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10 hours ago

We consider the action $S_{\phi q}$ involving only $\phi_{\mu\nu}$ and quark fields $q(x)$ in general frames with Poincar\'e metric tensor $P_{\mu\nu}$: \be S_{\phi q} = \int (L_{\phi q} + L_{gf})d^4 x, \ee %%%%%%%%15%%%%22%%%%%24%%%22%%%19 \be L_{gf}=\frac{1}{2g^2}\e_{\a\b}\left[\p_\mu J^{\mu\a} - \frac{1}{2}\e^{\a\ld}\p_{\ld} J^\mu_\mu\right] \left[\p_\nu J^{\nu\b} - \frac{1}{2}\e^{\b\ld}\p_{\ld} J^\nu_\nu\right], \ee %%%%16%%%%%%%23%%%%%25%%%23%%%%20 where $L_{\phi q}$ is given in (7) with the $T(4)$ gauge curvature $C_{\mu\nu\a}$ given by (5). We have included a gauge-fixing term $L_{gf}$ specified by (20) involving ordinary partial derivative to break the $T(4)$ gauge symmetry so that the solution of gauge field equation is well-defined. The reason for including $L_{gf}$ is that field equations with gauge symmetry are known to be not well defined in general and that it is a nuisance to find explicit solutions of such field equations without having a gauge-fixing term. The quark fields play the source for producing a gravitational potential field $\phi_{\mu\nu}$. The $T(4)$ gravitational field equation for symmetric tensor field, $\phi_{\mu\nu}=\phi_{\nu\mu}$ can be derived from (19), \be H^{\mu\nu} + A^{\mu\nu}= \frac{g^2}{2} Sym \ \left[ \overline{q} i\G^\mu D^\nu q - i(D^\nu \overline{q}) \G^\mu q \right]\equiv g^2 T^{\mu\nu} , \ee %%%%%26%%%17%%%%%%%%%24%%%%%%26%%%24%21 $$ H^{\mu\nu} = Sym \left[D_\ld (J^{\ld}_\rho C^{\rho\mu\nu} - J^\ld_\a C^{\a\b}_{ \ \ \ \b}P^{\mu\nu} + C^{\mu\b}_{ \ \ \ \b} J^{\nu\ld}) \right. $$ %%%%%%%%%%%%%%%%%%%%%%%%20%%% \be \left. - C^{\mu\a\b}D^\nu J_{\a\b} + C^{\mu\b}_{ \ \ \ \b} D^\nu J^\a_\a - C^{\ld \b}_{ \ \ \ \b}D^\nu J^\mu _\ld\right], \ee %%%%%%%27 %%%%%%%%%%18%%%%%%%%%25%%%27%%%%25%%522 \be A^{\mu\nu} =Sym \left[ \p^\mu \left(\p^\ld J_\ld{^\nu} - \frac{1}{2} \p^\nu J \right) - \frac{\e^{\mu\nu}}{2} \left(\p^\a \p^\ld J_{\ld\a} - \frac{1}{2} \p^\a \p_\a J \right)\right], \ee %%%19%%%%%%%%%%26%%%%%%%%28%%%%%26%%%523 where $D_{\mu}q=\p_{\mu}q$ and $J= J^\ld_\ld$. The symbol `Sym' in Eqs. (21)-(23) denotes that $\mu$ and $\nu$ should be made symmetric.

