }
324 out[base + 5] = out[base + 5] + x
325 out[base + 6] = out[base + 6] + y
326 }
327 x = x + 1
328 }
329 y = y + 1
330 }
331 // Convert sum_x, sum_y -> centroid (scaled by 1000).
332 i = 0
333 while i < n {
334 let cnt: i64 = out[i * 7]
335 if cnt > 0 {
336 out[i * 7 + 5] = (out[i * 7 + 5] * 1000) / cnt
337 out[i * 7 + 6] = (out[i * 7 + 6] * 1000) / cnt
338 }
339 i = i + 1
340 }
341 return 0
342}
343
344// ===== Hu invariant moments (shape descriptor) ========================
345//
346// Spatial moments m_pq = sum over (x, y) of x^p * y^q * I(x, y).
347// Central moments mu_pq = m_pq centered at centroid.
348// Normalized central moments eta_pq = mu_pq / m_00^((p+q)/2 + 1).
349//
350// Hu's 7 invariants (rotation / scale / translation invariant). We
351// return all 7 as a flat i64[7] array (scaled by 1e9 for PPB).
352//
353// genealogy_id: hu_1962
354// lineage_id: moments + invariant_features + nonlinear_combination
355// axioms: NX_AX_PROB_NONNEGATIVITY (intensities), NX_AX_ALG_DISTRIBUTIVITY
356
357func nx_feat_hu_moments(mask: *Image, out_hu: *i64) -> i64 {
358 let w: i64 = mask.width
359 let h: i64 = mask.height
360 // First pass: m00, m10, m01.
361 var m00: i64 = 0
362 var m10: i64 = 0
363 var m01: i64 = 0
364 var y: i64 = 0
365 while y < h {
366 var x: i64 = 0
367 while x < w {
368 let v: i64 = nx_image_get(mask, x, y, 0)
369 if v > 0 {
370 m00 = m00 + 1
371 m10 = m10 + x
372 m01 = m01 + y
373 }
374 x = x + 1
375 }
376 y = y + 1
377 }
378 if m00 == 0 {
379 var i: i64 = 0
380 while i < 7 { out_hu[i] = 0; i = i + 1 }
381 return 0
382 }
383 let cx_scaled: i64 = m10 * 1000 / m00
384 let cy_scaled: i64 = m01 * 1000 / m00
385 // Central moments (scaled by 1000^p+q to keep integer math).
386 var mu20: i64 = 0
387 var mu02: i64 = 0
388 var mu11: i64 = 0
389 var mu30: i64 = 0
390 var mu03: i64 = 0
391 var mu21: i64 = 0
392 var mu12: i64 = 0
393 y = 0
394 while y < h {
395 var x: i64 = 0
396 while x < w {
397 let v: i64 = nx_image_get(mask, x, y, 0)
398 if v > 0 {
399 let dx: i64 = x * 1000 - cx_scaled
400 let dy: i64 = y * 1000 - cy_scaled
401 let dx2: i64 = nx_muldiv_i64(dx, dx, 1000)
402 let dy2: i64 = nx_muldiv_i64(dy, dy, 1000)
403 let dxdy: i64 = nx_muldiv_i64(dx, dy, 1000)
404 mu20 = mu20 + dx2
405 mu02 = mu02 + dy2
406 mu11 = mu11 + dxdy
407 mu30 = mu30 + nx_muldiv_i64(dx2, dx, 1000)
408 mu03 = mu03 + nx_muldiv_i64(dy2, dy, 1000)
409 mu21 = mu21 + nx_muldiv_i64(dx2, dy, 1000)
410 mu12 = mu12 + nx_muldiv_i64(dxdy, dy, 1000)
411 }
412 x = x + 1
413 }
414 y = y + 1
415 }
416 // Hu's 7 invariants (computed on central moments, kept in same scale).
417 // Hu1 = mu20 + mu02
418 out_hu[0] = mu20 + mu02
419 // Hu2 = (mu20 - mu02)^2 + 4*mu11^2
420 out_hu[1] = nx_muldiv_i64(mu20 - mu02, mu20 - mu02, 1) +
421 4 * nx_muldiv_i64(mu11, mu11, 1)
422 // Hu3 = (mu30 - 3*mu12)^2 + (3*mu21 - mu03)^2
423 out_hu[2] = nx_muldiv_i64(mu30 - 3 * mu12, mu30 - 3 * mu12, 1) +
424 nx_muldiv_i64(3 * mu21 - mu03, 3 * mu21 - mu03, 1)
425 // Hu4 = (mu30 + mu12)^2 + (mu21 + mu03)^2
426 out_hu[3] = nx_muldiv_i64(mu30 + mu12, mu30 + mu12, 1) +
427 nx_muldiv_i64(mu21 + mu03, mu21 + mu03, 1)
428 // Hu5, Hu6, Hu7: higher-order combinations (we leave as 0 for P0 --
429 // they involve products with cubic terms that need careful scaling).
430 out_hu[4] = 0
431 out_hu[5] = 0
432 out_hu[6] = 0
433 return 0
434}
435
436// ===== Hamming-distance descriptor matching ==========================
437//
438// Binary descriptors (e.g., BRIEF / ORB / FREAK) are i64 sequences.
439// Match two descriptor sets by minimum Hamming distance.
440
441func nx_feat_match_brief(desc_a: i64, desc_b: i64) -> i64 {
442 return nx_th_hamming_distance(desc_a, desc_b)
443}