620ba102fd7
0 4

1 month ago

# Keeps 589 bright, boosts jewelry shine, replaces background, and maps to Casinofi duotone. import cv2, numpy as np from google.colab import files from PIL import Image # Upload your image when prompted up = files.upload() fn = list(up.keys())[0] img_bgr = cv2.imdecode(np.frombuffer(up[fn], np.uint8), cv2.IMREAD_COLOR) # --- Palette (BGR) --- HEX = lambda h: (int(h[5:7],16), int(h[3:5],16), int(h[1:3],16)) SHADOW = np.array(HEX("#0F1011"), np.float32) MID = np.array(HEX("#8E7A55"), np.float32) HILITE = np.array(HEX("#E6D2A1"), np.float32) HILITE_PLUS = np.array(HEX("#EBDDB7"), np.float32) # extra-bright cream for 589 # --- Helper: gradient map (shadow -> mid -> highlight) --- def gradient_map(gray01): g = gray01[...,None] t1 = np.clip(g/0.5, 0, 1) t2 = np.clip((g-0.5)/0.5, 0, 1) low = SHADOW*(1-t1) + MID*t1 high = MID*(1-t2) + HILITE*t2 return np.where(g<=0.5, low, high) hsv = cv2.cvtColor(img_bgr, cv2.COLOR_BGR2HSV) # --- Masks --- # Background (yellow) range bg_mask = cv2.inRange(hsv, (15, 120, 120), (40, 255, 255)) # tune if needed # Shirt (blue) range – helpful for separate contrast if you want shirt_mask = cv2.inRange(hsv, (95, 80, 40), (130, 255, 255)) # Numbers “589” (white-ish areas on shirt) gray = cv2.cvtColor(img_bgr, cv2.COLOR_BGR2GRAY) num_mask = cv2.threshold(gray, 210, 255, cv2.THRESH_BINARY)[1] # bright white # Jewelry (gold/yellow highlights) jew_mask = cv2.inRange(hsv, (12, 60, 120), (30, 255, 255)) # gold tones # Clean masks a bit def clean(m, k=3): kernel = cv2.getStructuringElement(cv2.MORPH_ELLIPSE, (k,k)) m = cv2.morphologyEx(m, cv2.MORPH_OPEN, kernel, iterations=1) m = cv2.morphologyEx(m, cv2.MORPH_CLOSE, kernel, iterations=1) return m bg_mask = clean(bg_mask, 5) shirt_mask= clean(shirt_mask, 5) num_mask = clean(num_mask, 3) jew_mask = clean(jew_mask, 3) # --- Step 1: Replace background with deep charcoal --- out = img_bgr.copy() out[bg_mask>0] = SHADOW # --- Step 2: Convert subject to Casinofi duotone --- # Work on non-background regions subj = out.copy() subj_mask = (bg_mask==0).astype(np.uint8)*255 subj_gray = cv2.cvtColor(subj, cv2.COLOR_BGR2GRAY).astype(np.float32)/255.0 mapped = gradient_map(subj_gray).astype(np.uint8) mapped = cv2.bitwise_and(mapped, mapped, mask=subj_mask) bg_area = cv2.bitwise_and(out, out, mask=bg_mask) out = cv2.add(mapped, bg_area) # --- Step 3: Boost numbers “589” to brighter cream and keep edges crisp --- num_rgb = np.zeros_like(out, dtype=np.uint8) num_rgb[:] = HILITE_PLUS num_layer = cv2.bitwise_and(num_rgb, num_rgb, mask=num_mask) out = cv2.bitwise_and(out, out, mask=cv2.bitwise_not(num_mask)) out = cv2.add(out, num_layer) # Optional: thin dark stroke around numbers edges = cv2.Canny(num_mask, 50, 150) stroke = cv2.dilate(edges, np.ones((2,2), np.uint8), iterations=1) out[stroke>0] = (out[stroke>0]*0 + SHADOW*0.9).astype(np.uint8) # --- Step 4: Jewelry shine (Screen-like brighten in cream) --- # Create a cream layer and blend additively where jewelry mask is j_layer = np.zeros_like(out, dtype=np.float32) j_layer[:] = HILITE j_mask_f = (jew_mask.astype(np.float32)/255.0)[...,None] out_f = out.astype(np.float32) out = np.clip(out_f + j_layer*0.35*j_mask_f, 0, 255).astype(np.uint8) # --- Step 5: Gentle contrast pop on subject only --- subj_mask3 = cv2.merge([subj_mask, subj_mask, subj_mask]) subj_pix = np.where(subj_mask3>0) sub = out.astype(np.float32) sub[subj_pix] = np.clip((sub[subj_pix]-20)*1.08 + 20, 0, 255) out = sub.astype(np.uint8) # Save cv2.imwrite("output_casinofi.png", out) files.download("output_casinofi.png") print("Done. Download output_casinofi.png")

21ReliCosmic
0 23